| INTERNATIONAL ATOMIC ENERGY AGENCY AUSTRALIAN NUCLEAR SCIENCE AND TECHNOLOGY ORGANISATION |
DISTANCE LEARNING MATERIALS
RADIATION PROTECTION
Module – 1.1
Prepared by Safety and Radiation Science
Australian Nuclear Science and Technology Organisation
With the assistance of consultants in Australia and the United Kingdom, and IAEA experts from Korea, Mongolia, New Zealand, the Philippines and Thailand
Use of this material, acknowledging the IAEA and ANSTO as the source, is permitted for non-profit training
Acknowledgements
This material has been prepared by an extensive team of international experts from the fields of radiation protection, medicine and education. It is not possible to mention by name all those who have had an input to; the initial planning; writing modules and workbooks; preparing and marking final assignments; proof-reading and editing; using the material and providing valuable feedback; organizing and hosting review meetings; and general administrative support.
The support of ANSTO management in providing the resource and encouragement is gratefully acknowledged.
The enthusiastic support of IAEA Technical Officers has been vital to the success of this project
PART 1
BASIC KNOWLEDGE
MODULE 1.1
STRUCTURE OF MATTER
1.OVERVIEW
As you study this module you will learn basic information about the structure and properties of atoms. With the help of later modules, this information will help you to understand why some atoms are radioactive, how radiation is produced and how radiation interacts with atoms in materials through which it passes. You will also learn about how atoms combine. This is particularly important in radiation protection as it will help you to understand the changes that ionizing radiation can produce in body tissue and how damage may be caused. Finally, this module will introduce you to important tools used in radiation protection such as the periodic table and the chart of nuclides.
Although you may already be familiar with some of the information in this module, it should prove to be useful revision material. Before you attempt the final assignment, it is advised that you complete the self-check questions at the end of each section successfully.
2.·
TIME ALLOCATION
It is estimated that you will need to spend four to six hours to complete this module before commencing the assignment. This estimated time is for your guidance only. Do not worry if you need more time to understand the module.
3.
MATERIALS
MATERIALS
In addition to writing materials, you will need a copy of the periodic table and a chart of nuclides to refer to while studying this module. These materials may be found in the accompanying booklet ‘Nuclides and Isotopes’.
NOW YOU ARE READY TO START WORK
5.
1.THE ATOM
1.THE ATOM
All matter is made up of small building blocks called atoms. These atoms cannot be broken up by any chemical means but they are able to join together to form materials. Individual atoms are very small (approximately 10-10 metres in diameter) and are impossible to observe directly with any measuring instruments. Despite their small size, atoms themselves are made up of a number of smaller subatomic particles known as protons, electrons and neutrons. As the mass of these particles is very small, a special unit called the atomic mass unit (symbol u or amu) is used to describe their mass. The atomic mass unit is defined as one twelfth of the mass of a carbon-12 atom and is equal to 1.66 x 10-24 grams.
5.11.1Protons, Electrons and Neutrons
Protons are positively charged particles with a mass of approximately 1u. They are found in the centre (or nucleus) of an atom and have a charge equal to +1.6 x 10-19 coulombs. This quantity of charge is known as the electronic charge and is given the symbol e.
Electrons have an equal but opposite negative charge (-1.6 x 10-19 coulombs) and are found in orbits around the nucleus. In general, the number of electrons in an atom is the same as the number of protons, so the atom has no overall charge. The electron has a much smaller mass than the proton (approximately 5 x 10-4 u or 1/1840 u). This mass is so small that for the purpose of describing changes to the structure of atoms during radioactive decay, it can be taken as zero.
Neutrons may be regarded as a combination of a proton and an electron and therefore has a mass of approximately 1u but no net electrical charge. Neutrons are found in the nucleus of the atom.
Table 1 summarizes the properties of these particles.
Table 1
The Properties of Particles in the Atom
Particle | Position in Atom | Mass (u) | Charge (e) |
Proton | Nucleus | 1 | +1 |
Electron | Orbit | 1/1840 | -1 |
Neutron | Nucleus | 1 | 0 |
5.21.2Bohrs’ Atomic Model
Although the exact structure of an atom is not known, a simple model known as Bohr’s atomic model (named after the physicist Neils Bohr) is used to describe both the structure and properties of atoms. According to this model, the structure of an atom is similar to that of the solar system with a heavy centre or nucleus (the sun) and lighter particles (the planets) orbiting the nucleus. In atoms, the heavier protons and neutrons form the nucleus making the nucleus positively charged. The lighter, negatively charged electrons are attracted to the nucleus by electrostatic forces and they orbit around the central area.
These electrons can only rotate around the nucleus in specific orbits known as shells and there is a limit to the number of electrons in each shell. The shells are called K, L, M and N shells and they can hold 2, 8, 18 and 32 electrons respectively. Note that electrons will start filling the N shell before the M shell has filled (e.g. potassium and calcium – see Appendix A). This is because sub-shells exist and the energy levels overlap. Electrons can change their orbit and move to different shells but only if energy is added to or released from an atom.
Electrons can change orbits (shells) but only if energy is added to or released from the atom.
A substance composed of a single type of atom is called an element. The element is determined by the number of protons in each atom. Each element is given an individual name and symbol such as helium (He) and carbon (C). Figure 1 illustrates the electron shells for zinc (Zn), an element with a total of 30 electrons. Note that this is a simple diagram but electron orbit diagrams for heavier elements can become quite complex.
Figure 1
The Electron Shells of Zinc
Appendix A shows how the electrons are arranged in the shells of the twenty lightest elements. From this information, draw a simple diagram to illustrate the electron shells for sodium (Na).
You should have drawn a diagram similar to that shown in Figure 1 but with 2 electrons in the K shell, 8 electrons in the L shell and 1 electron in the M shell. Now continue.
The chemical properties of an element are determined by the number of protons (and hence the number of electrons) it contains. Neutrons do not have an electric charge and therefore do not affect the chemical characteristics of the atom. However, different numbers of neutrons change the total mass of the atom and, in addition, change the stability of the nucleus. These properties are discussed further in Module 1.3, Ionizing Radiation and Radioactive Decay as they are important in determining whether an atom will emit radiation.
6.
SELF-CHECK 1
SELF-CHECK 1
Now see how much you have understood by answering the following questions in your workbook:
1.Match the terms atoms, protons, neutrons, electrons and element with the following descriptions:
Positively charged particles found in the nucleus of an atom.
Particles which orbit the nucleus of an atom in shells.
Basic building blocks of matter.
Particles without an electric charge found in the nucleus of atoms.
Material with atoms which all have the same number of protons.
2.Complete the following table:
Particle
Mass
(u)
Charge
(e)
Proton
Electron
Neutron
3.According to Bohr’s atomic model:
which particles make up the nucleus of an atom?
which particles orbit the nucleus?
can electrons move freely within atoms?
d)when is it possible for electrons to change orbits?
4.Using Appendix A, draw a simple diagram to show the number of electrons in each shell of a chlorine atom.
Now check your answers with the model answers in your workbook.
6.11.3Important Atomic Terms
An atom may be described in terms of the number of basic particles it contains. By using the following definitions it is possible to uniquely define the atomic structure of any atom.
.3.11.3.1Atomic number, neutron number and atomic mass
As explained earlier, each element is given an individual name and symbol. An alphabetical list of the elements and their symbols is given in Appendix B.
Turn now to Appendix B and find the symbols for the elements hydrogen, lithium, oxygen and potassium.
You should have found that the symbol for hydrogen is H, the symbol for lithium is Li, the symbol for oxygen is O and the symbol for potassium is K. Now continue.
The atomic number (symbol Z) is defined as the number of protons in the nucleus and is unique for each element. For example, Z for hydrogen is 1, for helium Z is 2 and for carbon Z is 6. Appendix C gives the atomic numbers for the twenty lightest elements.
Now look at Appendix C and find the atomic number (Z) for hydrogen lithium, oxygen and potassium.
You should have found that Z for hydrogen is 1, Z for lithium is 3, Z for oxygen is 8 and Z for potassium is 19. Now continue.
The number of neutrons in the nucleus is denoted by the symbol N. Although the number of neutrons for a given element may vary, the most commonly occurring neutron numbers are listed in Appendix C for the twenty lightest elements.
Turn now to Appendix C and find the neutron numbers for hydrogen, lithium, oxygen and potassium.
You should have found that N for hydrogen is 0, N for lithium is 4, N for oxygen is 8 and N for potassium is 20. Now continue.
The atomic mass is represented by the symbol A and is equal to the total number of protons (Z) and neutrons (N) in the nucleus of an atom. (The mass of the electrons is much smaller and not significant.) The relationship between the atomic mass number and the number of protons and neutrons can be represented by Equation 1:
A = Z + N1
For example, for a helium atom with two protons and two neutrons in the nucleus, the atomic mass is 4 (A = 4) and for a carbon atom with six protons and six neutrons in the nucleus, the atomic number is 12 (A = 12).
Using the information you have already found, calculate the atomic mass for hydrogen lithium, oxygen and potassium.
Check your answers with the atomic mass listed in Appendix C. You should have found that for hydrogen A = 1, for lithium A = 7, for oxygen A = 16 and for potassium A = 39. Now continue.
Although atomic mass is sometimes referred to as atomic weight, the first term is used for the purpose of radiation protection. By multiplying the atomic mass number by the atomic mass unit (u) you can find the approximate mass of the atom.
For example, a helium atom with an atomic mass of 4 will have an actual mass of approximately (4 x 1.66 x 10-24 g) or 6.64 x 10-24 g
Using the information you have already found, calculate the atomic mass in atomic mass units for hydrogen, lithium, oxygen and potassium.
You should have found that the atomic mass of hydrogen is 1.66 x 10-24 g, the atomic mass of lithium is approximately 1.16 x 10-23 g, the atomic mass of oxygen is approximately 2.66 x 10-23 g and the atomic mass of potassium is approximately 6.48 x 10-23 g. Now continue.
Each atom has a unique combination of atomic number and atomic mass and this is commonly displayed in the following standard form:
where A is the atomic mass, Z is the atomic number and X is the symbol for the element with Z protons.
Using this information, now write the most commonly occurring atoms of hydrogen, lithium, oxygen and potassium in standard form.
You should have written the following: , , , and .
There are a number of other ways of uniquely describing a nuclide including the element name or symbol preceded or followed by the atomic mass number. For example, may be represented by 12C, carbon 12, carbon-12, C12 or C-12).
.3.11.3.2Isotopes, radioisotopes, nuclides and radionuclides
An element may have atoms with the same number of protons but different numbers of neutrons. Thus, a carbon atom with six neutrons has an atomic mass number of 12 but a carbon atom with eight neutrons has an atomic mass number of 14. Atoms of a particular element which have different numbers of neutrons are called isotopes. Isotopes which emit radiation are called radioisotopes. Since isotopes all belong to the same element they are all chemically identical but they have a different mass and may have different radiation properties.
All isotopes of a particular element have identical chemical properties but they may have different radiation properties.
Consider the isotopes of hydrogen as an example. The most commonly occurring hydrogen atom has one proton and no neutrons. However, other isotopes of hydrogen exist with one neutron or two neutrons. Thus a hydrogen atom may have an atomic mass of 1, 2 or 3. The hydrogen isotopes with atomic mass 2 and 3 have special names to distinguish them from the most common hydrogen isotope with an atomic mass of 1. The hydrogen isotope with a mass of 2 is called deuterium or heavy hydrogen and like the hydrogen isotope with mass 1, it is stable. The hydrogen isotope with a mass number of 3 is called tritium but is different to the other isotopes in that it is radioactive (i.e. it is a radioisotope). These three isotopes of hydrogen are shown in Figure 2.
1 electron 1 electron1 electron
Hydrogen | Deuterium | Tritium |
Figure 2
The Isotopes of Hydrogen
The atomic structure of these three isotopes of hydrogen is summarized in Table 2.
Table 2
Atomic Structure of Hydrogen Isotopes
Hydrogen | Deuterium | Tritium | |
Symbol | |||
Number of Protons | 1 | 1 | 1 |
Number of Electrons | 1 | 1 | 1 |
Number of Neutrons (N) | 0 | 1 | 2 |
Atomic Number (Z) | 1 | 1 | 1 |
Atomic Mass (A) | 1 | 2 | 3 |
Isotopes of any element may also be called nuclides. However, a nuclide can refer to any element (and is a more general term) whereas isotopes must refer to the same element. A special term, radionuclide, is used to describe a nuclide which spontaneously emits radiation. They are written and described in exactly the same manner as general nuclides.
The atomic structure of a nuclide may be inferred from its symbol and atomic mass number. For example 14C means a carbon atom with an atomic mass of 14. Since the atomic number of carbon is 6 (i.e. carbon atoms have 6 protons in the nucleus), we can work out that 14C will have eight (14 - 6) neutrons. We also know that an uncharged atom will have six electrons, the same number as protons.
7.
SELF-CHECK 2
SELF-CHECK 2
Now see how much you have understood by answering the following questions in your workbook:
1.Match the terms atomic number, atomic mass, nuclide, isotopes, radionuclide, radioisotope with the following descriptions:
a)Atoms of a particular element which have the same number of protons but different numbers of neutrons.
b)The total number of protons and neutrons in the nucleus of an atom.
c)A general term referring to any isotope of any element.
d)The number of protons in an atom.
e) A nuclide which emits radiation.
f)An isotope which emits radiation.
Using Appendices A and C, provide the following information for the nuclide neon-20:
How many protons, electrons and neutrons are in this atom?
How many electrons are in the outer shell of this atom?
What is the atomic mass of the atom in atomic mass units?
Write this nuclide in standard form.
What are two other ways of expressing this nuclide?
3.Given that the atomic number of the radionuclide cobalt-60 (60Co) is 27, how many protons, neutrons and electrons are present in the atom?
Now check your answers with the model answers in your workbook.
8.2.HOW ATOMS COMBINE
As explained earlier, the chemical properties of an element depend on the number of protons and hence the number of electrons in the atom. For atoms of an element to be chemically stable, they must either have a filled outer electron shell (two or eight electrons respectively for the K and L shells) or have eight electrons in its outer orbit. Hence, most atoms do not exist separately but are attached to other atoms by chemical bonds. These bonds are formed by atoms sharing electrons (a covalent bond) or by transferring electrons (an ionic bond). Chemical bonds do not involve the nucleus of the individual atoms in any way and only affect the outer part of an atom.
It is important to note that the way atoms interact is an entire branch of science. The information provided here is only a very basic introduction. It will help you to understand the changes that ionizing radiation can produce in body tissue and why damage may be caused.
8.12.1Covalent Bonds
A simple example of covalent bonds (sharing of electrons) is the oxygen (O2) which we breath. In nature, a free atom of oxygen is very rare as it is very reactive and will combine with a second oxygen atom to become more chemically stable. Oxygen has an atomic number of 8 and therefore has a total of eight protons and eight electrons. The innermost (K) shell contains two of the electrons and the other six electrons are in the next shell (L). As the L shell needs eight electrons to be chemically stable, there are two spaces that need to be filled before stability can be achieved. Therefore, two oxygen atoms share two electrons each (a total of four shared electrons) so the outer shell of both atoms is full. Figure 3 shows an oxygen molecule. A molecule is formed when a group of two or more atoms are joined by chemical bonds.
Figure 3
An Oxygen (O2) Molecule
Atoms of one element can also interact with atoms of other elements. One of the most common examples of this is water. A water molecule consists of two hydrogen atoms combined with one oxygen atom and is given the chemical symbol H2O.
The oxygen atom shares one electron with each hydrogen atom to fill the hydrogen’s K shell (two electrons). The hydrogen atoms each share their one electron with the oxygen to fill the oxygen atom’s outer L shell (eight electrons). This is illustrated in Figure 4.
Figure 4
A Water (H2O) Molecule
8.22.2Ionic Bonds
In some atoms, the outer shell has only a few electrons but many holes (spaces in outer or inner shells that are available for electrons to fill). These atoms would therefore be chemically stable if they could lose the electrons in the outer shell to leave only the full number of electrons in the next inner shell. Such elements are known as metals. Other atoms have only a few holes in the outer shell and would be chemically stable if they gained electrons. These elements are known as non-metals.
When a metal element loses its electrons to a non-metal element, a salt is formed. A simple example of this is common salt which is made up of the elements sodium (Na) and chlorine (Cl). Sodium, with an atomic number of 11 has one electron in its outer shell, and chlorine with an atomic number of 17 has seven in its outer shell. With sodium losing one electron and chlorine gaining an electron, both elements will subsequently have eight electrons in their outer shell.
The overall electrical charge of sodium chloride (NaCl) is neutral as the total number of protons and electrons is the same. However, the sodium atoms have a positive charge (owing to loss of an electron) and the chlorine atoms have a negative charge (owing to the gain of an electron). These charged atoms are called positive and negative ions respectively and the resulting attraction between the ions is known as an ionic bond.
Note that the difference in charge of an ionic bond attracts atoms together such that they arrange themselves into a lattice (see Figure 5).
Figure 5
Structure of Sodium Chloride (NaCl) Salt
9.SELF-CHECK 3
Now see how much you have understood by answering the following questions in your workbook:
Match the terms covalent bond,ionic bond, molecule, metal, non-metal, salt, positive ion and negative ion with the following descriptions:
a)An element which needs to lose electrons to become chemically stable.
An atom with a positive charge.
A type of chemical bond where electrons are shared between atoms.
d)A group of atoms which are joined by chemical bonds.
e)An element which needs to gain electrons to become chemically stable.
A type of chemical bond formed by the attraction of positive and negative ions.
g)An atom with a negative charge.
h)A combination of a metal and a non-metal.
2.a)Using Appendix A, find the number of electrons in the outer shell of nitrogen.
b)Two nitrogen atoms may share electrons to fill the holes in their outer shells. Draw a diagram to illustrate the nitrogen (N2) molecule.
a)Using Appendix A, find the number electrons in the outer shell of calcium and fluorine.
What is likely to happen to make these elements more chemically stable?
Now check your answers with the model answers in your workbook.
10.3THE PERIODIC TABLE
As already mentioned, the number of protons and hence the number of electrons in an atom determines the chemical properties of the atom. As electrons are also restricted to certain orbits or shells, elements with similar numbers of electrons in their outer shells also display similar chemical properties.
Elements with similar numbers of electrons in their outer shells have similar chemical properties.
Hence, by grouping the elements according to how the electron shells are filled, elements with similar properties may be identified. A special table known as periodic table has been devised for this purpose (see Figure 6).
Figure 6
The Periodic Table
As you can see from Figure 6, the periodic table is divided into eight vertical columns. All elements in the same column have similar numbers of electrons in their outer shells and hence have similar chemical properties.
Elements in the same column of the periodic table have similar chemical properties.
For example, calcium (Ca), barium (Ba), strontium (Sr) and radium (Ra) are all in the same column of the periodic table and have similar chemical properties. As calcium is one of the major elements in the bones of humans, the other similar elements may be thought of as bone seekers as they will be treated by the body in the same way as calcium. This is important radiologically as it determines where the radiation will affect the person exposed to a radionuclide such as radium.
A more detailed periodic table is located on page 62 of the accompanying booklet, ‘Nuclides and Isotopes’. This booklet will be used throughout the course so take time to study it now. Using the booklet, find some of the simple atoms like hydrogen, helium or carbon. What information is given about these elements? How many columns are there in the table, excluding the transition elements?
The periodic table gives the name and symbol of each element, its atomic number and atomic weight (mass) (the average mass of all naturally occurring isotopes in atomic mass units), and may also give the electronic structure and physical properties such as density, boiling point and melting point. The periodic table may also be coloured to show the physical state (solid, liquid or gas) of the element as found in nature. There are eight columns in the table. The transition elements are those with atomic numbers between 21 and 30, 39 and 48, 57 and 80, and 89 and above. The elements with an atomic number greater than 92 are artificially produced, radioactive and do not exist to any significant degree in nature. However, these artificially produced elements are radiologically important as they are associated principally with nuclear facilities.
11.SELF-CHECK 4
Now see how much you have understood by answering the following questions in your workbook:
How are elements arranged in the periodic table?
The elements helium (He), neon (Ne) argon (Ar) and krypton (Kr) are all found in the same column of the periodic table. What is the chemical significance of this?
3.Which elements would you expect to have the same chemical properties as lithium (Li)?
Now check your answers with the model answers in your workbook.
12.4.THE CHART OF NUCLIDES
The periodic table displays information about all the elements and arranges them according to the number of electrons in each shell. However, for each element there may be several isotopes about which information is required. To look at all the isotopes of all the elements, the chart of nuclides is used.
The chart of nuclides displays all the nuclides, both naturally occurring and artificial, on the basis on the number of protons and neutrons in the nucleus. The number of neutrons is displayed on the x-axis (horizontal) and the number of protons on the y-axis (vertical). This results in all the isotopes of a certain element being displayed as a horizontal band on the chart of nuclides.
A section of the chart of nuclides is shown in Figure 7.
Number of protons (Z)
Note: Stable nuclides are shaded grey
Radionuclides are not shaded
Figure 7
A Section Of The Chart Of Nuclides
The whole chart of nuclides is shown from page 18 onwards in the accompanying booklet ‘Nuclides and Isotopes’. Look at it now.
The chart of nuclides contains a large amount of information, some of which is not required for general radiation protection work. At this stage in the course only the basic functions of the chart of nuclides are examined. As the course progresses more detailed information will be obtained from the chart. An annotated diagram on page 16 of the booklet describes the location and type of information to be found in each of the nuclide squares.
The basic information displayed on the chart of nuclides includes:
data on the particular element at the start of each row (similar to the information on the periodic table);
each nuclide defined by its atomic mass and symbol;
the abundance and/or half-life of the nuclide; and
the main and secondary methods of radioactive decay if the nuclide is radioactive.
For a specified element, the abundance is defined as the percentage of one isotope to the total, as occurring in nature.
The half-life is the time taken for half the atoms of the radionuclide to undergo radioactive decay; so the shorter the half-life, the quicker the radionuclide will decay. No half-life indicates no radioactive decay and that the nuclide is stable. Both half-life and methods of decay are discussed in detail in Module 1.3 Ionizing Radiation and Radioactive Decay.
Stable nuclides (those which do not undergo radioactive decay) and those with very long half-lives (greater than half a billion years) are generally shaded grey in the chart of nuclides. Naturally occurring nuclides which are radioactive are indicated by a black bar highlighting the isotope’s name.
Artificial nuclides are created by a number of technological processes. They are generally unstable and will undergo radioactive decay to stable nuclides. As they do not occur in nature, their abundance is not shown on the chart. Some elements, mostly those with high atomic numbers, do not occur in nature.
13.
SELF-CHECK 5
SELF-CHECK 5
Now see how much you have understood by answering the following questions in your workbook:
How are the nuclides displayed in the chart of nuclides?
How are the isotopes of a particular element shown in the chart of nuclides?
Using the chart of nuclides on page 18 of the accompanying booklet:
a) name the two stable isotopes of carbon found in nature.
b) name the radioactive isotope of carbon which occurs in nature.
c) which is the most abundant isotope of carbon in nature?
d) name four artificial isotopes of carbon.
Now check your answers with the model answers in your workbook.
14.
KEY POINTS
KEY POINTS
Atoms are the building blocks of all matter.
Atoms are made up of small particles called protons, electrons and neutrons.
Protons have a mass of one atomic mass unit and an electric charge of +1.
Neutrons have a mass of one atomic mass unit and no electric charge.
Electrons have a mass of 1/1840 of an atomic mass unit and an electric charge of -1.
According to Bohr’s atomic model, protons and neutrons form the nucleus of an atom and electrons orbit around the nucleus in well-defined orbits or shells.
Energy must be added to or released from the atom for an electron to change its orbit.
Atoms with the same number of protons are called elements.
The chemical properties of an element are determined by the number of protons and hence the number of electrons in an atom.
Atomic number (Z) is defined as the number of protons in the nucleus of an atom.
Atomic mass (A) is defined as the total number of protons and neutrons in the nucleus of an atom.
Isotopes are defined as atoms of a particular element which have different numbers of neutrons.
The term nuclide is a more general term used to describe any isotope of any element.
Isotopes which emit radiation are called radioisotopes.
Nuclides which emit radiation are called radionuclides.
All isotopes of a particular element have identical chemical properties but they may have different radiation properties.
Each atom has a unique combination of atomic number and atomic mass and this is commonly displayed in the following standard form:
The atomic structure of a nuclide may be inferred from its symbol and atomic mass number.
A covalent bond is a type of chemical bond where electrons are shared between atoms.
An ionic bond is a type of chemical bond formed by the transferral of electrons between atoms and the resulting attraction of positive and negative ions.
A positive ion is an atom with a positive charge.
A negative ion is an atom with a negative charge.
A molecule is defined as a group of atoms which are joined by chemical bonds.
A non-metal is defined as an element which needs to gain electrons to become chemically stable.
A metal is an element which needs to lose electrons to become chemically stable.
A salt is defined as a combination of a metal and a non-metal.
Atoms combine by either sharing electrons or transferring electrons between atoms.
As the electrons orbit the nucleus in well-defined shells, elements with similar numbers of electrons in their outer shell exhibit similar chemical characteristics.
The periodic table displays all the elements arranged on the basis of electron arrangement and hence similar chemical properties.
The chart of nuclides displays all the nuclides, both naturally occurring and artificial, on the basis on the number of protons and neutrons in the nucleus. The number of neutrons is displayed on the x-axis (horizontal) and the number of protons on the y-axis (vertical).
All isotopes of a certain element are shown as a horizontal band on the chart of nuclides.
Stable nuclides (those which do not undergo radioactive decay) and those with very long half-lives (greater than half a billion years) are generally shaded grey in the chart of nuclides.
Naturally occurring nuclides that are radioactive are indicated by a black bar highlighting the isotope’s name.
15.
FINAL ASSIGNMENT
FINAL ASSIGNMENT
Make sure that you understand the material in this module and have successfully completed the self-check questions before arranging a convenient time with your supervisor to complete the assignment. You will need to refer to the accompanying booklet ‘Nuclides and Isotopes’.
16.APPENDIX A
ELECTRON SHELL STRUCTURE
Element | Symbol | Total Number | ||||
Of Electrons | K | L | M | N | ||
Hydrogen | H | 1 | 1 | |||
Helium | He | 2 | 2 | |||
Lithium | Li | 3 | 2 | 1 | ||
Beryllium | Be | 4 | 2 | 2 | ||
Boron | B | 5 | 2 | 3 | ||
Carbon | C | 6 | 2 | 4 | ||
Nitrogen | N | 7 | 2 | 5 | ||
Oxygen | O | 8 | 2 | 6 | ||
Fluorine | F | 9 | 2 | 7 | ||
Neon | Ne | 10 | 2 | 8 | ||
Sodium | Na | 11 | 2 | 8 | 1 | |
Magnesium | Mg | 12 | 2 | 8 | 2 | |
Aluminium | Al | 13 | 2 | 8 | 3 | |
Silicon | Si | 14 | 2 | 8 | 4 | |
Phosphorus | P | 15 | 2 | 8 | 5 | |
Sulphur | S | 16 | 2 | 8 | 6 | |
Chlorine | Cl | 17 | 2 | 8 | 7 | |
Argon | Ar | 18 | 2 | 8 | 8 | |
Potassium | K | 19 | 2 | 8 | 8 | 1 |
Calcium | Ca | 20 | 2 | 8 | 8 | 2 |
17.APPENDIX B
ELEMENTS AND THEIR SYMBOLS
Name | Symbol | Name | Symbol | |
Actinium Aluminium (aluminum) Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Boron Bromine Cadmium Caesium Calcium Californium Carbon Cerium Chlorine Chromium Cobalt Copper Curium Dysprosium Einsteinium Erbium Europium Fermium Fluorine Francium Gadolinium Gallium Germanium | Ac Al Am Sb A As At Ba Bk Be Bi B Br Cd Cs Ca Cf C Ce Cl Cr Co Cu Cm Dy E Er Eu Fm F Fr Gd Ga Ge | Gold Hafnium Hahnium Helium Holmium Hydrogen Indium Iodine Iridium Iron Kurchatovium Krypton Lanthanum Lawrencium Lead Lithium Lutetium Magnesium Manganese Mendelevium Mercury Molybdenum Neodymium Neon Neptunium Nickel Niobium (columbium) Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus Platinum | Au Hf Ha He Ho H Im I Ir Fe Ku Kr La Lw Pb Li Lu Mg Mn Mv Hg Mo Nd Ne Np Ni Nb N No Os O Pd P Pt | |
APPENDIX B | ||||
Name | Symbol | Name | Symbol | |
Plutonium Polonium Potassium Praesodymium Promethium Protactinium Radium Radon Rhenium Rhodium Rubidium Ruthenium Samarium Scandium Selenium Silicon Silver Sodium Strontium | Pu Po K Pr Pm Pa Ra Rn Re Rh Rb Ru Sm, Sa Sc Se Si Ag Na Sr | Sulfur (sulphur) Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin Titanium Tungsten (Wolfram) Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium | S Ta Tc Te Tb Tl Th Tm Sn Ti W U V Xe Yb Y Zn Zr | |
18.APPENDIX C
PROPERTIES OF ELEMENTS
Element | Symbol | Atomic Number Z | Neutron Number* N | Atomic Mass* A |
Hydrogen | H | 1 | 0 | 1 |
Helium | He | 2 | 2 | 4 |
Lithium | Li | 3 | 4 | 7 |
Beryllium | Be | 4 | 5 | 9 |
Boron | B | 5 | 6 | 11 |
Carbon | C | 6 | 6 | 12 |
Nitrogen | N | 7 | 7 | 14 |
Oxygen | O | 8 | 8 | 16 |
Fluorine | F | 9 | 10 | 19 |
Neon | Ne | 10 | 10 | 20 |
Sodium | Na | 11 | 12 | 23 |
Magnesium | Mg | 12 | 12 | 24 |
Aluminium | Al | 13 | 14 | 27 |
Silicon | Si | 14 | 14 | 28 |
Phosphorus | P | 15 | 16 | 31 |
Sulphur | S | 16 | 16 | 32 |
Chlorine | Cl | 17 | 18 | 35 |
Argon | Ar | 18 | 22 | 40 |
Potassium | K | 19 | 20 | 39 |
Calcium | Ca | 20 | 20 | 40 |
* For the most commonly occurring stable atom.
19.GLOSSARY OF TERMS
Abundance | The percentage of one isotope to the total occurring in nature. |
Atom | The building blocks that make up all matter. |
Atomic mass (A) | The total number of protons and neutrons in the nucleus of an atom. |
Atomic mass unit | This is defined as one twelfth of the mass of a carbon-12 (12C) atom and is equal to 1.66 X 10-24g. |
Atomic number (Z) | The number of protons in the nucleus of an atom. |
Boiling point | The temperature at which a liquid changes to a vapour. |
Chemical bond | The way in which atoms are joined together. |
Chemical symbol | The letter(s) used to denote a particular element. |
Covalent bond | A type of chemical bond where electrons are shared between atoms. |
Density | The mass of material divided by its volume. |
Electron | A negatively charged particle orbiting the nucleus of an atom. |
Element | A substance in which all the atoms have the same number of protons. |
Half-life | The time taken for half of the atoms of a radionuclide to undergo radioactive decay. |
Ionic bond | A type of chemical bond formed by the transferral of electrons between atoms and the resulting attraction of positive and negative ions. |
Isotopes | Atoms of a particular element with different numbers of neutrons. |
Melting point | The temperature at which a solid changes to a liquid. |
Metal | An element which needs to lose electrons to become chemically stable. |
Molecule | A group of atoms which are joined by chemical bonds. |
Negative ion | A negatively charged atom. |
Neutron | An uncharged particle in the nucleus of an atom composed of a proton and an electron. |
Neutron number (N) | The number of neutrons found in the nucleus of an atom. |
Non-metal | An element which needs to gain electrons to become chemically stable. |
Nucleus | The positively charged centre of an atom, consisting of protons and neutrons. |
Nuclide | A general term referring to any isotope of any element. |
Orbit | The path of an electron around an atomic nucleus. |
Periodic table | The grouping of elements according to how the electron shells are filled. |
Positive ion | A positively charged atom. |
Proton | A positively charged particle found in the nucleus of an atom. |
Radioactive decay | The change that takes place in the nucleus of an atom to make it more stable. |
Radioisotope | An isotope which emits radiation. |
Radionuclide | A nuclide which emits radiation. |
Salt | A combination of a metal and a non-metal. |
Shell | A specific orbit which electrons take around the nucleus. |
INTERNATIONAL ATOMIC ENERGY AGENCY AUSTRALIAN NUCLEAR SCIENCE AND TECHNOLOGY ORGANISATION |
DISTANCE LEARNING MATERIALS
RADIATION PROTECTION
Module – 1.2
Prepared by Safety and Radiation Science
Australian Nuclear Science and Technology Organisation
With the assistance of consultants in Australia and the United Kingdom, and IAEA experts from Korea, Mongolia, New Zealand, the Philippines and Thailand
Use of this material, acknowledging the IAEA and ANSTO as the source, is permitted for non-profit training
Acknowledgements
This material has been prepared by an extensive team of international experts from the fields of radiation protection, medicine and education. It is not possible to mention by name all those who have had an input to; the initial planning; writing modules and workbooks; preparing and marking final assignments; proof-reading and editing; using the material and providing valuable feedback; organizing and hosting review meetings; and general administrative support.
The support of ANSTO management in providing the resource and encouragement is gratefully acknowledged.
The enthusiastic support of IAEA Technical Officers has been vital to the success of this project
PART 1
BASIC KNOWLEDGE
MODULE 1.2
BASIC MATHEMATICS
CONTENTS
20.OVERVIEW
This module is intended to provide you with the information and skills you will need to carry out the basic mathematics calculations in subsequent modules. An ability to manipulate numbers and equations successfully is important as it will help you to assess hazards arising from the use of sources of radiation. It is also important that you are able to use graphical methods to analyze measurement data, and that you can extract correct information from published graphs. An understanding of counting statistics will allow you to quantify the accuracy of the measurements that you have taken and help you to assess the level of hazard in the workplace.
Although you may already be familiar with some of the information in this module, it is advisable that you complete the self-check questions at the end of each section before attempting the final assignment.
21.
TIME ALLOCATION
It is estimated that you will need to spend eight to ten hours to complete this module before commencing the assignment. This estimated time is for guidance only. Do not worry if you need more time to understand the module.
22.MATERIALS
In addition to writing materials and your workbook you will need access to a scientific calculator or logarithmic tables, a ruler and log/log and log/linear graph paper.
Rounding a number means restricting the number of digits (single numbers) which are included when recording the number. There are certain rules which help us decide when numbers should be rounded and how they should be rounded. This section will help you to understand these rules and apply them correctly.
When you are carrying out a calculation the numbers you use will be in one of the following forms:
Whole numbers1;32;512
Whole numbers and decimals2.5;40.67;600.2
Decimals0.1;0.03;0.007
Fractions
For convenience, fractions will only be used when calculating results in the algebra section of this module. Fractions can be converted to decimals by dividing the number above the line (the numerator) by the one below the line (the denominator).For example, can be written as 3 4 = 0.75.
Throughout this training material, decimals points will be shown as ‘ . ’, e.g. 2.1, and thousands will be shown by leaving a space between the thousands and the hundreds digits, eg 13 456 means thirteen thousand four hundred and fifty six.
The number of digits which should be reported in the result of a calculation depends on the type of calculation and how accurate the result needs to be. One way of stating this is to decide on the number of significant figures to quote.‘0’ is not a significantfigure unless it is between two other numbers, for example 103, or unless it is the last digit after a decimal point, eg 2.10. (Both these numbers are examples of numbers with three significant figures.)For example, 13 456 to two significant figures can be written as 13 000 (note that the noughts are not significant). This is a convenient way of reporting a result but it does not indicate the size of the answer. For example, 13 000 and 2.1 can both represent rounding to two significant figures. The number of significant figures may, however, be an indication of the accuracy of the number. This is one of the major factors determining how many significant figures should be quoted.
Rounding may be done in terms of significant figures, as discussed in the last paragraph, or as decimal places. The number of decimal places is the number of digits after the decimal point. For example, the number 2.10 has two decimal places (but three significant figures).
It is normal practice to round up if the digit to be rounded is greater than, or equal to, five. For example the numbers 2.55, 2.56, 2.57, 2.58 and 2.59 would be written as 2.6 when rounded to two significant figures (or one decimal place). The numbers 2.50, 2.51, 2.52, 2.53 and 2.54 would be written as 2.5 when rounded to two significant figures (or one decimal place). This is called rounding down and is the normal practice for digits less than 5.
Table 1 shows how significant figures, decimal places and rounding are used.
Table 1
Significant Figures, Decimal Places and Rounding
Calculated | Number of Significant Figures | Number of Decimal Places | ||||
Number | Four | Three | Two | Four | Three | Two |
525.7910 | 525.8 | 526 | 530 | 525.7910 | 525.791 | 525.79 |
0.003417 | 0.003417 | 0.00342 | 0.0034 | 0.0034 | 0.003 | 0.00 |
There are two principal reasons why figures are rounded, namely,
to give a sensible answer, and
to indicate the accuracy of a measurement.
For some calculations, the answer is only sensible if the result is quoted to a pre-determined level of significance. A simple example of this would be if you wanted to calculate the number of people that could sit around a table which has a 345 cm circumference. If each person is allowed 75 cm of space, the answer will be 345 divided by 75, which is 4.6 people! Obviously, 0.6 of a person does not have any meaning when talking about how many people can sit around a table. If you apply the rounding rules given in Section 1.2 you will give the answer as five. But this is an example of ‘normal practice’ and does not necessarily provide a very sensible answer. To sit five people around the table would make it very crowded; in this case, four would be a better answer.
The accuracy of a number can be inferred from the number of decimal places or significant figures given in the number. For example if the length of a football field is given as 110 m, this implies that the field has been measured to the nearest 10 m. Its actual length may be anywhere between 105 m and 114 m. If the length of the field is recorded as 108.54m, this implies that it has been measured to the nearest one hundredth of a metre (centimetre). This would represent a very accurate measurement. The number of decimal places quoted in this case is determined by the method of measurement. It is obviously not sensible to quote the length of the football field as 108.54 m if the measurement was done with a tape having the metre as the smallest unit. It would be more sensible to quote 109 m, ie rounded to the nearest metre.
There are some simple rules that can be applied to determine how many decimal places or significant figures should be quoted in a number. These rules are as follows:
Think about what the answer means. (As in the example of fitting people around a table.)
If the number is the result of a calculation, it should be quoted to the same number of decimal places or significant figures as the least accurate number used in the calculation. For example,
2.1 x 3.45 x 1.3 = 9.4185 = 9.4 (rounded)
If the number is a measurement, consider how it was obtained and what its accuracy might be. (As in the football field example.)
Consider how accurate the result needs to be. (For example, the answer may only need to be to the nearest ten.)
24.SELF-CHECK 1
Now see how much you have understood by answering the following questions in your workbook:
Write the following numbers to 3 significant figures:
3 212
5 678
203 456
Write the following numbers to 2 decimal places:
0.0023
3.567
25.995
Write the distances to the accuracy required:
15.6 m to the nearest metre.
123 m to the nearest ten metres.
3 567 m to the nearest thousand metres.
Now check your answer with the model answers in your workbook.
Algebra is a branch of mathematics used for solving problems. Equations are constructed in which letters are substituted for the unknown quantities. A relationship is obtained between known and unknown values. For example, y = b + 2 means that the value of y is always two units more than the value of b.
An equation is a mathematical sentence which relates two or more quantities. Equations can be used to determine the value for some factor which changes because of the change in a related factor. A good example of this is the simple equation which relates the temperature measured in degrees celsius (ºC) to the same temperature measured in degrees fahrenheit (ºF):
F = 1.8C + 32
This equation means that one division on the celsius scale is equal to 1.8 divisions on the fahrenheit scale. (There are 100 divisions between the freezing point and boiling point of water on the celsius scale and 180 divisions on the fahrenheit scale.) The +32 indicates that there is a difference between the two scales of 32 fahrenheit divisions, ie 0ºC, the freezing point of water, is equivalent to 32ºF. The equation can be used to find the fahrenheit equivalent of any celsius temperature.
Example
What is 25ºC in degrees fahrenheit?
C = 25
F = 1.8C + 32
Substitute in C = 25
F = 1.8 x 25 + 32 = 77
This means that 25ºC is equivalent to 77ºF.
An equation can be designed from given information. For example, we might need to design an analogue scale for a radiation monitor for which the needle position on the scale is equal to twice the current from the detector. If we write the needle position as x and the current as c, we can produce an equation
x = 2c
If the needle is on the third mark when the current is zero, ie there is an offset of 3, the equation becomes
x = 2c + 3
This equation can then be used to calculate the position of the needle for any value current by substituting the value of the current into the equation.
For c = 1, the value of x can be calculated as 5.
Similarly, for c = 2, x = 7, and so on for any value of c.
!
In this system of writing equations, 2c means 2 multiplied by c. Other ways of writing 2 multiplied by c are 2.c or 2*c. A full stop or an asterisk can be used to prevent confusion with x, which is sometimes used as a multiplication sign or to represent an unknown.Also means 2 divided by a. Another way of writing 2 divided by a is 2/a.
The following information shows how equations can be manipulated to find the value of any of the terms:
The simplest rule to remember is that the two sides of an equation must be treated in exactly the same way. When manipulating the equation, when you change one side, you must always do the same to the other.
This can be demonstrated as follows:
Y = 2a + 3d
To obtain 2a on its own, we need to subtract 3d from the right hand side. If we subtract 3d from the right we must do the same to the left to maintain the balance, as follows:
Y = 2a + 3d
Y - 3d = 2a + 3d -3d
Y - 3d = 2a
Another way of thinking about this is change the side - change the sign.
This can also be seen for fractions in the following equation:
To calculate a, it must be on its own on one side of the equation. This can be achieved as follows:
Multiply each side by 3d to give
S x 3d = x 3d
As mentioned above, S multiplied by 3d can be more clearly written as 3dS:
3dS = 2a
Divide both sides by 2 to give
We have now found a in terms of S and d.
Be careful when there is more than one term in the denominator, such as 3d + 2b. Sometimes brackets are used to link the terms together. (This is a good idea and you will be less likely to make a mistake.) An example is shown below:
S =
S(3d + 2b) = .(3d + 2b)
S(3d + 2b) = 2a
Terms inside the brackets are linked; you must remember to carry out the same calculations on each value in the bracket if you want to move them to the other side of the equation. The term outside the brackets multiplies each term inside the brackets. So the equation becomes
3dS + 2bS = 2a
Note that it does not matter in what order the numbers and letters are written. In other words 3dS is the same as 3Sd which is the same as dS3 or S3d or any other combination. However, it is usual to write the number first, followed by the letters in alphabetical order.
The left hand side of the equation is divided by 2 to obtain the term a by itself. Note that every term must be divided by 2.
=
dS + bS = a
Now try the same method to obtain the term b by itself.
Start with S =
You should have gone through the following steps:
S =
S(3d + 2b) = (3d + 2b)
S(3d + 2b) = 2a
=
3d + 2b =
3d - 3d + 2b = - 3d
2b = - 3d
b =
b =
As you become familiar with manipulating equations, you will find that you do not need to write the simple steps, for example
2b = - 3d
will be written
b =
without the intermediate step.
The sign of a number or an unknown changes to the opposite sign when it is moved to the other side of the equation.
When letters and numbers appear next to each other, they are multiplied.
2a or 2.a or 2*a are the short ways of writing 2 x a.
When letters and numbers appear one above the other, the number on top (called the numerator) is divided by the number below (the denominator).
or a/2 are the short ways of writing a 2.
When a denominator is moved to the other side of the equation it becomes a numerator.
When a numerator is moved to the other side of the equation it becomes a denominator.
When the numerator or denominator contains more than one number linked by a + or - sign they should be linked together by brackets and treated as a single term until they can be separated easily.
25.SELF-CHECK 2
Now see how much you have understood by answering the following questions in your workbook:
Write the following imaginary statement as an algebraic equation using the letters shown:
The level of radiation (R) from an exposure unit is equal to the half the unit’s quoted output (O) and divided by the number of absorber plates (p).
Use the equation a = b - 2c to find
a)the value of b in terms of a and c; and
b)the value of c in terms of a and b.
3.Find the value of b from the equation
if a = 2, f = 3, c = 1 and d = 4.
Now check your answers with the model answers in your workbook.
When you are measuring or calculating quantities to do with radioactivity and radiation protection there will be occasions when the values may be very large or very small. It is helpful to write these numbers in a way which makes them easier to use. One way of doing this is to use exponents (also called powers or indices) and scientific notation. Note that the word ‘indices’ is the plural form of ‘index’.
For example,
22 is the same as 2 x 2 or two to the power of two. We generally refer to this as two squared.
23 is the same as 2 x 2 x 2 or two to the power of three. We generally refer to this as two cubed.
Two is called the base of the number and three is the exponent, power or index.
Multiplying and dividing numbers written in the form of exponents follows simple rules, provided that the same base is used.
bm x bn = bm+n[1]
For example:
22 x 23 = 25
Prove this yourself by working out the values of 22, 23 and 25.
A special case of this multiplication is when a number written in exponent form is multiplied by itself n times.
bm x bm x bm x bm x (n times) = bm+m+m+m+(n times) = (bm)n
(bm)n = bmn[2]
For example,
(22)2 = 22 x 22 = 24
Prove this yourself by working out the values of 22 and 24.
bm ÷ bn = bm-n[3]
For example,
25 ÷ 22 = 25-2 = 23 = 2 x 2 x 2 = 8
Prove this yourself by working out the values of 25, 22 and 23.
The exponent does not have to be a whole number but may be a fraction or a number with decimal places. If the exponent is a fraction in the form of 1/m, where m is a whole number, it is called a root. If n is two, then the power is called the second or square root, if n is three, it is the third or cube root, if n is four it is the fourth root, and so on.
For example,
91/2 = the square root of 9 = √9 = 3
81/3 = the cube root of 8 = 3√8 = 2
b1/m = m√b[4]
Occasionally, the exponent may be shown as zero. In this case, a general rule applies where any base with an exponent of zero is equal to 1.
b0 = 1[5]
For example,
10 = 1
20 = 1
If the exponent is a negative number, e.g. 2-3, it means that the result is the reciprocal of the positive exponent, i.e. one divided by the positive exponent (1/23).
b-p = 1/bp[5]
For example,
10-1 = 1/10 = 0.1
10-2 = 1/102 = 1/100 = 0.01
10-3 = 1/103 = 1/1000 = 0.001
Figure 1 summarises the rules of exponents. Remember that these rules only apply if the same base is used.
Figure 1
The Rules of Exponents
A scientific calculator may be used to find exponents. Although this may vary from calculator to calculator, the basic method is to use the xy (or yx) button. Firstly, press the number corresponding to the base (e.g. 2 in the calculation of 23), then press the xy (or yx) button. Finally, press the number corresponding to the exponent (e.g. 3 in the calculation of 23). Note that some calculators may also have a x1/y (or y1/x) button which can be used in a similar way to calculate exponents involving fractions. If you have a scientific calculator you might like to practice using the examples of exponent calculations given above. If you do not have a scientific calculator, you will need to calculate by long hand or by using logarithms (see Section 2).
The normal way that numbers are written is based on a system of 10, eg every time we complete one set of ten units we move on to the next set as follows:
10 digits become the value ten (10).
10 lots of ten become one hundred (100 or 102).
10 lots of one hundred become one thousand (1 000 or 103).
10 lots of one thousand becomes ten thousand (10 000 or 104).
We call this system base 10 or the decimal system. Other bases in use in some industries are base 2 (the binary system used in electronics) and base 16 (the hexadecimal system used in computers).
Very large or very small numbers can be written in a simple form using powers to the base ten. Scientific notation is a way of writing numbers by putting only one digit before the decimal point and using powers of ten. The use of scientific notation makes it easier to manipulate very large or very small numbers without making a mistake.
For numbers greater than ten, the power of ten will always be positive. The following examples show numbers written in scientific notation:
12.3 = 1.23 x 101
123 = 1.23 x 102
123 000 000 = 1.23 x 108
For numbers less than one, the power of ten will always be negative, meaning that the number is being divided by the power of ten. The following examples show small numbers written in scientific notation:
0.123 = 1.23 x 10-1
0.0123 = 1.23 x 10-2
0.0000000000123 = 1.23 x 10-11
The base 10 value is often replaced by the letter E, particularly on computer generated tables. ‘E’ stands for exponent. Here are some examples:
1.25 x 102 = 1.25 E 02
3.57 x 104 = 3.57 E 04
1.23 x 10-3 = 1.23 E - 03
Occasionally d (for decimal) is used in place of E, but this is not common.
26.SELF-CHECK 3
Now see how much you have understood by answering the following questions in your workbook:
1.Calculate these values:
a) 23
b) 34
Write base y raised to the power x.
Multiply or divide the following exponents but leave the answers as a power:
a) 23 x 2-4
b) 23 2-4
c) b1/3 x b2/3
d) c2 ca
4.Using the rules of exponents calculate the following:
a) 161/2
70
2-2
5.Write the following numbers in scientific notation:
a)3 500
b)23
c)56 784
Now check your answers with the model answers in your workbook.
In the days before calculators, logarithms (or logs as they are usually called) were devised as a way of making difficult calculations simpler. It is much easier to add numbers together than to multiply them. Similarly, it is much easier to subtract numbers than to divide and the original purpose of logs was to allow this simplification. Nowadays, most people use electronic calculators to perform difficult calculations and logs are rarely used for this purpose. However, an understanding of how logs work is particularly important in radiation protection as they provide a basis for understanding the mechanisms of radioactive decay.
Logs are used to convert numbers into powers of a particular base.
For example, the number y may be expressed in an imaginary numbering system by writing it as base b raised to the power x as follows:
y = bx [1]
Remember that the log of a number is the power to which the base is raised. If you apply this definition to the number y, then log y to the base b (logb) is equal to x. This is written as follows:
logb y = x [2]
You will remember from Section 3 that multiplication and division of numbers raised to a power are carried out by addition and subtraction of the powers. Since logs convert numbers to powers, the multiplication or division of any number can now be carried out by simple addition or subtraction. This is the advantage of logs.
The rules of exponents can be rewritten in terms of logs as shown in Figure 2. These rules apply to all logs, but remember that the base must be the same throughout the equation.
Figure 2
The Rules of Logs
There are two bases which are most commonly used in logs ─ the base 10 (our normal system of counting) and base e (where e is a continuous number approximately equal to 2.718 and which has special meaning in the field of radiation protection). Logs to the base 10 are called common logs, (or Briggsian logs), and logs to the base e are called natural logs (or Napierian logs).
27.SELF-CHECK 4
Now see how much you have understood by answering the following questions in your workbook:
Use the definition of a log to work out the following log values:
a)log10 1
b)log10 10
c)log10 100
Using your answers from question 1 and using the rules of logs, work out the following log values: (Take the value of log10 3 as 0.4771.)
a)log10 (3 x 100)
b)log10 33
c)log10 (3 100)
d)log10 (1/3)
What are the two bases most commonly used in logs?
Now check your answers with the model answers in your workbook.
Remember that common logs are logs to the base 10. They may be written as log10 but are generally just written as log. Hence, common log equations may be written in the form:
logy = x [1]
where y is the number that you want the common log of and x is the corresponding common log value.
There are two ways of finding the common log of a number. The most convenient way is to use a scientific calculator. The other, more traditional method is to use common log tables. The log tables method is shown in detail in Appendix A. If you do not have access to a scientific calculator, you will need to study this method of working out common logs. If you have access to a scientific calculator, you do not need to study this method but you may be interested in doing so.
As different types of calculator compute common logs in different ways, it would be impossible to explain all of the methods in this module. In general, however, by pressing the ‘log’ button on your calculator either before or after the number you want the common log of, you should be able to find the corresponding log value. Try computing the following common logs values using your calculator:
a)log1
b)log10
c)log100
You should get the answers a) 0, b) 1 and c) 2 (as you have already worked out in question 1 of self-check 4).
If you have any difficulties in using your calculator to find common logs, you are advised to refer to the calculator’s instruction manual or to ask your supervisor for help.
Now you know how to find the common log of a number. However, it is often necessary to be able to convert known common log values back into numbers. This is basically done by inversing equation 1 in section 5.1 and is known as taking the antilogarithm (or antilog for short) of a common log value. In mathematical terms, antilogs of common logs are abbreviated to log-1 and antilog equations may be written in the form:
y = log-1x [2]
where y is the number corresponding to the known common log value x.
In simple terms, to find the original number of a common log value we need to use the calculator or log tables backwards. The log tables method for finding the antilogs of common logs is detailed in Appendix A but the calculator method is simpler. In general, you can find the antilog of a common log value by pressing the ‘shift’ or ‘inverse’ button on your calculator then the ‘log’ button either before or after the value you want the antilog of. Try computing the following antilogs using your calculator:
a)log-10
b)log-11
c)log-12
You should get the answers a) 1 b) 10 and c) 100. (Note that this is the reverse of the calculations you carried out in section 5.2).
Again, if you have any difficulties in using your calculator to find antilogs, you are advised to refer to the calculator’s instruction manual or to ask your supervisor for help.
28.SELF-CHECK 5
Find the common log values of the following numbers by using your calculator:
a) 4 567
b) 1.09
Find the common antilogs (log-1) of the following log values by using your calculator:
a) 3.5482
b) 1.4114
Now check your answers with the model answers in your workbook.
Remember that natural logs are also known as logs to the base e (where e is a continuous number approximately equal to 2.718). Log to the base e of a number may be written as ln. For example loge3, can be written as ln 3. Like common logs, natural log equations can be written in the form:
lny = x [1]
where y is the number that you want the natural log of and x is the corresponding natural log value.
Although you could use logs to the base e to carry out multiplication and division in the same way as logs to the base 10 they are not normally used for that purpose. They are, however, useful in solving some of the special properties of radiation which you will learn about in other modules.
Like common logs, there are also two ways of finding the natural log of a number – either by using a calculator or by using natural log tables. The method of using natural log tables is shown in detail in Appendix B. Again, if you do not have access to a scientific calculator, you will need to study this method of working out natural logs. Those students who do have access to a scientific calculator do not need to study this method but you may be interested in doing so.
In general, natural logs can be computed on a calculator by pressing the ‘ln’ button either before or after the number you want the natural log of. Try computing the following natural logs using your calculator:
a)ln1
b)ln10
c)ln100
You should get the answers a) 0, b) 2.3026 and c) 4.6052.
If you have any difficulties in using your calculator to find natural logs, you are advised to refer to the calculator’s instruction manual or to ask your supervisor for help.
Now you know how to find the natural log of a number, you need to learn how to convert known natural log values back into numbers. Again this is done by taking the antilog of the log value. In mathematical terms, antilogs of natural logs are abbreviated to ln-1 and natural antilog equations may be written in the form:
y = ln-1x [2]
where y is the number corresponding to the known natural log value x.
The method of finding antilogs of natural logs is similar to the method used for common logs in that you need to use the calculator or log tables backwards. The log tables method for finding the antilogs of natural logs is detailed in Appendix B but the calculator method is simpler. In general, you can find the antilog of a natural log value by pressing the ‘shift’ or ‘inverse’ button on your calculator then the ‘ln’ button either before or after the value you want the antilog of. Try computing the following natural antilogs using your calculator:
a)ln-10
b)ln-12.3026
c)ln-14.6052
You should get the answers a) 1 b) 10 and c) 100. (Note that this is the reverse of the calculations you carried out in section 6.2).
Again, if you have any difficulties in using your calculator, refer to the calculator’s instruction manual or to ask your supervisor for help.
29.SELF-CHECK 6
1.Find the natural log values of the following numbers by using your calculator:
4.65
46.5
Find the natural antilogs of the following natural log values by using your calculator:
a)0.693
b)2.708
Now check your answers with the model answers in your workbook.
Remember that the definition of the log of a number is the power to which the base has to be raised to equal the number as follows:
ln y = x[1]
If this definition is applied to a number y which equals ex (y = ex), then:
ln ex = x[2]
As e is a constant number, ex depends on the value of x. We therefore say that e is a function of x. In addition, as x is the exponent of e, ex is known as the exponential function.
Exponential functions are very important in radiation protection as they give a useful mathematical description of physical phenomena such as radioactive decay. Furthermore, the relationship ln ex = x is a very important relationship which is used in deriving equations for radioactive decay and half-lives.
Note from equation 2, that if we want to convert ex to an ordinary number, we need to take the ln of it. This is a very important fact to remember when manipulating radioactive decay equations.
We find the value of exponential functions in the same way as we find antilogs of natural logs. This can be shown as follows:
From above:
ln ex = x[1]
Taking the antilog of both sides:
ex = ln-1 x[2]
Therefore, if we find the antilog of a natural log value, we can find the value of the exponential function.
The log tables method for finding the value of exponential functions is detailed in Appendix B. In general, you can find the value of exponential functions by pressing the ‘shift’ or ‘inverse’ button on your calculator then the ‘ln’ button either before or after the value you want the antilog of. Notice that your calculator should show the exponential ‘ex’ above the ‘ln’ key. Try computing the following exponentials using your calculator:
a)e1
b)e3.5
c)e-2
You should get the answers a) 2.718 (i.e. e) b) 33.115 and c) 0.135
Many of the calculations of radioactive decay require you to be able to manipulate equations involving natural logs and exponential functions. It is therefore important that you try to memorise the rules of manipulating equations from section 2.2 and the log rules from section 4.4 as these rules are particularly useful for manipulating radioactive decay equations.
From section 2.2, you will remember that what we do to one side of an equation, we must do to another. If we have an equation:
a = ex[1]
and we wish to find x, this can be done by finding the ln values of each side as follows:
ln a = ln ex[2]
Butln ex = x
soln a = ln ex = x
Hence
ln a = x[3]
where a = ex
This is an important rule to remember as it will be used in later modules to show how radioactive decay equations can be manipulated.
From section 7.1, we know that
ln ex = x[1]
This property can also be shown by using log rules. Remember that:
logb (m)n = n logb m[2]
and
logb b = 1[3]
Hence:
ln ex = x ln e = x[4]
30.SELF CHECK 7
Now see how much you have understood by answering the following question in your workbook:
Find the value of the following exponential functions by using your calculator:
a)e1.335
b)e 10.3562
c)e-5.5
Using the rules of manipulating equations and the rules of logs to prove that b = ext is the same as ln b = xt.
Now check your answers with the model answers in your workbook.
Graphs are a means of using drawings to show mathematical relationships between two or more measurements or sets of data. These measurements or sets of data are called variables. Graphs can be used for the following purposes:
To show information as a picture to make it easier to understand. A graph represents a mathematical equation of the relationship between two variables.
To investigate the relationship between the variables. For example, the count rate of a radioactive source decreases with time. This can be shown graphically by plotting the count rate at certain times on a graph.
To estimate unknown values of variables which cannot be measured, (maybe because they lie outside the range of collected data).For example, the count rate/ time graph can be used to predict the count rate of the radioactive source at some time in the future.
To obtain information which can be derived from measured data. For example, the time taken for half a radioactive sample to decay (half-life) can be estimated from the count rate/time graph.(This will be explained in Module 2.3.)
To increase the accuracy of data.
A graph has two axes; the horizontal axis, usually called the x axis, and the vertical axis, usually called the y axis. The axes are marked off in a suitable scale and points are plotted on the graph corresponding to x and y values.
Figure 3 below shows how a point is plotted on a simple graph. The plotted point corresponds to a value of x equal to 3, and a value of y equal to 6.This can be written as the point (3,6).
Figure 3
A Simple Graph
It is usual practice to plot the variable which is being controlled on the x-axis and the other variable on the y-axis. For example, in the count rate/time graph considered earlier, time would be plotted on the x-axis and count rate on the y-axis.
In the simple graph shown in Figure 3, the axes are marked in a linear scale. Each axis is divided into equal divisions to cover the range of data collected. Note that it is not necessary for both axes to have the same scale. Nor is it necessary for the zero to be shown. Scales may start at any number unless there is a good reason for showing the zero.(It may actually be a data point.)
One or both axes may also be marked in a log scale. This is an advantage if the variables are related by an exponential function. It may also be useful if the numbers in the data have a very large range (hundreds or thousands). In a log scale, the axis is marked off in equal sections corresponding to 100, 101, 102, etc. Each of these larger sections is called a cycle and is divided into divisions corresponding to a log scale. Figure 4 shows an example of log/linear graph paper in which the x-axis is linear and the y-axis is log.
Figure 4
Log/linear Graph Paper
This is called two cycle log/linear graph paper because the log scale has two cycles. It could be used for plotting data from one (100) to one hundred (102), or from ten (101) to a thousand (103) or for any equivalent range. Log/linear graph paper is used for plotting counting data against time for a radioactive source.
Figure 4 shows an example of graph paper in which both scales are two cycle log. Log/log graphs are used when the numbers to be plotted extend over a large range. You will find examples in reference books. It is important that you can read the log scales correctly in order to extract correct information from the graph.
Figure 4
Log/log Graph Paper
!
Care must be taken when plotting numbers on log scales. It is very easy to make a mistake. Notice that log scales do not have a zero.Information may be obtained for points on a graph between measured data points by drawing lines from the graph line to the x- and y-axes. This is called interpolation. Lines AB and BC on Figure 5 show how the y value corresponding to x = C can be found by interpolation. A line is drawn from the value C on the x-axis up to the graph line at point B. This is shown by the grey dotted line. A horizontal line is then drawn from B across to the y-axis. This is shown by another grey dotted line. The point at which this line intersects the y-axis gives the value of y corresponding to x = C.
Information may be obtained for values beyond the measured data.(The values may be higher or lower than the measured data.)This is called extrapolation. Figure 5 shows how the graph line has been extrapolated to find the value of y when x equals zero. The graph has been extended backwards to cut the y-axis at point D. This is shown by the black dotted line. The point D gives the value of D corresponding to x equals zero.
Figure 5
A Graph Illustrating Interpolation and Extrapolation
It is important to remember what a graph means. Interpolation or extrapolation may not be valid.
When a graph is drawn using data obtained from an equation, eg a graph of x against y where the data are obtained from the equation y = 2x2, a line or curve can be drawn connecting all the points. There will be no errors in the numbers (assuming that the calculations have been done correctly). Graphs used in radiation protection are usually drawn from experimental data. All experimental data, especially counting data from radioactive materials will have errors. The size of the errors can be shown on a graph by plotting error bars. (You will learn how to calculate errors in counting data later in the module.) The line or curve drawn on the graph will not necessarily pass through each plotted point. It should be drawn so that the points are evenly scattered on either side, and it should pass through all the error bars (assuming that they have been plotted correctly). This is called the line of best fit. The process of drawing a graph and putting in a line of best fit allows the accuracy of individual data points to be increased.
Figure 6 shows a line of best fit with data points either side of it and error bars.
Figure 6
A Graph Drawn from Experimental Data
This refers to the area between the graph line and the x-axis. It may have some significance, especially if the x-axis measures time. The area can be found accurately by a mathematical process called integration. Although you should know that integration means the area under the curve, learning the process of integration is beyond the scope of this course. The area may also be found approximately by counting the squares on the graph paper. Two situations in radiation protection where the area under a graph has some significance are given here:
A graph of counts against radiation energy for a given radionuclide. This type of graph is obtained by a process called gamma spectrometry which is discussed in a later module. Figure 7 shows a simple example. The area under the graph gives the total counts for the radioactive sample.
Figure 7
Graph of Number of Counts Against Energy for a Radioactive
Sample
A graph of radiation dose rate against time. The area under the graph gives the total dose. This will be mentioned later in the course when you learn about radiation doses caused by the intake of radionuclides. Figure 8 gives an example of a dose rate against time graph. The curve shows how the dose rate to a given body organ following an intake of radioactive material changes over a fifty year time interval. The area under the curve gives the total dose to the body organ.
Figure 8
Graph of Dose Rate Against Time
These examples are given to help you understand why the area under the curve may be important in radiation protection. Do not worry if you do not understand the specific example at this stage.
There are many types of graphs but only those which have some relevance to radiation protection are considered here. Three types will be considered:
Those which illustrate a linear relationship between two variables.
Those which illustrate an exponential relationship between two variables.
Those which use log/log graph paper because the data extends over a large range.
Table 2 contains data for six similar radioactive sources. The meaning of the term activity and the unit in which it is measured are not important at this stage.
Table 2
Radioactive Sources and Activity
Number of Sources | Amount of Activity |
1 | 2 |
2 | 4 |
3 | 6 |
4 | 8 |
5 | 10 |
6 | 12 |
If the data are plotted on a graph using linear scales, it will look like Figure 9. The number of sources (the variable which is being controlled) is plotted on the x-axis and the activity on the y-axis. A straight line can be drawn though all the points. This shows that it is a linear relationship.
Figure 9
Graph of Number of Sources Against Activity
Interpolation can be used to predict the activity of 1.7 sources as shown by the dotted lines on the graph. The activity of 1.7 sources would be about 3.5 units. The graph has been extended past the measured points to find the activity of eight sources. This is an example of extrapolation.
In Section 7, you learnt about the exponential function ex. Many relationships used in radiation protection are exponential e.g. the law of radioactive decay, and you should be able to plot a graph of exponential data. You should also be able to obtain necessary information from this graph. If the data are plotted on linear graph paper, a curve like the one shown in Figure 10 is obtained.
Figure 10
Exponential Graph on Linear Graph Paper
If the same data are plotted on log/linear graph paper, it looks like Figure 11.
Figure 11
Exponential Graph on Log/linear Graph Paper
There are four log cycles represented on this graph paper. You can see that when the data from an exponential relationship are plotted on log/linear graph paper, a straight line can be drawn. It is much easier to draw a straight line through points than it is to try to fit a curve. Another advantage of the log axis is that it enables both small and large numbers to be plotted with equal accuracy. An example is given in Example 1.
Question
By using the data in Table 3 and plotting a graph on log/linear graph paper, find the value of y when x equals 7.
Table 3
Data for Graph
Value of y | 1.8 | 3.3 | 10.4 | 33 | 102 | 310 |
Value of x | 1 | 2 | 4 | 6 | 8 | 10 |
The data in Table 3 is to be plotted on log/linear graph paper and the graph used to find the value of y when x equals 7. First try plotting the graph yourself, and then use it to find the required value. Then look at the answer below.
Answer
Step 1You must first decide how many log cycles are required on the graph paper. The y values range from 1.8 to 310. 1 to 10 is one cycle; 10 to 100 is the second cycle; 100 to 1000 is the third cycle. Therefore three-cycle graph paper is needed.
Step 2Mark the scales on the axes.
Step 3Plot the points. Be careful plotting numbers on the log scale.
Your graph should look like Figure 12 below:
Figure 12
Log/Linear Graph of y against x
Step 4Find the point (A) on the x-axis where x equals 7. Draw a line up from that point to the graph line. (AB on Figure 13 below.)
Step 5Draw a line from B parallel to the x-axis across to the y-axis. (BC on Figure 13 below.)
Step 6Read the value on the log axis at point C. Be careful when reading the log scale. (C = approximately 56.)
Figure 13
Log/Linear Graph of y against x
The important thing about log/log graphs is that you are able to extract information from them correctly. Look at the example given in Figure 14.
Figure 14
Example of a Log/Log Graph
Notice that both the x and y scales are logarithmic. The x-axis is measuring time in days following a nuclear reactor shutdown. The y-axis is measuring the amount of radioactivity in the fuel (TBq or terabecquerels) per unit of reactor power (MW or megawatts). The time values go from one to 1 000 days and the radioactivity values go from 1 000 to 100 000 TBq, so a log scale has been used to cover the large numerical range of data. It does not matter if you do not understand what the values on the y-axis mean. Just make sure you can read the scale by estimating the value of the radioactivity at 10 days and at 120 days. Then look at the answer below.
If you follow the 10 day line up to where it cuts the graph and then draw a line across the y-axis the intercept on the y-axis will tell you the radioactivity at 10 days. The intercept is approximately 2 x 104 (or 20 000) TBq/MW. Do the same thing for a time of 120 days. The intercept on the y-axis is approximately 7 x 103 (or 7 000) TBq/MW.
31.SELF-CHECK 8
Now see how much you have understood by answering the following questions in your workbook:
Calculate the values of y in the equation y = x2 for values of x equal to 1, 2, 3, 4, 5.Plot these values against x using normal linear graph paper.
Plot the following data on log/linear graph paper.
Value of a | Value of b |
1 | 1 |
1.5 | 4 |
2.0 | 16 |
2.5 | 70 |
3.0 | 300 |
Use your graph to estimate the value of b when a equals 2.2 and when a equals 4.0.
Use the log/log graph given in Figure 14 to estimate the value on the y-axis for time equal to:
1 day
80 days
1 000 days
Now check your answers with the model answers in your workbook.
The mathematics of probability and statistics is quite complex. In this section you will be introduced to a few of the simpler concepts which will allow you to work out the errors associated with counting radioactive sources.
Probability is described as the extent to which an event is likely to take place. This could be the chance that a particular side of a coin will be facing upwards after the coin has been thrown in the air and caught. As there are two faces to a coin and only one will be showing (assuming that it does not balance on its edge), the probability that a particular side will be showing is equal to the number of actions (eg number of coin tosses) divided by the possible outcomes (eg one face or the other). In this simple case, the probability would be ½ or 0.5 or 50%. A probability of 1.0 or 100% exists for an event that must occur. A probability of zero means that an event will definitely not occur.
There are many areas of mathematics which deal with probabilities. However, the only areas of relevance to radiation protection are those dealing with the counting of radioactive samples. This topic will be covered in the following section and most of the examples will deal specifically with this type of counting.
The decay of radioactive material is described in detail in Module1.3 Ionizing Radiation and Radioactive Decay. It will be used in this module to help explain the mathematical concepts of probability and counting statistics. At this stage you do not need to understand how materials decay.
Consider what would happen if you were asked to collect data on the coin tossing example described in Section 9.1. In theory, for every 100 tosses of the coin it should land on one particular face 50 times. However, you know that this will not necessarily happen. If you toss the coin for ten sets of 100 tosses you may obtain the numbers 47, 56, 49, 54, 53, 54, 48, 47, 51 and 46. The more sets of 100 tosses you do the closer you will get to an average of 50, the number predicted by the theory. These variations in results are not due to any problem with the coin tossing but are a product of the statistical nature of coin tossing.
In a similar way, if you were to count a radioactive sample several times you would obtain a range of different results. The variation in counts occurs because of the statistical nature of the behaviour of radiation, not because the counter is not working correctly. Table 4 contains a set of counting data for a radioactive sample that was counted 240 times. The first row contains the number of counts in a given time interval. The second row contains the number of times each result was obtained, i.e. the frequency of the count.
Table 4
Sample Counting Data
Counts | 52 | 60 | 73 | 78 | 82 | 92 | 98 | 108 | 121 | 147 |
Count Frequency | 3 | 10 | 21 | 30 | 39 | 41 | 38 | 28 | 20 | 10 |
If the data are plotted on a graph, the overall outcome will look like Figure 15 below.
Figure 15
Graph of Sample Counting Data
This curve is called a Gaussian or Normal Distribution curve. (You may also have heard the terms ‘binomial distribution’ or ‘Poisson distribution’. For radioactivity measurements, these forms of distribution can all be considered to be the same provided that counts are above about 30.) The shape of the curve indicates the statistical nature of radioactive decay. The highest point on the curve gives the value of the most probable count, in this case 92. The width of the curve gives the range of values over which the measured count could vary and is a measure of the error in the counts. You can work out the sample average (or mean) count by summing all the counts and dividing by the number of times the count was performed as shown in Equation 1:
= [1]
where is the mean count of the sample
n is the sum of the counts (Note that is a sign meaning sum of..)
N is the number of times the count was performed
So, for the data given above:
n = (52 x 3) + (60 x 10) + (73 x 21) + (78 x 30)+ (82 x 39) + (92 x 41) + (98 x 38) + (108 x 28) + (121 x 20) + (147 x 10) = 22 237
N = 240
Hence
= = 92.65
Since part of a count cannot exist, the mean count of the sample is given as 93.
In a true normal distribution the average or mean value is the same as the most likely value.
Standard deviation is a way of assessing the uncertainty of a value by quantifying the width of a distribution curve such as that shown in Figure 15. The smaller the standard deviation the narrower the curve will be (i.e. the data are more closely grouped). If the data cover a wide range of numbers then the curve will be wide and the standard deviation is large. This is illustrated in Figure 16. (The symbol for standard deviation is, the Greek letter sigma.) A small standard deviation means that both the data and the calculated mean value of the data are more certain.
Figure 16
Distributions
The area under the normal distribution curve can be divided into segments of equal width on either side of the peak of the curve. These segments are called standard deviations. They measure how much the data deviate from the mean value. The size of the segments are chosen so that plus or minus one standard deviation (written as ± covers 68.26% of the data, ± 2covers 95.46% of the data and ± 3 covers 99.74% of the data. This is shown in Figure 17.
Figure 17
Normal Distribution and Standard Deviations
Note that confidence levels are usually rounded to the nearest 1%. Thus ± 1covers 68% of the data and ± 2covers 95% of the data.
Whenever only a single measurement of count (nsc) is taken from a radioactive sample, this count is considered as being the mean result (i.e. = nsc). The standard deviation of the sample is taken to be the square root of the count as follows:
where scis the standard deviation of a single measurement of count
nsc is the number of counts
Example 1 shows how standard deviation for a single measurement of count may be calculated in practice.
Example 1
Question
A radioactive sample was counted and found to have a count of 566 counts. What is the standard deviation of the count?
Answer
From Equation 2:
sc = = = 24 (to two significant figures (2 sf))
Hence, the standard deviation in the count is 24 counts (to 2 sf).
When we determine the count from a radioactive sample, we need to take into consideration the naturally occurring background count (this is further explained in Module 1.3 Ionizing Radiation and Radioactive Decay.). Hence, when determining the net standard deviation, we need to consider the standard deviation for both the background count and the sample count. To do this, we first need to determine the standard deviation associated with each and then we need to determine the cumulative standard deviation. This is determined as follows:
scnet =
wheresc = = standard deviation in the single count
b = = standard deviation in the background count
Hence
scnet = [3]
wherescnet is the net standard deviation in the count (i.e. the single count corrected for background)
nsc is the number of counts from the sample
nb is the number of background counts
Example 2 shows how the net standard deviation for a single measurement of count (corrected for background) may be calculated in practice.
Example 2
Question
A radioactive sample was counted and found to have a count of 566 counts. A background count was measured at 20 counts. What is the standard deviation of the count corrected for background?
Answer
nsc = 566
nb = 20
From Equation 3:
scnet = = = 24 counts (to 2 sf)
Hence, the standard deviation in the count (corrected for background) is 24 counts (to 2 sf).
Note that the standard deviation from Example 1 is equal to that of Example 2 (to 2 sf). This is because the background count is very low in comparison to the sample count. Hence, for counts where the background count is much lower than the sample count, the contribution to the standard deviation is negligible and may be ignored and we can calculate the standard deviation for a sample by using Equation 2 above.
Section 9.3.1. shows how to work out the sample standard deviation for a single measurement of count but this is not applicable for a single measurement of count rate (i.e. sc = only applies to total counts, not to count rate). This is because, when considering count rate, we also need to take into account the time. Hence, if a single measurement is made of count rate, the standard deviation of the sample is given as follows:
wherescris the standard deviation of a single count rate measurement
R is the measurement rate
t is the measurement time
Example 3 shows how the standard deviation for a single measurement of count rate may be calculated in practice.
Example 3
Question
A sample is counted for five minutes and showed a count of 7 280 counts. What is the standard deviation of this count rate?
Answer
R = = 1 456 counts per minute (cpm)
T = 5 minutes
From Equation 4:
Hence, the standard deviation in the count rate is 17 cpm (to 2 sf).
Again, when determining the count rate from a radioactive sample, we should take into consideration the naturally occurring background count rate. Hence, when determining the net standard deviation, we need to consider the standard deviation for both the background count rate and the sample count rate. To do this, we first need to determine the standard deviation associated with each and then we need to determine the cumulative standard deviation. This is determined as follows:
scrnet = [5]
wherescr = = standard deviation in the single measurement of count rate
b = = standard deviation in the background measurement rate
scrnet = the standard deviation of the single measurement of count rate corrected for background
Example 4 shows how the net standard deviation for a single measurement of count rate (corrected for background) may be calculated in practice.
Example 4
Question
A sample was counted for 5 minutes and had a count of 7 280 counts. Background on this counter was measured at 32 cpm with a counting time of 30 minutes. What is the net standard deviation for this sample?
Answer
Rscr = 7 280 = 1456 cpm
5
Rb = 32 cpm
scr = = = 17 cpm (to 2 sf)
b = = = 1 cpm (to 1 sf)
From Equation 5:
scrnet === 17 cpm (to 1 sf)
Hence the standard deviation (corrected for background) is 17 cpm (to 2 sf).
Again, by comparing Examples 3 and 4, it can be seen that the contribution to the net standard deviation from the background count rate is very small in comparison to that from the sample count rate. Hence, for most count rate measurements (except for very low count rates) the background standard deviation may be ignored and we can calculate the standard deviation for a sample by using Equation 4 above.
Data are much more likely to be good data if a series of single measurements are taken where possible. For example, it is more accurate to take five readings of count and average them than to take just one reading (note that all of the measurements must be taken under the same conditions to be valid). In this case, the mean is taken as being the sum of the five readings of count divided by the number of counts (see Equation 1) and hence, calculation of the standard deviation becomes more complex (see Equation 6):
[6]
where is the standard deviation for a series of measurements of count
is the mean of the counts
n is the value of the single measurement of count
N is the total number of measurements performed
Example 4 shows how this is applied to a set of data.
Example 5
Question
The results of ten counts on the same sample are given below. Find the standard deviation of the counts.
Sample | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Result (n) | 10 | 9 | 7 | 10 | 9 | 12 | 7 | 10 | 12 | 10 |
Answer
Step 1First calculate the average value of n () by adding up all the results and dividing by the number of results (10).
= = = 9.6
Step 2Calculate the difference between each result and the average value (n - ).
Step 3Square the values obtained in step 2 to remove negative values ((n - )2).
The values obtained in steps 2 and 3 are shown below.
n | 10 | 9 | 7 | 10 | 9 | 12 | 7 | 10 | 12 | 10 |
n - | 0.4 | -0.6 | -2.6 | 0.4 | -0.6 | 2.4 | -2.6 | 0.4 | 2.4 | 0.4 |
(n - )2 | 0.16 | 0.36 | 6.76 | 0.16 | 0.36 | 5.76 | 6.76 | 0.16 | 5.76 | 0.16 |
Step 4Sum all the values of (n - )2.
(n - )2= 26.4
Step 5The number of measurements (N) is equal to 10. Divide the value obtained in step 4 by N - 1.
Step 6Take the square root of the value obtained in step 5.
counts
The standard deviation of the counts is 1.7 counts.
When taking measurements from radioactive materials, it is important to be aware of the possible error in your measurement. We do this by quoting our measurements to a particular confidence level which is based on different numbers of standard deviations. For example, if we quote our measurements to within one standard deviation, we have confidence that our measurements will fall within this range 68% of the time. Hence, this range is known as the 68%(or 1 confidence level. This 68% confidence level is also known as the standard error of the mean as it is the error associated with one standard deviation.
Confidence levels can be quoted at different levels andTable 5 summarises the number of standard deviations equivalent to commonly used confidence levels.
Table 5
Confidence Levels
Confidence Level
(%)
Number of Standard Deviations
50
0.7
68
1.0
90
1.6
95
2.0
Hence, the answers to Examples 1and 2 can be quoted as 566 24 counts (at the 68% or 1 confidence level) or 566 48 (at the 95% or 2 confidence level). Likewise, the answers to Examples 3 and 4 can be written as 7280 17 counts per minute (at the 68% or 1 confidence level) or 7280 34 counts per minute (at the 95% or 2 confidence level).
If more than one measurement is taken (as in Example 5), the value of the standard error will be reduced as the more measurements taken give a result closer to the true mean. In this case, the standard error (i.e. at the 68% or 1 confidence level) is given by
E = [7]
whereE is the standard error
is the standard deviation of the multiple measurements
N is the number of measurements performed
and the error at the 95% confidence level is taken as twice this value.
Hence, for Example 5, the standard error is given by:
E == 0.5 counts
This can therefore be quoted as 9.6 0.5 counts (at the 68% or 1 confidence level) or 9.6 1 count (at the 95% or 2 confidence level).
Note that the error in counting data is normally quoted at the 95% (or 2) confidence level. This means that only 5% of the measured data would be expected to be outside this range and is thus considered as acceptable accuracy.
Error bars should be shown on graphs to indicate the accuracy of the data points. The size of the error bar is dependent on the value of the standard deviation. The error may be given as plus or minus one standard deviation (the standard error) or quoted to a specific confidence level, normally 95% for counting data. It is normal procedure to assume that the error in time measurements is negligible compared with the error in the counting data. Figure 18 shows how the error bars for a count of 100 would appear on a graph.
Figure 18
Plotting Error Bars
Remember that the standard deviation for a single count of 100 is found by taking the square root of the number (sc= √100 = 10). Now look at Table 5 to find out how many standard deviations are equivalent to the 95% confidence level.
The error at the 95% confidence level is equal to two standard deviations, i.e. ± 20. Line A shows the error bar plotted at the 95% confidence level. The standard error is plus or minus one standard deviation (± 10 in this example). Line B shows the error bar plotted for standard error.
32.SELF-CHECK 9
Now see how much you have understood by answering the following questions in your workbook:
What percentage of measured data would you expect to find within the following ranges:
a)1
b)2
Assume that you have measured the count from a radioactive sample and have a result of 64 counts. What is the result quoted to:
a)the 95% confidence level (number ± the variation)?
b)the 90% confidence level (number ± the variation)?
The following set of measurements have been obtained: 65, 68, 64, 59, 68, 61, 59, 64, 64, 62. Find the mean and give the error at the 95% confidence level.
Now check your answers with the model answers in your workbook.
33.KEY POINTS
ROUNDING
When rounding whole numbers or decimals of 5,6,7,8,9 the next size unit (tenths, units, tens, etc) is increased by 1. For example 0.5 becomes 1; 107 becomes 110.
When rounding whole numbers or decimals of 1,2,3,4, the next size unit (tenths, units, tens, etc) remains the same. For example 0.4 becomes 0; 103 becomes 100.
ALGEBRA
Algebra is a way of calculating unknown values by constructing equations where we substitute letters for the ‘unknown’ and combine these with the known values, e.g. Y = b + 2.
When solving an equation, remember that the two sides of an equation must balance.
When manipulating an equation, remember what you do to one side you must do to the other.
POWERS
cb is the same as writing the base c raised to the power b, or c multiplied by itself b times.
b2 is the same as b x b. In this case we say the b is squared.
b3 is the same as b x b x b. In this case we say the b is cubed.
b-2 is the same as writing 1
b2
b-3 is the same as writing 1
b3
b1/2 is the square root, also written as √b.
b1/3 is the cube root, also written as 3√b.
LOGARITHMS
Logs are used to convert numbers into powers of a particular base.
Multiplication and division of numbers raised to a power is carried out by addition and subtraction of the powers. As logs convert numbers to powers, the multiplication or division of any number can be carried out by simple addition or subtraction.
There are 5 rules of logs which you should remember.
Logs to the base 10 are called common logs and logs to the base e are called natural logs.
It is often necessary to convert log values back into numbers. This is known as taking the antilogarithm(or antilog) of a log value.
The exponential function (ex) can be found in the same way as finding the antilog of a natural log.
To convert ex to an ordinary number you must take the natural log of it.
GRAPHS
Graphs are a way of showing information as a picture. In many cases this makes that information easier to understand. Graphs are also useful to show the variation in one value as another value changes.
A graph is plotted, with a vertical line (y-axis) and a horizontal line (x-axis). These axes represent the two types of value we wish to plot.
Log graphs do not have a value of 0. You should therefore remember that when you read a log graph, the cycles scales start at 1.0 and goes to 10 of the power you are using.
PROBABILITY
If only one measurement of count is made, the standard deviation is taken as the square root of the count:
sc =
If only one measurement of count rate is made, the standard deviation is taken as:
scr =
The standard deviation of single measurements of count or count rate can be corrected for background. However, if the count from the radioactive source is much larger than that from background, the contribution to the standard deviation from background may be ignored.
If a series of single measurements of count are made, the standard deviation is given by the following equation:
The standard error for a single measurement of count or count rate may be taken as 1.
The standard error for a series of single measurements of count or count rate may be taken as . The error at the 95% confidence level is taken as twice this value.
The error in counting data is usually quoted to the 95% confidence level.
34.FINAL ASSIGNMENT
35.APPENDIX A
How To Find The Common Log Of A Number Using Log Tables
A log number consists of two parts; the number before the decimal point, called the characteristic, and the number after the decimal point, called the mantissa. Example 1 shows you how to find the log of a number using the common log tables. Work through the example and then try the sample questions yourself.
Example 1
Question
Find the common log of the number 123.4 (log 123.4) by using the common log tables given on page 79.
Answer
Step 1 | Write the number in scientific notation. 123.4 = 1.234 x 102 |
Step 2 | The power of ten becomes the characteristic. The power of ten is 2 so the characteristic is 2 |
Step 3 | By using log tables and following the method below, find the number 1.234 and hence the mantissa: In the log tables, the figures in the left hand column are the whole number and the first decimal place (0.0). The figures in the top row are the second decimal (0.00). In the left hand column find 1.2; then move along the row of numbers to the column under 3. This is the mantissa of 1.23 and equals 0.0899. Now look at the column under 1.24 and find the mantissa. You will see the number 0.0934. We need the log of 1.234, somewhere between the logs of 1.23 and 1.24. We can therefore estimate the mantissa of 1.234 as approximately 0.0915. |
Step 4 | To find the log of 123.4, combine the characteristic and the mantissa. Hence the log of 123.4 is 2.0915 or log 123.4 = 2.0915 |
NOTE | The mantissa given in log tables is always a positive value and does not depend on the location of the decimal point in the original number. This means that the numbers 0.01234, 0.1234, 1.234, 12.34 etc. will all have the same mantissa. However, the characteristic for a number less than one will be negative. Therefore the log of a number less than one will consist of a negative characteristic and a positive mantissa, eg the log of 0.1234 has a characteristic of -1 and a mantissa of 0.0915. The log is written with a bar across the top of the characteristic, eg .0915. This information is included so that you can understand why logs are written with bars over the characteristic. It does not affect the way you use logs. See how the logs of the following numbers have the same pattern. log 123.4 = 2.0915 log 12.34 = 1.0915 log 1.234 = 0.0915 log 0.1234 = .0915 log 0.01234 = .0915 |
36.SELF-CHECK 10
1.Find the common logs of the following numbers by using the common log tables on page 79:
a)4 567
b)0.4567
2.Find the common logs of the following numbers by using the common log tables in Appendix A:
a)1.09
b)125
c)0.00897
Now check your answers with the model answers in your workbook.
Finding the Number Corresponding to a Log Value Using Log Tables
The number corresponding to a given log value is called the antilogarithm (or antilog for short) and is abbreviated to log-1. In simple terms, to find the original number of a log value, we have to use the log tables backwards.
Example 2 shows how to find the antilog of a number using the common log tables on page 79.
Example 2
Question
Find the common antilog of the log value 2.0915 (log-1 2.0915).
Answer
Step 1 | Separate the characteristic and the mantissa. The characteristic is 2 and mantissa is 0.0915. |
Step 2 | The characteristic becomes the power of ten. The power of ten is 2 (102). |
Step 3 | By using log tables and following the method below, find the number corresponding to the mantissa: Remember that this time we are using the log tables backwards. We need to look in the tables (not in the side column) to find the mantissa. In the table the closest numbers to the mantissa are 0.0899 and 0.0934. Now look up the corresponding numbers in the left column and at the top of the column. This gives a number somewhere between 1.23 and 1.24. We can estimate the number as 1.235. |
Step 4 | To find the original number corresponding to log-1 2.0915, combine the corresponding number (1.235) and the power of ten (102). Hence the antilog of 2.0915 is 1.235 x 102 orlog-1 2.0915 = 1.235 x 102 |
37.SELF-CHECK 11
1.Find the common antilogs (log-1) of the following log values by using the common log tables on page 79:
a)3.657
b).657
2.Find the common antilogs (log-1) of the following log values by using the common log tables on page 79:
a)3.5482
b)1.4114
c).6537
d).1178
Now check your answers with the model answers in your workbook.
As previously mentioned, logs can be used to make calculations simpler. Example 3 shows how multiplication can be performed using logs.
Example 3
Question
Find the answer to the following calculation by using the log tables on page 79.
1350 x 350 = ?
Answer
To find the answer to this calculation, we need to use our rules of logs. We have to consider the calculation in three stages. This calculation uses all the things that we have learnt so far about logarithms. It is therefore important that you understand the previous notes before you try to follow this example.
Stage 1First we need to use our rules of logs to convert the whole calculation to logs.
Step 1 | Applying the rules of logs to the calculation gives the following: log (1350 x 350) = log 1350 + log 350 |
Step 2 | The log tables have numbers from 1.0 to 9.99. To find the logs of the numbers in the calculation, first write the numbers in scientific notation: 1350 = 1.350 x 103 350 = 3.50 x 102 |
Step 3 | Look up 1.350 in the log tables: In the log tables the figures in the left hand column are the whole number and the first decimal place, 0.0. The figures in the top row are the second decimal 0.00. In the left hand column find 1.3, then move along the row of numbers to the column under 5. This is the log of 1.35 and equals 0.1303. This is the mantissa of log 1350. |
Step 4 | Combine the mantissa and the characteristic. Remember that the characteristic is the power of ten, which in this case is 3. log 1350 = 3.1303 |
Step 5 | Now do the same for the number 350. This gives the following: log 350 = 2.5441 |
Stage 2We now have our calculation in log values. By applying the rules of logs, we can do the calculation much more simply by adding rather than by multiplying.
Step 1 | Applying the rules of logs to the calculation gives the following: log (1350 x 350) = log 1350 + log 350 |
Step 2 | Now we can add the two log values together to obtain a log value answer to the calculation: log (1350 x 350) = 3.1303 + 2.5411 = 5.6744 |
Stage 3Now we have the log value answer to our calculation. To find the ordinary number answer, we need to convert our log value back to an ordinary number. To do this we need to find the antilogarithm (log-1) of the log value (5.6744) That is, we need to find log-1 5.6744.
Step 1 | Separate the characteristic and the mantissa. The characteristic is 5 and the mantissa is 0.6744 |
Step 2 | The characteristic becomes the power of ten. The power of ten is 5 (105). |
Step 3 | Look up the log value in the log tables to find the number corresponding to the mantissa: Remember that this time we are using the log tables backwards. We need to look in the tables (not in the side column) to find the mantissa. In the table the closest numbers to the mantissa are 0.6739 and 0.6749. Now look up the corresponding numbers in the left column and at the top of the column. This gives a number somewhere between 4.72 and 4.73. We can estimate the number as corresponding to 4.725. |
Step 4 | To find the original number corresponding to log-1 5.6744, combine the corresponding number (4.725) and the power of ten (105). Hence the antilog of 5.6744 is orlog-1 5.6744 = 4.725 x 105 |
Step 5 | We have now converted our antilog back to an original number and hence we now have a solution to our original multiplication question: 1350 x 350 = 4.725 x 105 |
Logs can also be used to perform division. Example 4 below shows how to do this.
Example 4
Question
Find the answer to the following calculation by using the log tables given in Appendix A.
0.175 ÷ 345 = ?
Answer
As in the previous example, we proceed in three stages.
Stage 1First we need use to our rules of logs to convert the whole calculation to logs.
Step 1 | Applying the rules of logs to the calculation gives the following: log (0.175 345) = log 0.175 - log 345 |
Step 2 | The log tables have numbers from 1.0 to 9.99. To find the logs of the numbers in the calculation, first write the numbers in scientific notation, as follows: 0.175 = 1.75 x 10-1 345 = 3.45 x 102 |
Step 3 | Look up 1.75 in the log tables: In the log tables the figures in the left hand column are the whole number and the first decimal place, 0.0. The figures in the top row are the second decimal 0.00. In the left hand column find 1.7, then move along the row of numbers to the column under 5.This is the log of 1.75 and equals 0.2430. This is the mantissa of log 0.175. |
Step 4 | Combine the mantissa and the characteristic. Remember that the characteristic is the power of ten, which in this case is -1. log 0.175 = .2430 |
Step 5 | Now do the same for the number 345. This gives the following: log 345 = 2.5378 |
Stage 2We now have our calculation in log values. By applying the rules of logs, we can do the calculation much more simply by subtracting rather than by dividing.
Step 1 | Applying the rules of logs to the calculation gives the following: log (0.175 345) = log 0.175 - log 345 |
Step 2 | Now we can subtract the two log values to obtain a log value answer to the calculation: log 0.175 - log 345 = .2430 - 2.5378 = .7052 |
Stage 3Now we have the log value answer to our calculation. To find the ordinary number answer, we need to convert our log value back to an ordinary number. To do this we need to find the antilogarithm (log-1) of the log value (.7052) That is, we need to find log -1.7052.
Step 1 | Separate the characteristic and the mantissa. The characteristic is and the mantissa is 0.7052. |
Step 2 | The characteristic becomes the power of ten. The power of ten is -4 (10-4). |
Step 3 | Look up the log value in the log tables to find the number corresponding to the mantissa: Remember that this time we are using the log tables backwards. We need to look in the tables (not in the side column) to find the mantissa. In the table the closest numbers to the mantissa are 0.7050 and 0.7059. Now look up the corresponding numbers in the left column and at the top of the column. This gives a number somewhere between 5.07 and 5.08. We can estimate the number as corresponding to 5.072. |
Step 4 | To find the original number corresponding to log-1 .7052, combine the corresponding number (.7052) and the power of ten (10-4). Hence the antilog of .7052 is 5.072 x 10-4 orlog-1 .7052 = 5.072 x 10-4 |
Step 5 | We have now converted our antilog back to an original number and hence we now have a solution to our original multiplication question: 0.175 ÷ 345 = 5.072 x 10-4 |
38.SELF-CHECK 12
Now see how much you have understood by answering the following questions in your workbook:
1.Find the answers to the following calculations by using the common log tables on page 79:
a)679 x 345 = ?
b)9 876 x 1 234 = ?
2.Find the answers to the following calculations:
a)0.0257 ÷ 2.56 = ?
b)0.0012 ÷ 4.79 = ?
Now check your answers with the model answers in your workbook.
TABLE OF COMMON LOGARITHMS
39.APPENDIX B
NATURAL (NAPIERIAN) LOGARITHMS
Natural log tables can be used for the following purposes:
To find the natural log of a number.
To find the value of ex.
Using natural log tables for numbers less than 10
The natural log for numbers from 1.0 to 9.99 may be obtained from the natural log tables (see Table 6).
Example 1
Question
Find the natural log (ln) of 3.85 by using the natural log tables.
Answer
The natural log of 3.85 can be read directly from the table:
ln 3.85 = 1.3481
Natural Log Tables for numbers greater than 10
For numbers greater than 9.99 the values of natural logs for 10, 100, 1 000, etc. are required. These are given on page 86 for powers of ten up to 109.
Example 2
Question
Find the natural log of 38.5 by using the natural log tables.
Answer
The natural log of 38.5 is found by writing 38.5 in scientific notation and using the rules of logs, thus:
38.5 = 3.85 x 10
ln 38.5 = ln (3.85 x 10) = ln 3.85 + ln 10
ln 38.5 = 1.3481 + 2.3026 = 3.6507
ln 38.5 = 3.6507
When finding the value of ex , it is important to consider whether the value of x is a positive (+) or a negative (-) number. This is because different methods are used for evaluating positive and negative values of x. The size of x is also important in evaluating ex .The following sections show the methods to be used for evaluating different values of x.
Natural log tables are used ‘backwards’ to find positive values of ex . We do this in the same way as we find antilogs in the common log system.
Example 3
Question
Find the value of e0.7031 by using the natural log tables.
Answer
The term, e 0.7031, can be evaluated by finding 0.7031 in the table (not in the side columns) of the natural log tables. You will find it in the row for 2.0 under the column for 2.
e0.7031 = 2.02
Notice that if the number is not in the table you will have to find the closest number and make an approximation as you did with common logs.
Natural log tables can be used to find values of ex for x values between 0.0000 and 2.3026 by reading directly from the tables. For values greater than 2.3026 the natural log for an appropriate power of ten must be subtracted to bring the number into the range 0.0000 to 2.3026.
Question
Find the value of e8.2341 by using the natural log tables given in Appendix B.
Answer
The term e8.2341 is outside the range of the natural logs table. It can be evaluated using the following method:
Step 1 | The maximum value in the table is 2.3026. The number 8.2341 is outside this value by 5.9315 (8.2341 - 2.3026). |
Step 2 | To bring 8.2341 back into the range of the table, a number greater than 5.9315 (but less than 8.2341 so that it doesn’t go negative) must be subtracted. Look at the natural logs for powers of ten and find the value which meets these conditions. In this case it is 6.9078 which is ln 103 (to four decimal places). 8.2341 - 6.9078 = 1.3263 8.2341 = 6.9078 + 1.3263 8.2341 = ln 103 + ln 3.768 |
Step 3 | Using the rule of logs this becomes 8.2341 = ln (3.768 x 103) |
Step 4 | This is of the form ln y = x, where y = ex. Therefore e8.2341 = 3.768 x 103 |
There will be many cases where your answers to radiation calculations will be in the form of e-x. To calculate ex for negative values of x, you use a similar method to that used for calculating large numbers.
Since ln 10-1 = - ln 10 (applying the rules of logs), the natural logs of the negative powers of ten are the same as for the positive powers of ten but with a negative sign in front. This is demonstrated in Example 6:
Question
Find the value of e-0.6 by using the natural log tables given in Appendix B.
Answer
Step 1 | Find the number corresponding to the log of a power of ten which when added to -0.6 will produce a positive number between 0 and 2.3026. -0.6 + 2.3026 = 1.7026 -0.6 = 1.7026 - 2.3026 |
Step 2 | Look up 1.7026 in the natural log tables. This corresponds to approximately 5.489. Also from the log tables, 2.3026 corresponds to 10 (or 101). |
Step 3 | From above: -0.6 = ln 5.489 - ln 101 |
Step 4 | Using the rule of logs nlogb m = logb (mn) ln 101 = ln 10-1. Therefore: -0.6 = ln 5.489 + ln 10-1 |
Step 5 | Again using the rule of logs logb (mn) = logb m + logb n -0.6 = ln (5.489 x 10-1) |
Step 6 | From Section 6.3,ln a = x is the same as a = ex. Therefore: e-0.6 = 5.489 x 10-1 |
40.SELF CHECK 13
Now see how much you have understood by answering the following question in your workbook:
1.Find the natural log values (ln) for the following numbers by using the natural log tables.
4.65
46.5
465
Find the value of e 10.3562 by using the natural log tables.
Find the natural log of 56 (ln 56) by using the natural log tables.
4.Find the value of e1.335 by using the natural log tables.
5.Find the value of e-5.5 by using the natural log tables.
Now check your answers with the model answers in your workbook.
NATURAL LOG TABLES
The natural logarithm of a number is the exponent of the power to which the base e (2.7182818) must be raised in order to equal the number.
Example:loge 4.12 = ln 4.12 = 1.4159
The table gives the natural logarithms of numbers from 1.00 to 9.99 directly, and permits finding logarithms of numbers outside that range by the addition or subtraction of the natural logarithms of powers of 10.
Example:ln 679 = ln 6.79 + ln 102 = 1.9155 + 4.6052 = 6.5207
ln 0.0679 = ln 6.79 - ln 102 = 1.9155 - 4.6052 = -2.6897
Natural Logarithms of 10k
ln 10 = 2.302585ln 104 = 9.210340ln 107 = 16.118096
ln 102 = 4.605170ln 105 = 11.512925ln 108 = 18.420681
ln 103 = 6.907755ln 106 = 13.815511ln 109 = 20 723266
To obtain the common logarithm, the natural logarithm is multiplied by log10 e, which is 0.434294 or log10 N = 0.434294 ln N.
Table 6 NATURAL LOG TABLES
N | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
7.2 | 1.9741 | 1.9755 | 1.9769 | 1.9782 | 1.9796 | 1.9810 | 1.9824 | 1.9838 | 1.9851 | 1.9865 |
7.3 | 1.9879 | 1.9892 | 1.9906 | 1.9920 | 1.9933 | 1.9947 | 1.9961 | 1.9974 | 1.9988 | 2.0001 |
7.4 | 2.0015 | 2.0028 | 2.0042 | 2.0055 | 2.0069 | 2.0082 | 2.0096 | 2.0109 | 2.0122 | 2.0136 |
7.5 | 2.0149 | 2.0162 | 2.0176 | 2.0189 | 2.0202 | 2.0215 | 2.0229 | 2.0242 | 2.0255 | 2.0268 |
7.6 | 2.0281 | 2.0295 | 2.0308 | 2.0321 | 2.0334 | 2.0347 | 2.0360 | 2.0373 | 2.0386 | 2.0399 |
7.7 | 2.0412 | 2.0425 | 2.0438 | 2.0451 | 2.0464 | 2.0477 | 2.0490 | 2.0503 | 2.0516 | 2.0528 |
7.8 | 2.0541 | 2.0554 | 2.0567 | 2.0580 | 2.0592 | 2.0605 | 2.0618 | 2.0631 | 2.0643 | 2.0656 |
7.9 | 2.0669 | 2.0681 | 2.0694 | 2.0707 | 2.0719 | 2.0732 | 2.0744 | 2.0757 | 2.0769 | 2.0782 |
8.0 | 2.0794 | 2.0807 | 2.0819 | 2.0832 | 2.0844 | 2.0857 | 2.0869 | 2.0882 | 2.0894 | 2.0906 |
8.1 | 2.0919 | 2.0931 | 2.0943 | 2.0956 | 2.0968 | 2.0980 | 2.0992 | 2.1005 | 2.1017 | 2.1029 |
8.2 | 2.1041 | 2.1054 | 2.1066 | 2.1078 | 2.1090 | 2.1102 | 2.1114 | 2.1126 | 2.1138 | 2.1150 |
8.3 | 2.1163 | 2.1175 | 2.1187 | 2.1199 | 2.1211 | 2.1223 | 2.1235 | 2.1247 | 2.1258 | 2.1270 |
8.4 | 2.1282 | 2.1294 | 2.1306 | 2.1318 | 2.1330 | 2.1342 | 2.1353 | 2.1365 | 2.1377 | 2.1389 |
8.5 | 2.1401 | 2.1412 | 2.1424 | 2.1436 | 2.1448 | 2.1459 | 2.1471 | 2.1483 | 2.1494 | 2.1506 |
8.6 | 2.1518 | 2.1529 | 2.1541 | 2.1552 | 2.1564 | 2.1576 | 2.1587 | 2.1599 | 2.1610 | 2.1622 |
8.7 | 2.1633 | 2.1645 | 2.1656 | 2.1668 | 2.1679 | 2.1691 | 2.1702 | 2.1713 | 2.1725 | 2.1736 |
8.8 | 2.1748 | 2.1759 | 2.1770 | 2.1782 | 2.1793 | 2.1804 | 2.1815 | 2.1827 | 2.1838 | 2.1849 |
8.9 | 2.1861 | 2.1872 | 2.1883 | 2.1894 | 2.1905 | 2.1917 | 2.1928 | 2.1939 | 2.1950 | 2.1961 |
9.0 | 2.1972 | 2.1983 | 2.1994 | 2.2006 | 2.2017 | 2.2028 | 2.2039 | 2.2050 | 2.2061 | 2.2072 |
9.1 | 2.2083 | 2.2094 | 2.2105 | 2.2116 | 2.2127 | 2.2138 | 2.2148 | 2.2159 | 2.2170 | 2.2181 |
9.2 | 2.2192 | 2.2203 | 2.2214 | 2.2225 | 2.2235 | 2.2246 | 2.2257 | 2.2268 | 2.2279 | 2.2289 |
9.3 | 2.2300 | 2.2311 | 2.2322 | 2.2332 | 2.2343 | 2.2354 | 2.2364 | 2.2375 | 2.2386 | 2.2396 |
9.4 | 2.2407 | 2.2418 | 2.2428 | 2.2439 | 2.2450 | 2.2460 | 2.2471 | 2.2481 | 2.2492 | 2.2502 |
9.5 | 2.2513 | 2.2523 | 2.2534 | 2.2544 | 2.2555 | 2.2565 | 2.2576 | 2.2586 | 2.2597 | 2.2607 |
9.6 | 2.2618 | 2.2628 | 2.2638 | 2.2649 | 2.2659 | 2.2670 | 2.2680 | 2.2690 | 2.2701 | 2.2711 |
9.7 | 2.2721 | 2.2732 | 2.2742 | 2.2752 | 2.2762 | 2.2773 | 2.2783 | 2.2793 | 2.2803 | 2.2814 |
9.8 | 2.2824 | 2.2834 | 2.2844 | 2.2854 | 2.2865 | 2.2875 | 2.2885 | 2.2895 | 2.2905 | 2.2915 |
9.9 | 2.2925 | 2.2935 | 2.2946 | 2.2956 | 2.2966 | 2.2976 | 2.2986 | 2.2996 | 2.3006 | 2.3016 |
41.GLOSSARY OF TERMS
Antilogarithm | The number corresponding to a given log value. It is often written as log-1. |
Axis (pl. axes) | A graph has two axes, an x-axis and a y-axis. The axes show the scale for measured data points. |
Base | The starting number for a system of numeration. |
Characteristic | The part of a log number before the decimal place. |
Common logarithm | Logarithms to the base 10. It is often written as log. |
Cubed | A number multiplied by itself three times. |
Cycle | Large section of a log scale graph covering one power of 10. |
Decimal | Numerical system based on the number 10. |
Denominator | The number below the line of a fraction. |
Digit | A single number (e.g. the number 1234 contains four digits). |
e | A number approximately equal to 2.718. |
Equation | A mathematical sentence that relates two or more quantities. |
Error Bar | Lines plotted on a graph to show the possible errors in a measured data point. |
Exponent | The exponent of a number is the number of times it is multiplied by itself. (See index and power.) |
Exponential function | The exponential function ex is a useful mathematical function for describing radioactive decay. |
Extrapolation | A way of obtaining information for points on a graph beyond the measured data points. |
Frequency | The number of times a particular event occurs. |
Graph | A way of using diagrams to show mathematical relationships. |
Index (pl. indices) | The index of a number is the number of times it is multiplied by itself. (See exponent and power.) |
Integration | A mathematical process used to find the area under the line or curve on a graph. |
Interpolation | The information obtained from points on a graph between measured data points. |
Level of confidence | The degree of certainty that a particular event will occur. It is usually written as a percentage. |
Line of best fit | A line or curve on a graph that fits the measured data points (including the error bars) in the best possible way. |
Linear scale | A scale of a graph which is divided into equal divisions corresponding to equal number ranges. |
Logarithm | The power to which a base must be raised to produce the number. |
Logarithmic scale | A scale of a graph which is divided into equal sections corresponding to 100, 101, 102 etc. Each division covers a different number range. |
Mantissa | The part of a log number after the decimal place. |
Mean | The average of a group of numbers. This is sometimes known as the arithmetic mean. |
Natural logarithm | Logarithm to the base e. This is often written as ln. |
Numerator | The number above the line of a fraction. |
Power | The power of a number is the number of times it is multiplied by itself. (See exponent and index.) |
Probability | A number between 0 and 1 which quantifies the chance of an event occurring. |
Reciprocal | The reciprocal of the number x is one divided by x, which is written as 1/x or x-1. |
Rounding | A way of restricting the number of digits included in the recorded number. |
Scientific notation | A way of writing numbers, especially very large or very small numbers, using powers to the base 10. |
Significant figures | The number of important digits that should be shown in a number. |
Squared | A number multiplied by itself. |
Standard deviation | A measure of the expected deviation from a particular measurement. |
INTERNATIONAL ATOMIC ENERGY AGENCY AUSTRALIAN NUCLEAR SCIENCE AND TECHNOLOGY ORGANISATION |
DISTANCE LEARNING MATERIALS
RADIATION PROTECTION
Module – 1.3
Prepared by Safety and Radiation Science
Australian Nuclear Science and Technology Organisation
With the assistance of consultants in Australia and the United Kingdom, and IAEA experts from Korea, Mongolia, New Zealand, the Philippines and Thailand
Use of this material, acknowledging the IAEA and ANSTO as the source, is permitted for non-profit training
Acknowledgements
This material has been prepared by an extensive team of international experts from the fields of radiation protection, medicine and education. It is not possible to mention by name all those who have had an input to; the initial planning; writing modules and workbooks; preparing and marking final assignments; proof-reading and editing; using the material and providing valuable feedback; organizing and hosting review meetings; and general administrative support.
The support of ANSTO management in providing the resource and encouragement is gratefully acknowledged.
The enthusiastic support of IAEA Technical Officers has been vital to the success of this project
PART 1
BASIC KNOWLEDGE
MODULE 1.3
IONIZING RADIATION AND RADIOACTIVE DECAY
CONTENTS
42.OVERVIEW
As you study this module you will learn about the different kinds of ionizing radiation, how and why atoms undergo radioactive decay, and where radiation comes from. A knowledge of how radioactive decay occurs and the properties of the radiation emitted is essential for you to understand the radiation sources you may encounter in your workplace and the risks associated with them. The information in this module will provide you with the tools you will need for later learning modules and also in your day to day health physics tasks.
There are practical activities associated with this module. You will find the information in your workbook. If the equipment is available, you should arrange a suitable time for doing practical work with your supervisor. If suitable equipment is not available, you may have to wait until a workshop is held.
Although you may already be familiar with some of the information in this module, it is important that you complete the self-check questions at the end of each section successfully before continuing.
43.
TIME ALLOCATION
It is estimated that you will need to spend six to eight hours to complete this module before commencing the assignment. The estimated time is for your guidance only. Do not worry if you need more time to understand the module. Laboratory work is not included in this time estimate. Remember that you must have completed the practical work satisfactorily before receiving credit for this module.
44.MATERIALS
During the early 1900’s, it was found that some naturally occurring substances undergo a spontaneous change in their structure to make them more stable. Such substances are known as radioactive and radioactive decay is defined as the change that takes place in the nucleus of an atom to make it more stable.
The structure of the nucleus of a nuclide determines whether or not it will be radioactive. A nucleus is stable for certain configurations of protons and neutrons and unstable for others. This is similar to the dependence of the atom’s chemical stability on the arrangement of the orbital electrons. If a nucleus does not have a stable arrangement, it will decay and form a more stable nuclide.
The process of radioactive decay results in the emission of charged particles and rays. The most common emissions are alpha particles, beta particles and gammarays. Other possible emissions include positrons, x-rays, and very rarely neutrons.
The particles and rays emitted from radioactive decay possess enough energy to remove electrons from material through which they pass. In other words, these emissions are classed as ionizing radiation (where ionizing radiation is defined as any particle or ray which has sufficient energy to remove electrons from atoms, molecules or ions). Although the major source of ionizing radiation is from radioactive decay of radionuclides, there are other sources and these alternative sources are discussed in detail in Section 5 of this module.
Note that the effects of ionizing radiation from any source are of particular concern in the human body where it can interact with biological cells and may cause damage to tissues and organs.
The energy of ionizing radiation is measured in electronvolts (eV) which is a very small unit of energy, even in atomic terms. One electronvolt is the amount of energy gained by an electron accelerating across a potential difference of one volt and is mathematically equivalent to 1.6 x 10-19 joules. In practice, the energy of ionizing radiation is usually given in multiples of electronvolts such as kiloelectronvolts (keV or 103 eV) or megaelectronvolts (MeV or 106 eV).
As already mentioned, the most common emissions resulting from radioactive decay are alpha particles, beta particles and gammarays. Other possible emissions include positrons, x-rays, and very rarely neutrons.
Alpha particles consist of two protons and two neutrons tightly bound together. This may be thought of as a helium nucleus (He) with an atomic mass of 4u and a charge of +2e. Alpha particles are denoted by the symbol , the Greek lower case letter for ‘A’.
Beta particles are basically electrons which have been ejected from the nucleus of radionuclides. They are produced when a neutron in the nucleus changes into a proton and an electron. The proton remains in the nucleus and the electron is emitted as a beta particle. Like electrons, beta particles have small mass (approximately 1/1840 u) and a single negative charge (i.e. a charge of –1e). They are given the symbol , the Greek lower case letter for ‘B’ but are sometimes written - to indicate the negative charge of the emitted electron.
Gamma rays are electromagnetic radiation which come from the nucleus of an atom. Electromagnetic radiation consists of packets of energy called photons which are transmitted in the form of waves at the speed of light. Gamma rays have no mass and no charge and are given the symbol , the Greek lower case letter for ‘G’.
Positrons come from a proton which has changed into a neutron and a positive electron (a positron). The neutron stays in the nucleus and the positron is ejected at high speed. Positrons are similar to beta particles in most respects but the main difference is that positrons have a positive charge. Hence, positrons are given the symbol +to indicate their similarities and differences to beta particles.
Like gamma rays, x-rays are also electromagnetic radiation with no mass and no charge. However, x-rays differ from gamma rays in that gamma rays are produced by changes in the nucleus of an atom whereas x-rays are produced when atomic electrons undergo a change in orbit. X-rays are usually referred to by name rather than by symbol, but you may see the symbol X used for x-rays.
As you have already learnt in Module 1.1 Structure of Matter, neutrons (symbol n) are particles found in the nucleus of an atom with a mass of 1u and no charge.
Table 1 summarizes the properties of each type of ionizing radiation which may be produced as a result of radioactive decay.
Table 7
Summary Of The Properties Of Each Type Of Ionizing Radiation
Type of Radiation
Symbol
Mass
u*
Charge
e#
Alpha
4
+2
Beta
-
1/1840
-1
Gamma
0
0
Positron
+
1/1840
+1
X-ray
X
0
0
Neutron
n
1
0
* In atomic mass units
# In units of electron charge
46.SELF-CHECK 1
Now see how much you have understood by answering the following questions in your workbook:
Match the terms radioactive material, radioactive decay, ionizing radiation, electronvolt, alpha particle, beta particle, gamma ray, positron, x-ray and neutron with the following descriptions:
A particle similar to an electron but positively charged.
The change that takes place in the nucleus of an atom to make it more stable.
A particle consisting of two protons and two neutrons.
A substance which undergoes a spontaneous change in its structure to make it more stable.
A similar particle to an electron which is ejected from the nucleus of an atom at high speed.
A particle with no charge which is very rarely emitted as a result of radioactive decay.
The unit mathematically equivalent to 1.6 x 10-19 joules which is used to describe the energy of ionizing radiation.
Electromagnetic radiation emitted when electrons move from higher energy states to lower energy states.
Any particle or ray which possesses enough energy to remove electrons from atoms, molecules or ions.
Electromagnetic radiation emitted from the nucleus of an atom.
2.Complete the following table:
Type of Radiation
Symbol
Mass
u
Charge
e
Alpha
Beta
Gamma
Positron
X-ray
Neutron
3.Which two types of ionizing radiation are more often associated with other sources rather than radioactive decay?
Now check your answers with the model answers in your workbook.
As already mentioned, when radionuclides undergo radioactive decay, particles and rays are emitted from the atom. The way in which decay occurs is different for each particular radionuclide and their decay modes differ in both the particles produced and also the energy of the emitted particle or ray. The chart of nuclides provides valuable information regarding radioactive decay modes and decay energies and it is important that you learn how to use the information correctly.
As you have already learnt in Module 1.1 Structure of Matter, the chart of nuclides may be used to find the both stable and unstable nuclides. Remember that the stable nuclides form a rough band running diagonally up and to the right on the chart. As a general rule, most stable nuclides have slightly more neutrons than protons and this is particularly for true nuclides with higher atomic mass. Also, the closer a nuclide is to the line of stability, the more stable it is. This is reflected by these nuclides having longer half-lives.
In addition to providing information about stability, the chart of nuclides may also be used to determine how a particular radionuclide will decay. It provides information about the type of radiation emitted and the energy of the radiation.
Look at your chart of nuclides. In small writing near the centre of each nuclide box are the decay modes of the radionuclide and the energy of the radiation. The decay modes are given in order of abundance, so the first mode shown is the most common decay method for the radionuclide. The energy of the emission is given in MeV for alpha and beta radiation and keV for gamma or X-rays. Using the chart of nuclides, find the radionuclide iodine-131. What is the type and energy of the most common decay mode for this radionuclide?
The most common decay mode for iodine-131 is emission of a beta particle with an energy of 0.606 MeV.
Note that, although the most common decay modes are given in the chart of nuclides, there may be other less common modes which are not listed. Also, sometimes two different decay modes are associated and this is not necessarily shown on the chart. Hence, the chart of nuclides should be used as a guide to decay modes rather than an absolute reference.
The chart of nuclides can also be used to predict what the products of a particular decay may be. Section 2.4 shows you how to use your chart of nuclides to predict the outcomes of radioactive decay.
The most common modes of radioactive decay are by emission of alpha particles, beta particles and gamma rays. Other possible decay modes include positron emission and very rarely neutron emission. X-rays are not usually an immediate product of radioactive decay, but they may be produced as a product of other decay modes.
Alpha particles are emitted from the nucleus with high energies ranging from 4 to 8 MeV. The energy of emission is well-defined and is characteristic of the particular radionuclide from which it came.
When a radionuclide emits an alpha particle, its atomic number (Z) is decreased by two (owing to the loss of two protons), and its atomic mass number is decreased by four (owing to the loss of two protons and two neutrons). On the chart of nuclides, alpha decay (denoted by ) is seen to shift the radionuclide diagonally down and to the left two squares
Use your chart of the nuclides to find out what happens to polonium-216 when it decays by alpha emission. What is the energy of this decay?
If you move diagonally down to the left two squares you come to lead-212. The energy of the alpha decay is shown in the polonium-216 nuclide box as 6.7785 MeV.
This decay can be written in the form of a decay equation as follows:
Or more commonly as:
Note that alpha particles are usually emitted by heavy nuclei elements such as uranium and radium.
Beta particle are emitted from the nucleus with a distribution of energies up to a maximum which is dependent on the particular radionuclide. Figure 1 shows the energy distribution of beta particles emitted from phosphorus-32. The average energy is represented by the symbol .
Figure 1
Beta Energy Distribution
When a radionuclide emits a beta particle, its atomic number increases by one (as there is now one more proton in the nucleus), but the atomic mass number stays the same (the change was from a neutron to a proton). Beta decay (denoted by -) shifts the radionuclide diagonally up and one square left on the chart of nuclides.
Use your chart of the nuclides to find out which nuclide is formed when phosphorus-32 decays by beta emission. What is the energy of this decay?
If you move up and one square left you will come to sulphur-32, a stable nuclide. The energy of decay is shown in the phosphorus-32 box as 1.709 MeV.
This decay can be written in the form of a decay equation as follows:
Or more commonly as:
-
Beta decay occurs in nuclei which are rich in neutrons, such as radionuclides produced in a nuclear reactor. Neutron-rich nuclides are on the right of the line of stability on the chart of nuclides.
Gamma rays are emitted as a way for the nucleus of radioisotopes to release excess energy and become more stable. They are usually emitted following alpha or beta decay and, as only energy is released and not particles, both the atomic number and atomic mass of the radionuclide are unchanged during gamma emission. Hence, after this type of gamma emission, there is no shift on the chart of nuclides.
Look at your chart of nuclides again and find radon-220. This radionuclide decays by alpha emission to polonium-216. Note that underneath the alpha symbol in the radon-220 box there is also a gamma emission (denoted by ). Although this equation could be written in a similar way to the equation for alpha emission in Section 2.3.2, a more detailed way of writing this equation is as follows:
Note that gamma rays are emitted from the nucleus with well-defined energies ranging up to several megaelectronvolts (MeV). The energies released are characteristic of the emitting radionuclide and can be used to identify radionuclides.
46.1.12.4.3.1Isomeric transition
Gamma ray emission usually happens immediately after the initial decay (approximately 10-10 seconds after). However, some radionuclides do not remove this excess energy so quickly and there may be a time lapse of minutes or even hours before the gamma ray is emitted. In this case, the radionuclides are known as metastable radionuclides and are denoted by an mfollowing the mass number. After a certain amount of time, the gamma ray will finally be emitted and this process is known as an isomeric transition.
Radionuclides which exhibit metastable states are shown on the chart of the nuclides as a vertically divided square. The left hand side of the square shows the properties of the metastable state whereas the right hand side shows the properties of the normal radionuclide. When a radionuclide undergoes isomeric transition (denoted by the symbol IT), it will shift to the right hand side of the square on the chart of nuclides.
Use your chart of nuclides to find technecium-99. Note that the square is divided into two, indicating that this radionuclide may exist in a metastable state (Tc-99m). On the left hand side, the decay mode is denoted by the letters IT. This indicates that Tc-99m may undergo isomeric transition to Tc-99. This isomeric transition would then shift the radionuclide from the left hand side of the box (Tc-99m) to the right hand side (Tc-99).
Technecium-99m actually results from the beta decay of molybdenum-99 and the whole process can be shown by equation as follows:
+ - +
or more commonly as:
Positron decay usually only occurs in nuclei which have an excess of protons. When a radionuclide undergoes positron decay, its atomic number is reduced by one (as there is one less proton in the nucleus), but the atomic mass stays the same (the change was from proton to neutron). Positron decay (denoted by the symbol +) shifts the radionuclide diagonally down one square to the right on the chart of nuclides. This is the opposite of the shift which occurs when beta particles decay.
Look at your chart of nuclides. You will see proton-rich radionuclides on the left of the stability line. Find the oxygen-15 nuclide. What is its most common decay mode and what does it decay to?
From the chart of nuclides, the most common decay mode for oxygen-15 is positron emission. If you move down diagonally one square to the right you come to nitrogen-15 so this is the nuclide formed when oxygen-15 decays by positron emission.
This decay can be written in the form of a decay equation as follows:
Or more commonly as:
+
Note that positrons (like beta particles) are emitted with a range of energies up to a maximum.
X-rays are not spontaneously emitted from atoms without another process taking place. Hence, X-ray emission is associated with such modes of decay as internal conversion and electron capture but is not a decay mode in its own right. In fact, x-ray emission is more commonly associated with artificial production in x-ray generators (see Section 5.2.1) than radioactive decay.
Internal conversion is another process which serves to remove excess energy from the nucleus and is an alternative to gamma ray emission. The process of internal conversion involves the excess energy being transferred to an orbital electron from the inner shells of the atom (either K or L shells). This electron is then ejected from the atom and is rather like a beta particle but with only a single energy rather than a range of energies. The ejected electron leaves a vacancy in an inner electron shell, which is filled by an electron moving from an outer shell. As the electron moves from a higher to a lower energy level, energy is released in the form of a characteristic x-ray. Therefore, during internal conversion, an electron and an x-ray are emitted from the atom instead of a gamma ray.
Internal conversion, like gamma emission, does not affect the atomic number or mass of the nucleus but does reduce the energy level of the atom. Internal conversion is given the symbol e-in the chart of nuclides.
Electron capture is a process which occurs in atoms with an excess of protons. During electron capture, an electron in the innermost electron shell (the K shell) is captured by a proton in the nucleus and forms a neutron. As an electron is removed from the K shell, an electron from an outer shell will change orbits to fill the gap. As the electron moves from a higher to a lower energy level, energy is released in the form of an x-ray. The x-ray emitted as a result of electron capture is characteristic of the resulting nuclide, not the original radionuclide which underwent decay.
When a radionuclide undergoes electron capture, its atomic number is reduced by one (as there is one less proton in the nucleus), but the atomic mass stays the same (the change was from proton and electron to neutron). Hence, electron capture is similar to positron emission in that the radionuclide is shifted diagonally down one square to the right on the chart of nuclides. Electron capture is given the symbol on the chart of nuclides.
Look at your chart of the nuclides and find oxygen-15 again. You will notice that its alternative method of decay is by electron capture. What does this radionuclide decay to by electron capture?
The resulting nuclide is nitrogen-15, the same product as in positron decay.
Note that all positron-emitting nuclides are also able to decay by electron capture.
Although some by-products of nuclear reactors are capable of emitting neutrons, neutron emissionis not normally associated with radioactive decay. Instead, neutron emission is more often associated with artificial production in nuclear reactors or in manufactured neutron sources (see Section 5.2.3). Neutron emission is discussed in this section for completeness only and you should remember that neutron emission by radioactive decay is a rare occurrence.
Neutron emissionby radioactive decay is very rare. It is more often associated with artificial production in nuclear reactors or in manufactured neutron sources.
When a radionuclide undergoes neutron emission, its atomic mass number (A) is reduced by one as there is one less neutron in the nucleus. Hence, the radionuclide is shifted one square to the left on the chart of nuclides. Neutron decay is represented on the chart of nuclides with an n.
46.22.5Summary of Radioactive Decay Modes
A summary of shifts in the chart of nuclides due to radioactive decay is shown in Figure 2.
Figure 2
Shifts In The Chart Of Nuclides Due To Radioactive Decay
Table 2 summarizes the main modes of decay and describes the changes which occur in the nucleus of the radionuclide.
Table 8
Summary of Radioactive Decay Modes
Decay Mode | Symbol | Common Source | Change In Z | Change In N | Change In A |
Alpha | | Heavy nuclei | -2 | -2 | -4 |
Beta | - | Excess neutrons | +1 | -1 | 0 |
Gamma | | Excess energy | 0 | 0 | 0 |
Internal Conversion | IT | Excess energy | 0 | 0 | 0 |
Positron | + | Excess protons | -1 | +1 | 0 |
X-ray* | X | (X-ray tubes) | | | |
Internal Conversion | e- | Excess energy | 0 | 0 | 0 |
Electron Capture | | Excess protons | -1 | +1 | 0 |
Neutron* | n | Excess neutrons | 0 | -1 | -1 |
(Neutron sources, nuclear reactors) | | | |
* These emissions are more often associated with other sources than radioactive decay
47.SELF-CHECK 2
Now see how much you have understood by answering the following questions in your workbook:
1.Use your chart of nuclides to find the types and energies of radiation emitted by the following radioisotopes. What do these radionuclides decay to?
Be-7.
Na-22.
P-32.
Po-210.
2.Which two modes of decay result in products with a range of energies?
Fill in the gaps with a suitable word or phrase:
The emission of _______ ____ is usually associated with alpha or beta decay and serves to remove excess energy from the nucleus of an atom.
Radionuclides which do not immediately emit a gamma ray immediately following another decay but emit the gamma ray after several minutes or hours are known as _________ radionuclides.
The process by which a gamma ray is released from a nucleus after several minutes or hours is known as an _________ _________.
4.Which two modes of decay result in the production of characteristic x-rays?
5.What are the two products of internal conversion?
Now check your answers with the model answers in your workbook.
Decay parameters are physical quantities which describe the way in which a radionuclide decays. Such quantities include the decay constant, activity and half-life and each quantity is characteristic of a specific radionuclide. Some mathematical expressions are used in the following sections to describe the decay parameters. If you are unsure of exponentials or logarithms take time now to look again at the relevant sections of Module 1.2 Basic Mathematics.
The radioactive decay of radioactive material is random in nature and it is impossible to estimate exactly when a particular atom is going to decay. However, if a large number of atoms are looked at as a single unit, the decay will follow a well-defined statistical pattern, known as the radioactive decay law.
This law may be expressed as an exponential equation and is shown in Equation 1:
N = N0e-T[1]
whereN0 is the original number of nuclei present,
T is the time which has passed,
is the radioactive decay constant, and
N is the number of nuclei remaining after the decay time.
The radioactive decay constant is the fraction of the atoms which undergo decay in a unit time such as a second or a year.
The decay constant for a particular radionuclide is fixed and does not change, irrespective of any chemical or physical change of the nuclide.
.3.13.2.1Definition
In radiation protection, it is more important to know how much radiation is being emitted rather than how many radioactive atoms remain in the sample. Hence a quantity known as activity is used to define the number of disintegrations of the radioactive material taking place in a unit time (usually seconds).
The activity (A) of a radionuclide is defined as the number of disintegrations per second of a radioactive material.
Note that activity and atomic mass number have the same symbol (A) and number of nuclei and number of neutrons have the same symbol (N). You must therefore be careful that you understand that the meaning of each symbol whenever they are used.
.3.13.2.2Quantities and units
The unit for activity is the becquerel(Bq) and one becquerel is equivalent to one disintegration per second.
1 Bq = 1 disintegration per second
Note that the first unit of activity was the curie (Ci) which was originally defined as the quantity of activity having the same number of atoms decaying per second as one gram of radium-226. The curie was later redefined as 3.7 x 1010 disintegrations per second (or 37 gigabecquerels).
1 Ci = 3.7 x 1010 Bq = 37 GBq
In radiation protection, it is often necessary to convert from between prefixes (kilo, mega, giga etc) and Table 3 lists the unit prefixes most commonly used.
Table 9
Unit Prefixes
Fractions
Multiples
Symbol
Prefix
Factor
Symbol
Prefix
Factor
d
deci
10-1
k
kilo
103
c
centi
10-2
M
mega
106
m
milli
10-3
G
giga
109
micro
10-6
T
tera
1012
n
nano
10-9
p
pico
10-12
Example 1 shows how to convert between prefixes.
Example 1
If the activity of a radionuclide is quoted as 10 megabecquerels (10 MBq),
a)what is this in becquerels?
From Table 3, mega means a factor of 106. So, to convert from megabecquerels to becquerels, we need to multiply by a factor of 106 as follows:
10 MBq = 10 x 106 Bq = 107 Bq
Answer: 10 MBq is equal to 107 Bq
b)what is this in gigabecquerels (GBq)?
From Table 3, mega means a factor of 106 and giga means a factor of 109. Therefore the prefix mega means that the quantity is 103 (or 1000 times) smaller than micro. Hence:
10 MBq = 10 x 10-3 GBq = 10-2 GBq = 0.01 GBq
Answer: 10 MBq is equal to 0.01 GBq
It is also often necessary to convert from the old units of activity (curies) to the new units (becquerels) and vice versa. Table 4 lists useful conversion factors for the old and new units of activity.
Table 10
Useful Conversions for Units of Activity
Curies to Becquerels
Becquerels to Curies
1 Ci = 37 kBq
1 mCi = 37 MBq
1 Ci = 37 GBq
103 Ci = 37 TBq
1 Bq = 2.7 x 10-11 Ci
1 kBq = 2.7 x 10-8 Ci
1 MBq =2.7 x 10-5 Ci = 27 Ci
1 GBq = 2.7 x 10-2 Ci = 27 mCi
1 TBq = 2.7 x 10 Ci = 27 Ci
Examples 2 and 3 show how these conversions may be done.
Example 2
A radioactive source is quoted with an activity of 5 microcuries (5 Ci). What is this activity in becquerels (Bq)?
Answer: From Table 4, 1 Ci = 37 kBq.
Hence 5 Ci = 5 x 37 kBq = 185 kBq
5 Ci is equal to 185 kBq or 1.85 x 105 Bq
Example 3
A radioactive source is quoted with an activity of 200 megabecquerels (200 MBq). What is this activity in curies (Ci)?
Answer: From Table 4, 1 MBq = 2.7 x 10-5 Ci = 27Ci.
Hence 200 MBq = 200 x 2.7 x 10-5 Ci = 540 x 10-5 Ci
= 5.4 x 10-3 Ci = 5.4 mCi
200 MBq is equal to 5.4 mCi or 5.4 x 10-3 Ci
The term half-life is used to describe the rate at which a radionuclide decays and is written as T1/2. Each radionuclide has a unique and unalterable half-life: for carbon-14 it is 5715 years; for tritium (hydrogen-3) it is 12.32 years; for phosphorus-32 it is 14.28 days.
The half-life is defined as the time taken for half the atoms in a sample to decay.
Therefore at T = T1/2, N = . By substituting this into the radioactive decay equation (Equation 1), it is possible to determine the relationship between and T1/2. This derivation is shown below:
From Equation 1
N = N0e-T
SubstitutingN = andT = T1/2
=
=
Taking natural logs (ln) of both sides of the equation
ln (1/2) =
By using log rules and rearranging the equations
ln (1/2) = -T1/2
T1/2 = - = - = -1 []
T1/2 =
T1/2 =
=[2]
As shown in Equation 2 above, there is a fixed relationship between the decay constant and the half-life; a short half-life means that a large proportion of atoms are decaying in unit time and hence the decay constant is large. Conversely, a long half-life means that not many of the atoms are decaying in unit time and hence the decay constant is small. Half-life is generally used to describe the rate of decay as it allows you to interpret how stable a radionuclide is and how quickly it will decay.
The half-life of a particular radionuclide may be found from the chart of nuclides. The half-life is displayed in medium size numerals in the upper section of the radionuclide box. It also has a letter beside it indicating the unit of time (a for annums (years), d for days, h for hours, m for minutes and s for seconds). If no half-life is shown, the nuclide is stable. A question mark indicates that the half-life is unknown.
Use your chart of nuclides to find iodine-131. What is the half-life of this radionuclide?
From the chart of nuclides, the half-life for iodine-131 is 8.020 days.
48.SELF-CHECK 3
Now see how much you have understood by answering the following questions in your workbook.
Match the terms radioactive decay law,decay constant, activity, becquerel, curie and half-life with the following descriptions:
The new unit of activity equivalent to 1 disintegration per second.
The number of disintegrations per second.
The fraction of unstable atoms which decay in unit time.
The shape of the radioactive decay curve.
The time taken for half the radioactive atoms in a sample to decay.
The old unit of activity equivalent to 3.7 x 1010 disintegrations per second.
A radioactive source has an activity of 100 millicuries (mCi). Convert this activity to:
megabecquerels (MBq).
becquerels (Bq).
kilobecquerels (kBq).
3.A radioactive source has an activity of 500 megabecquerels (MBq). Convert this activity to:
microcuries (Ci).
millicuries (mCi).
curies (Ci).
4.Use your chart of nuclides to find the half-life of the following radionuclides:
sulphur-35.
gallium-66.
technecium-99.
technecium-99m.
Now check your answers with the model answers in your workbook.
48.13.4Calculating Activity
The activity of a radionuclide is proportional to the number of unstable nuclei as shown in Equation 3:
A = N[3]
whereA is the activity of a radionuclide
is the radioactive decay constant, and
N is the number of nuclei remaining after the decay time.
Therefore activity, like the number of unstable nuclei, varies exponentially and can be written as shown in Equation 4:
A = A0e-T[4]
whereA0 is the original number of nuclei present,
T is the time which has passed,
is the radioactive decay constant, and
A is the number of nuclei remaining after the decay time.
The variation of activity with time is shown graphically in Figure 3.
Figure 3
Variation of Activity with Time
Equation 4 can be manipulated to give an easier way to calculate activity:
A = A0e-T[4]
Substituting for n
where n is the number of half-lives which have elapsed (n = )
Taking natural logs (ln) of both sides of the equation and applying log rules
Substituting for T1/2 = and applying log rules
n ln 2 = ln 2n =
2n =
A = [5]
whereA is the activity at time T,
A0 is the initial activity, and
n is the number of half-lives which have elapsed
!
It is important that the same time scale is used for T1/2 , and the time T. If the half-life is in years, T must be in years. If the half-life is in seconds, T must be in seconds.
Radioactive sources are labelled with the activity of the source and the time at which this activity was determined. This allows you to calculate the activity at any other time using either Equation 4 or Equation 5. There is also another method of roughly estimating activity and all three methods are shown in Example 4.
Question
A caesium-137 (Cs-137) source had an activity of 800 MBq on 1st January 1973. What will its activity be on 1st July 2030?
Answer
Method 1
For the first method we will use Equation 4:
A = A0e-T
and also Equation 2 above:
=
From the chart of nuclides, the half-life of Cs-137 is 30.17 years so T1/2 =30.17 y.
Hence
= y-1 = 2.30 x 10-2 y-1
The original activity was 800 MBq so A0 = 800 MBq
The time interval between 1st January 1973 and 1st July 2030 is 57.5 years.
Hence
A = 800 e-.023 x 57.5 = = 800 e-1.32
If you have a scientific calculator, use the ex button to find the value of e-1.32. If you do not have a scientific calculator you will need to use natural logarithms to find this value.
From these calculations
e-1.32 = 0.267 and
A = 800 x 0.267 = 214 MBq
Therefore, the activity of Cs-137 on 1st July 2030 will be 214 MBq.
Method 2
For the second method, we will use Equation 5:
A =
wheren =
From the chart of nuclides, T1/2 =30.17 y.
The time interval (T) between 1st January 1973 and 1st July 2030 is 57.5 years.
So, the number of half-lives, n= = 1.91.
The activity of the source on 1st January 1973 was 800 MBq. (A0 = 800 MBq)
Substituting these values into Equation 5 gives:
A =
If you have a scientific calculator, use the yx button (or the xy button on some calculators) to find the value of 21.91. If you do not have a calculator then you will need to use logarithms.
From these calculations
21.91 = 3.76 and
A = = 213 MBq
Therefore, the activity of the Cs-137 on 1st July 2030 will be 213 MBq.
Note that the difference of 1 MBq in the answers to the above two methods is due to rounding adjustments.
Method 3
If only an approximate answer is required, you can estimate the number of half-lives and then ‘step’ the activity down the corresponding number of times. In this case the elapsed time is approximately two half-lives. After one half-life, the activity would have decayed from 800 MBq to 400 MBq. After the second half-life the activity would have decayed to 200 MBq. Since the elapsed time is not quite two half-lives, we would expect slightly more than 200 MBq to remain. If we are calculating the activity in order to assess potential hazards this method is close enough. However, if we are calculating the activity for calibration purposes, we must use either method 1 or method 2. The first two methods both give accurate answers.
49.SELF-CHECK 4
You have found an old radioactive source in the back of a cupboard in your laboratory. It is labelled as being Co-60 with an activity of 3 Ci, as measured on the 1st January 1966.
What was the original activity of the source in becquerels (Bq)?
Use the chart of nuclides to find the half-life of Co-60.
Calculate the activity (in Bq) of the source on 13 August 1997.
Technecium-99m is commonly used for diagnostic purposes in nuclear medicine. If a patient is scheduled to have an injection of 500 MBq of technecium-99m at 16:00 hrs but the quantity of radioactivity is obtained at 11:00 hrs, what quantity of activity will need to be obtained at 11:00 hrs to ensure that the correct activity is administered at 16:00 hrs?
Now check your answers with the model answers in your workbook.
49.13.5Measuring the Half-Life of A Radionuclide
This section contains background information in relation to the first Practical Activity of the course. In this practical, you will be expected to find the half-life of a radionuclide by measurement but it is important that you understand the theory behind the practical before you begin.
.3.13.5.1Introduction
It is possible to estimate the half-life of some radionuclides by taking measurements of counts or count rates over a suitable time. Note that, count (for any length of time provided that it is the same for every count) or count rate can be used in place of activity, and the half-life may then either be calculated or be obtained graphically.
.3.13.5.2Half-life by calculation
From Equation 5
A =
whereA is the activity at time T
A0 is the initial activity
n is the number of half-lives which have elapsed
Rearranging this equation gives Equation 6:
2n = [6]
By taking the count or count rate at two different times to be indicative of the activity of a sample, then the value of 2n can be determined.
To find n from Equation 6, it is necessary to take logs of both sides. It does not matter whether you take common logs (log10) or natural logs (loge or ln) but here we will take natural logs. Equation 6 then becomes
ln 2n = ln
n ln 2 = ln
n = [7]
But
n =
Rearranging
T1/2 = [8]
So, when n has been found from Equation 7, you can use Equation 8 to find the value of the half-life.
A certain amount of radioactivity is always present in the atmosphere (see Section 5) and hence whenever we measure counts or count rate, we need to correct for this background radiation. The easiest way to do this is to take a number of readings without the source present and take the average of these readings. This background count may then be subtracted from all measurements where the source is present to obtain a true result.
Counts or count rates should be corrected for background to ensure a true result.
Note that, in most cases the background count is very small when compared to the sample count and the correction will make very little difference to your answer. However, for the purpose of this course, all practical measurements should be corrected for background to ensure a true result.
Example 5 shows how the half-life of a radionuclide may be determined by calculation.
Question
A sample is counted and found to have 952 counts per minute. Seven minutes later it is measured again and has a count of 148 counts per minute. A background measurement gave 6 counts per minute. What is the half-life of the sample?
Answer
Initial activityA0 = 952 - 6 = 946
Activity seven minutes laterA = 148 - 6 = 142
Hence
= = 6.66
Using Equation 7
n = = = =2.74
This means that the number of half-lives (n) in 7 minutes is 2.74.
Using Equation 8:
T1/2=
T1/2 = 2.55 minutes
Therefore, the half-life of the sample is 2.55 minutes.
.3.13.5.3Graphical method
In the graphical method, the counts or count rates are plotted against time on a graph. Remember that it is not necessary to measure the actual activity, counts (or count rate) are good enough provided that the same detector and counting geometry is used for all data collection.
If you plot the data on linear graph paper, you obtain an exponential curve. If (on log-linear graph paper) you plot time on the linear x axis and counts (or count rate) on the log y axis, you will expect to obtain a straight line from which you can obtain the half-life. More details are given in Practical Activity in your workbook. This method is sometimes used as a guide to identify radionuclides, particularly beta emitters.
This half-life estimation is only valid for pure radionuclides and will not be valid if the sample contains a mixture of radionuclides.
50.PRACTICAL ACTIVITY
In this practical activity you will measure the half-life of a radioactive substance. Details of the procedure to follow are given in your workbook. You should contact your supervisor to arrange a suitable time to do the practical. Note that if it is not possible for you to do the laboratory work, your supervisor will give you some counting data to analyze.
The becquerel, although telling us how much activity is present, does not tell us anything about the physical size of the material. Hence, the term specific activity(SA) is used to give the concentration of a pure radionuclide in terms of activity per unit mass or unit volume.
Specific activity (SA) is defined as the activity per unit mass or unit volume of a particular radionuclide.
The unit of specific activity is either becquerels per kilogram or becquerels per cubic metre. In practice, becquerels per gram (Bq g-1), or sometimes becquerels per millilitre (Bq mL-1) (if the isotope is in solution) are more commonly used.
The specific activity of a material can give an indication of the relative hazard. If a material has a high specific activity, a small mass or volume may be a hazard. Conversely, a large mass or volume of low specific activity may not be a hazard.
If N is equal to the number of radioactive atoms in one gram of the substance, then the specific activity in becquerels per gram is N. This is shown in Equation 9 below:
SA = N[9]
But N can be represented by Equation 10
N = 6.03 x 1023[10]
M
where6.03 x 1023 is a constant known as Avogadro’s constant
M is atomic weight in grams
In practice, the atomic mass A is commonly used instead of the atomic weight as it gives sufficient accuracy.
Substituting into Equation 9
SA = x 6.03 x 1023
A
Substituting for = from Equation 2
SA = 0.693 x 6.03 x 1023
T1/2 A
Hence
SA = 4.18 x 1023[11]
T1/2 x A
whereSA is the specific activity in becquerels per gram (Bq g-1)
A is the atomic mass of the radionuclide
T1/2 is the half-life of the radionuclide in seconds
Hence Equation 11 gives a useful expression for specific activity in terms of atomic mass and half-life of the radionuclide.
Once the specific activity of a radionuclide is known, it is possible to calculate the number of grams present in a particular radioactive source. This is given by Equation 12:
Number of grams = Activity of the source (in Bq)[12]
Specific Activity (in Bq g-1)
Note that Equations 11 and 12 relate to samples of pure radionuclides only. They are not applicable when a sample contains mixed radionuclides.
Example 6 shows how the specific activity and the amount of radionuclide present in a source may be determined by calculation.
Example 6
Question
Using the chart of nuclides, find the half-life sulphur-35. What is the specific activity of this radionuclide? How many grams of sulphur-35 would be present in a 1 gigabecquerel (GBq) source?
Answer
The atomic mass of sulphur-35 is 35.
From the chart of nuclides, the half-life of sulphur-35 is 87.2 days (87.2 x 24 x 60 x 60 seconds).
Substituting into Equation 11
SA = 4.18 x 1023
87.2 x 24 x 60 x 60 x 35
SA = 1.59 x 1015 becquerels per gram (Bq g-1)
A 1 GBq source is equivalent to 1 x 109 Bq
Hence, from Equation 12
Number of grams = 1 x 109 = 6.3 x 10-7 g = 63 g
1.59 x 1015
Hence, the specific activity of suphur-35 is 1.59 x 1015 Bq g-1 and the amount of radionuclide present in a 1 GBq source would be 63 micrograms (g).
The specific activity is high for a radionuclide with low atomic mass and short half-life. A small spill of such a radionuclide may present a serious hazard. Conversely, the specific activity is low for radionuclides with high atomic mass and long half-lives and a small spill would present much less of a hazard.
51.SELF-CHECK 5
1.A sample of a pure radionuclide is counted for five minutes at 11.00 a.m. and found to have a count of 55 430. It is counted for five minutes again at 3.10 p.m. and has a count of 1 750. The average five-minute background count was 20. What is the half-life of the radionuclide?
What is the specific activity of phosphorus-32? How many grams of this radionuclide would there be in a 50 MBq source?
Now check your answers with the model answers in your workbook.
51.14.1Decay Chains
As you have already learnt, radioactive decay occurs in atoms as a way of making them more stable. The more stable nuclide which results from this radioactive decay has a special name and is known as the progeny (or daughter). Progeny is the term accepted by the IAEA and will be used throughout this course but you may see the term daughter used in some textbooks. The original radionuclide is called the parent.
Note that the words ‘more stable’ are used above. This is because when a radionuclide decays, it does not necessarily form a stable nuclide. It may form another radioactive substance instead.
When a radionuclide decays, it may decay to another radioactive nuclide.
Hence, when a parent radionuclide decays to form its progeny, the progeny may also be radioactive and will undergo radioactive decay itself (i.e. the progeny becomes a parent radionuclide and decays to another progeny). This second progeny may also be radioactive and, if so, will then decay to another radionuclide. This process will be repeated until the atom finally reaches a stable form. This path to stability is called a decay chain or decay series and these paths can vary in both length and complexity.
Using the chart of nuclides it is possible to investigate the decay chain for a particular radionuclide. To do this you start at the initial radionuclide, look at the most probable decay mode and shift to the appropriate progeny nuclide. You repeat this for each subsequent progeny nuclide until a stable nuclide is reached. Note that for some radionuclides, there may be two possible decay paths.
Krypton-90 is an artificial radionuclide which is commonly produced in nuclear reactors (see Section 5). Use your chart of nuclides to find krypton-90 and follow its decay chain.
Krypton-90 decays by beta emission to rubidium-90m (remember that split boxes indicate metastable radionuclides with the metastable state being shown on the left side). Rubidium-90m then either decays directly by beta emission to strontium-90, or decays first to rubidium-90 (by internal conversion) then to strontium-90 (by beta emission). Strontium-90 decays by beta emission to yttrium-90m, and then yttrium-90m decays to zirconium-90m (either by isomeric transition to yttrium-90 followed by beta emission or less commonly directly by beta emission). Zirconium-90m quickly undergoes an isomeric transition to stable zirconium-90.
This decay chain can be shown in the following way:
Kr-90 Rb-90m Sr-90 Y-90m Y-90 Zr-90m Zr-90
Rb-90
It is important to remember that decay chains may have several alternative paths. A particular radionuclide may decay by one path for the majority of time but still have a significant alternative path.
Decay chains may have several alternative paths.
In the krypton-90 example you have just looked at, there are two places in the chain where alternatives exist; rubidium-90 and yttrium-90 may decay directly by beta emission or they may decay through metastable states to become stable. The chart of nuclides does not provide enough information to determine the relative probabilities of the different decay modes. If more detailed information on a particular decay chain is required, this should be sought from sources other than the chart of nuclides.
When looking at decay chains, it is important to note not only the modes of decay, but also the half-lives of each transformation. This is because the relative half-lives of each decay can lead to situations which have important repercussions for radiation protection. For example, a condition known as secular equilibrium can lead to the total activity of the sample being much greater than the activity of the original parent radionuclide. The other conditions discussed in this section are transient equilibrium and no equilibrium.
.3.14.2.1Secular equilibrium
In the krypton-90 example above, we looked at the modes of decay but did not look closely at the half-lives of each decay.
Using your chart of nuclides, look at the main decay chain for krypton-90 again and note the half-lives of each decay.
You should have noted the half-lives as follows:
Kr-90 Rb-90m Sr-90 Y-90m Y-90 Zr-90m Zr-90
where s = seconds, m = minutes, h = hours, d = days, y = years.
Look at the half-life for strontium-90. In comparison to the transformation from krypton-90 to strontium-90 and the transformation from yttrium-90 to zirconium-90, the transformation from strontium-90 to yttrium-90 is much longer. If we now consider the case where pure strontium-90 decays to yttrium-90 then, over time, the amount of yttrium-90 will build up in the sample. However, as the yttrium-90 decays much faster than the strontium-90, a point will be reached where the amount of strontium-90 decaying at any one time will be equal to the amount of yttrium-90 decaying. In other words, the activity of the strontium-90 parent will be equal to the activity of the yttrium-90 progeny. When this occurs, the yttrium-90 is said to be in secular equilibrium with its parent radionuclide, strontium-90.
In general, secular equilibrium occurs in decay chains whenever the parent nuclide has a much longer half-life than its progeny. It takes a time equal to about seven half-lives of the progeny for the activity of the progeny to be the same as the activity of the parent, i.e. to reach secular equilibrium (see Figure 4).
Figure 4
Secular Equilibrium
Secular equilibrium has important repercussions in radiation protection in terms of the total activity of a sample. For example, when secular equilibrium is reached in the strontium-90 and yttrium-90 case, the activity of the sample will double because of the two radionuclides decaying simultaneously. In some cases, secular equilibrium occurs at a number of places along the decay chain and this can greatly increase the total activity of a sample.
Secular equilibrium can occur at a number of places along the decay chain and this can greatly increase the total activity of the sample.
In general, the total activity of a sample in which secular equilibrium occurs n times is taken as n + 1 times the activity of the parent radionuclide. This is shown by Equation 13:
Atot = (n + 1) Apar[13]
whereAtot is the total activity of the sample
n is the number of times in which secular equilibrium occurs in the decay chain
Apar is the initial activity of the parent
This is shown by Example 7.
Example 7
Question
What is the total activity of a sample containing 1 MBq of lead-210?
Answer
From the chart of nuclides, lead-210 (T1/2 = 22.6 y) decays to bismuth-210 (T1/2 = 5.01 d) which decays to polonium-210 (T1/2 = 138.38 d) and then to stable lead-206. As bismuth and polonium both decay much more rapidly than the original lead, secular equilibrium occurs twice in the decay chain (i.e. n = 2).
As the sample contains 1 MBq of lead-210, then from Equation 13:
Atot = (2 + 1)1 MBq = 3 MBq
Hence, the total activity of the sample will be 3 MBq.
.3.14.2.2Transient equilibrium
Now consider the case wherethe half-life of the progeny is slightly less than that of the parent. Obviously there can be no progeny if the parent has not decayed so if the parent is initially pure, the progeny activity starts from zero. As the parent decays, the progeny will start decaying at a slower rate. Hence, the activity of the progeny will build up in the sample until it reaches a maximum. After this point, the progeny seems to decay with the same half-life as the parent. When this occurs, the progeny is decaying at the same rate as it is being produced and transient equilibrium has been reached (see Figure 5).
Figure 5
Transient Equilibrium
The time after which transient equilibrium occurs depends on the relative half-lives of the parent and progeny (i.e. on). The shorter the half-life of the progeny relative to the parent, the quicker transient equilibrium is attained.
Transient equilibrium is again an important concept in radiation protection as the total activity of the sample is greater than that of the greater than that of the parent nuclide alone. An example of this is at the end of a decay chain known as the thorium decay series. In this decay chain, lead-212 (T1/2 = 10.64 h) decays to bismuth-212 (T1/2 = 1.009 h) which decays to polonium-212 (T1/2 = 0.298 s) and then to stable lead-208. Note that lead-212 and bismuth-212 have half-lives of the same order of magnitude. Hence after a short period of time, lead-212 and bismuth-212 will reach transient equilibrium. As lead-212 is a naturally occurring atmospheric isotope, this radionuclide and its progeny may be seen as part of routine air sampling results. Hence, for accurate interpretation of air sampling results, corrections must be made for the activity of lead-212 and its progeny.
.3.14.2.3No equilibrium
Whenever the parent nuclide has a much shorter half-life than its progeny, equilibrium is not possible. After several of the parent’s half-lives there is no significant parent activity remaining and the only radionuclide left is the progeny (see Figure 6).
Figure 6
No Equilibrium
From Figure 6, it can be seen that, as the parent nuclide decays, the progeny activity increases to a maximum and then decays at its own characteristic rate. In the meantime, the parent decays away because of its short half-life. Hence, in the case of no equilibrium, the total activity of the sample decreases continuously.
The activity of the progeny, after decay of the parent, depends on the ratio of the half-lives of the parent and the progeny and can be calculated from Equation 14:
A2 =[14]
WhereA1 is the initial activity of the parent
A2 is the activity of the progeny when all the parent has decayed
T1 is the half-life of the parent nuclide
T2 is the half-life of the progeny nuclide
Example 8 shows how Equation 14 is used in practice.
Example 8
Question
Cerium-146 is an artificial radionuclide which may be produced in a nuclear reactor. Using the chart of nuclides, find the decay chain for this radionuclide and the half-lives of each decay. What would the activity of the progeny be after all the cerium-146 from a 10 MBq source had decayed away?
Answer
From the chart of nuclides, cerium-146 (T1/2 = 13.5 m) decays by beta emission to praseodymium-146 (T1/2 = 24.2 m) and then again by beta emission to stable neodymium-146.
If the source of cerium-146 was 10 MBq then from Equation 14:
A2 = = 5.6 MBq
Hence, the activity of praseodymium-146 remaining after all the cerium-146 had decayed away would be 5.6 MBq.
A useful way of remembering this is, if the half-life of the progeny is a thousand times longer than the half-life of the parent, the activity of the progeny will be approximately a thousandth of the parent’s initial activity.
Note that, in the case of the parent being shorter-lived than the progeny, what is generally quoted is the activity of the progeny. This is because the progeny is the long-term contributor to the activity of the sample, not the parent.
.3.14.2.4Summary of relative half-lives
Table 5 summarizes the three types of relative half-life situations.
Table 11
Summary of Relative Half-life Situations
Situation | Condition under which it occurs | Total activity of sample | Time after which it occurs |
Secular Equilibrium | T1 >> T2 | Increases | Approx 7T2 |
Transient Equilibrium | T1 > T2 | Increases | Depends on |
No Equilibrium | T1 < T2 | Decreases | Immediately |
Note: T1 = Activity of Parent
T2 = Activity of Progeny
52.SELF-CHECK 6
Now see how much you have understood by answering the following question in your workbook:
Starting at U-238, use the most common modes of decay to determine the most probable decay chain. Write down the name of each nuclide in the decay chain, and the type of radiation emitted and its energy. This particular decay chain is commonly called the uranium series.
a)Under what conditions does secular equilibrium occur?
After how many half-lives of the progeny is secular equilibrium considered to have been attained?
Use your chart of nuclides to predict the total activity of a 25 MBq argon-42 source.
Fill in the gaps with a suitable word or phrase:
Transient equilibrium occurs when the half-life of the ________ is slightly greater than that of the __________. When transient equilibrium occurs, the total activity of the sample _________. The time after which the parent and progeny are considered to be in transient equilibrium depends on the ratio of the _________ half-life to that of the _________.
4.Use your chart of nuclides to find the half-lives of Tc-99m and its decay product, Tc-99. If 300 MBq of Tc-99m is used in a medical procedure, how much Tc-99 is left after the parent nuclide has decayed away?
Now check your answers with the model answers in your workbook.
Sources of ionizing radiation may be either natural or artificial. Natural sources have existed since the formation of the earth. Artificial sources of radiation have only been produced during this century but now contribute significantly to the radiation doses received by people through medical, occupational and public exposure.
52.15.1Ionizing Radiation from Naturally Occurring Sources
We are exposed every day to radiation from our environment. Natural background radiation has three main sources:
Cosmic radiation which comes from outside our earth.
Terrestrial radiation which comes from the rocks of the earth.
Radioactivity in our food and drink.
This is shown by Figure 7.
Figure 7
Natural Radiation Exposures
Cosmic radiation consists of particles and rays. Our atmosphere protects us from most of the effects of cosmic radiation. However, if we live several hundred metres above sea level or do a lot of flying our exposure to cosmic radiation is increased. Cosmic rays can interact with stable nuclides in our atmosphere and form such radionuclides as C-14, Be-7 and H-3.
Natural radionuclides produced by cosmic bombardment are called cosmogenic. You may have heard of carbon dating which is used to find out the age of certain organic materials. Carbon-14 is incorporated in living matter together with stable carbon in the ratio in which it naturally occurs. The age of organic material can be determined by measuring the ratio of carbon-14 to stable carbon and using the 5568 year half-life of carbon-14.
Terrestrial radiation comes from naturally occurring radionuclides in the earth’s crust. These radionuclides are called primordial and have half-lives in the order of a billion (109) years. They have been in existence since the formation of the earth. The major radionuclides in this category are uranium-238, uranium-235, thorium-232 and potassium-40. The first three radionuclides have decay chains associated with them and these are called the uranium, actinium and thorium series respectively. The uranium and thorium radionuclides have longer half-lives than their progeny, and it may be assumed that all the progeny radionuclides are in secular equilibrium with the parent radionuclide. This assumption is only valid provided that the parent or progeny are not being removed from the original material by some chemical or physical process.
The major part of exposure from terrestrial radiation is caused by radon (radon-222) and, to a lesser extent, thoron (radon-220). Radon and thoron are gases which form part of the uranium and thorium decay chains. Because they are gases they can seep out from where they are produced in rocks or the building materials of our homes, and then be inhaled along with their short-lived progeny. The inhalation of radon and its progeny is the single biggest source of radiation exposure in the world.
The exposure we receive from radioactivity in our food and drink is due mainly to potassium-40. Whenever we eat or drink, we take naturally occurring potassium-40 into our bodies where it is built up in body tissue, particularly muscle. Most of us will have a few kilobecquerels of potassium-40 in our bodies.
As well as natural radiation, we are also exposed to ionizing radiation from artificial sources. Such sources include x-ray generators, artificial radionuclides and neutron sources.
X-rays can be produced as a result of some modes of decay but are more often produced artificially in x-ray generators. X-ray generators depend on a process known as bremsstrahlung which is German for braking radiation). Bremsstrahlung x-rays are produced when high speed, charged particles (usually electrons) are slowed down rapidly by striking a target of high atomic number. This process occurs in an x-ray tube and the basic elements of a modern x-ray tube are shown in Figure 8.
Figure 8
A Typical X-ray Tube
In the x-ray tube shown above, electrons are produced by heating a metal filament. The electrons are accelerated towards the target by a large electric field produced by a high voltage applied between the anode and cathode. The focusing cup concentrates the electrons onto the target which is usually made of a metal such as tungsten. The electrons are slowed down rapidly (i.e. they brake quickly) and produce a broad range of x-rays. In some cases, very high-energy electrons may emit electrons from the inner shells of the target atoms. When this happens, x-rays with discrete energies which are characteristic of the target material will be emitted. Such emissions are known as characteristic x-rays.
X-ray generators have widespread use, both in industry and in medicine, and will be discussed in more detail in the Part 4 modules.
Artificial radionuclides may be artificially produced by a number of processes including:
Fission
Neutron activation and
Ion bombardment.
Using these techniques, a wide range of radionuclides can be produced which are either uncommon or not found in nature. These isotopes are of use in a wide range of practices including medicine and industrial processes. However, they also may produce unwanted radionuclides such as the activation products in the structure of a nuclear reactor.
52.1.15.2.2.1Fission
Fission is the process which occurs in nuclear reactors and involves splitting a heavy nucleus into smaller nuclei. The resulting fission products are often radioactive. Iodine-131 is a fission product which can be used in the treatment of thyroid cancer. Another fission product, molybdenum-99, is used to make generators which produce the medical radioisotope technetium-99m. Fission products are shown on the chart of nuclides by a small black triangle in the right hand corner of the nuclide box.
Fission is also the process which occurs in atomic bombs. If fission products are released into the environment as a result of atomic weapon testing or through an accident at a nuclear power station they may be hazardous. The most important isotopes released in this way are the radioiodines and caesium-137.
52.1.25.2.2.2Neutron activation
Neutron activation involves the absorption of a neutron from a neutron source to create a heavier nuclide. The most common neutron source is a nuclear reactor in which neutrons are emitted as part of the fission reaction. This process can be used to produce cobalt-60 by activating atoms of stable cobalt-59. It can also be a problem when steel materials containing iron, cobalt, zinc, and chromium form part of the structure of the reactor. These materials will become radioactive by absorbing neutrons and hence be a secondary source of radiation.
52.1.35.2.2.3Ion bombardment
Ion bombardment involves charged particles with high energies hitting a suitable target material. These particles are absorbed into the target and it becomes radioactive. Sources of ion beams include cyclotrons and linear accelerators. Positron-emitting isotopes such as fluorine-18 and oxygen-15 can be made this way for medical use.
As already mentioned in Section 2.2.6, under certain conditions neutrons can be emitted from the nucleus of an atom but neutron emission is not usually associated with radioactive decay (although there are a few fission products with very short half-lives that emit neutrons). The biggest source of neutrons is the nuclear reactor in which neutrons are produced as a result of the fission of heavy nuclides such as uranium or plutonium. Californium-252 is a radionuclide which usually decays by alpha emission but will occasionally undergo fission and produce neutrons.
All other neutron sources are the result of nuclear reactions caused by a charged particle with a high energy hitting a target nucleus. This occurs in accelerators and also in encapsulated neutron sources like those used in industrial gauges. In an encapsulated source, an alpha emitter such as americium-241 is powdered and mixed with powdered beryllium. The high-energy alpha particles from the americium bombard the beryllium nucleus and neutrons are produced.
53.SELF-CHECK 7
What are the three main sources of background radiation?
How could your exposure to cosmic radiation be increased?
Name the radionuclide which is present in our food or drink?
Which naturally occurring radioactive gas is responsible for the largest part of our terrestrial exposure?
Fill in the gaps with a suitable word or phrase:
Three processes which may be used to produce artificial radionuclides are __________, __________ __________ and __________ __________. __________ is a process which occurs in nuclear reactors and involves splitting a heavy nucleus into smaller nuclei. __________ __________ involves charged particles with high energies hitting a suitable target material. Heavier nuclides can be produced in nuclear reactors by absorption of a neutron. This process is known as __________ __________.
a) What is the biggest source of neutrons?
Name two other neutron sources.
7.How are x-rays produced in an x-ray generator?
Now check your answers with the model answers in your workbook.
54.KEY POINTS
Some substances undergo a spontaneous change in their structure to make them more stable. Such substances are known as radioactive. Radioactive decay is defined as the change that takes place in the nucleus of an atom to make it more stable.
Ionizing radiation is defined as any particle or ray which has sufficient energy to remove electrons from atoms, molecules or ions.
The energy of ionizing radiation is measured in electronvolts (eV) where 1 eV is equivalent to 1.6 x 10-19 joules.
Ionizing radiation includes alpha particles, beta particles, gamma rays, positrons, x-rays and neutrons.
Alpha particles (symbol ) are made up of two protons and two neutrons. They have a mass of 4u and a charge of + 2e.
Beta particles (symbol -) are electrons which are ejected from the nucleus of an atom. They have a mass of 1/1840u and a charge of -1e.
Gamma rays (symbol ) are electromagnetic radiation which comes from the nucleus of an atom. They have no mass and no charge.
Positrons (symbol +) come from a proton which has changed into a neutron and a positive electron. They have a mass of 1/1840u and a charge of +1e.
X-rays (symbol X) are produced when atomic electrons undergo a change in orbit. They have no mass and no charge.
Neutrons (symbol n) are particles which are found in the nucleus of an atom. They have a mass of 1u and no charge.
Radionuclides may decay by alpha emission, beta emission, gamma ray emission (including internal conversion), positron emission, internal conversion, electron capture and very rarely by neutron emission.
The chart of nuclides can be used as a guide to the mode of decay of each radionuclide.
Alpha particles are emitted from the nucleus with well-defined energies characteristic of the nuclide from which it came.
Alpha emission shifts the radionuclide diagonally down and to the left two squares.
Beta particles are emitted from the nucleus with a distribution of energies up to a maximum characteristic value.
Beta emission shifts the radionuclide diagonally up and one square to the left on the chart of nuclides.
Gamma rays are emitted from the nucleus of an atom as a way of removing excess energy and becoming more stable. They are emitted with well-defined energies and are usually emitted following alpha or beta decay.
Gamma rays are usually emitted immediately after the initial alpha or beta decay and in this type of emission, there is no shift on the chart of nuclides.
Occasionally there may be a delay in the emission of a gamma ray following the initial mode of decay and the nucleus remains in an excited state (i.e. with excess energy) for a period of time. In this case, the radionuclide is known as a metastable radionuclide and is denoted by the symbol m. Metastable radionuclides are shown on the chart of nuclides
When the nucleus of a metastable radionuclide loses its energy by gamma ray emission, it is said to undergo an isomeric transition.
Isomeric transitions are denoted on the chart of nuclides by IT and shift the radionuclide from the left hand side of the radionuclide box to the right hand side.
Positrons are emitted from radionuclides with a broad range of energies up to a characteristic maximum.
Positron decay shifts the radionuclide diagonally down one square and to the right on the chart of nuclides.
X-ray emission is not a decay mode in its own right, but is associated with such decay mechanisms as internal conversion and electron capture.
In internal conversion (symbol e-), an electron and x-ray are produced with no shift on the chart of nuclides.
In electron capture (symbol ), an electron in the innermost shell is captured by a proton in the nucleus to form an electron. An electron from an outer shell fills the gap and energy is released in the form of an x-ray.
Electron capture shifts the radionuclide diagonally down one square to the right in the chart of nuclides.
Neutron emission by radioactive decay is very rare. It is more often associated with artificial production in nuclear reactors or in manufactured neutron sources.
When a radionuclide undergoes neutron decay (symbol n), the radionuclide is shifted one square to the left on the chart of nuclides.
Radioactive decay is statistical in nature and follows an exponential decay law.
The radioactive decay constant is the fraction of the atoms which undergo decay in a unit time such as a second or a year.
The activity varies over time as the atoms decay and this is expressed in the equation A = A0e-t.
The activity (A) of a radionuclide is defined as the number of disintegrations per second of a radioactive material and has the unit of the becquerel (Bq).
1 Bq = 1 disintegration per second
The first unit of activity was the curie (Ci) which was originally defined as the quantity of activity having the same number of atoms decaying per second as one gram of radium-226. The curie was later redefined as 3.7 x 1010 disintegrations per second (or 37 gigabecquerels).
1 Ci = 3.7 x 1010 Bq = 37 GBq
The half-life of a radionuclide is defined as the time taken for half the atoms in a sample to decay.
Specific activity (SA) is defined as the activity per unit mass or unit volume of a particular radionuclide.
The specific activity of a material can give an indication of the relative hazard. If a material has a high specific activity, a small mass or volume may be a hazard. Conversely, a large mass or volume of low specific activity may not be a hazard.
By using the chart of nuclides, it is possible to find out how a radionuclide decays and what nuclide it decays to. The path can be continued until the atom becomes stable. This is called a decay chain or series.
Decay chains may have several alternative paths.
The more stable nuclide which results from this radioactive decay has a special name and is known as the progeny (or daughter). The original radionuclide is called the parent.
If a radionuclide has a long half-life, any progeny products with a much shorter half-life will have the same activity as the parent after a decay period of approximately seven half-lives. When the progeny products have the same activity as their long-lived parent, they are said to be in secular equilibrium.
Secular equilibrium is important in radiation protection as the activity of a sample can be greatly increased depending on the number of times equilibrium is reached in the decay chain.
When the half-life of the parent is much shorter than that of the progeny, no equilibrium is possible
Radionuclides are present both as a result of natural processes and artificial activities.
Natural background radiation has three main sources: cosmic radiation which comes from outside our earth, terrestrial radiation which comes from the rocks of the earth and radioactivity in our food and drink.
As well as natural radiation, we are also exposed to ionizing radiation from artificial sources. Such sources include x-ray generators, artificial radionuclides and neutron sources.
X-ray generators produce x-rays by firing high speed electrons at a target. The electrons are rapidly slowed and this results in x-rays being produced.
Artificial radionuclides may be artificially produced by a number of processes including: fission, neutron activation and ion bombardment.
Fission involves splitting a heavy nucleus into smaller nuclei.
Neutron activation involves the absorption of a neutron from a neutron source to create a heavier nuclide.
Ion bombardment involves charged particles with high energies hitting a suitable target material. The target then becomes radioactive.
Neutrons are artificially produced in nuclear reactors, accelerators and encapsulated neutron sources.
FINAL ASSIGNMENT
This assignment is to be completed under test conditions, so spend some time now studying this module. Then contact your supervisor to arrange a suitable time to complete the assignment.
55.GLOSSARY OF TERMS
Activity | The number of disintegrations of a nucleus occurring per second. |
Alpha particle | A particle consisting of two protons and two neutrons tightly bound together, and which is ejected from the nucleus during radioactive decay. |
Beta particle | An electron which is ejected from the nucleus of a radionuclide at high speed during radioactive decay. |
Cosmic radiation | Radiation which comes from outside the planet Earth. |
Cosmogenic | Cosmogenic radionuclides are produced by interaction of cosmic rays with stable nuclides in the Earth’s atmosphere. |
Daughter | The more stable nuclide which results from radioactive decay. (See progeny). |
Decay constant | The fraction of atoms which undergo decay in a unit of time. |
Decay parameters | The characteristics (decay constant, activity, and half-life) of a specific radionuclide. |
Decay series | The paths in which radionuclides decay in order to obtain stability. |
Electromagnetic radiation | Energy which travels in the form photons at the speed of light. |
Electron capture | A process whereby an electron in the innermost electron shell is captured by a proton in the nucleus to form a neutron. As a result, characteristic x-rays are produced. |
Electronvolt | The amount of energy gained by an electron accelerating across a potential difference of one volt and is mathematically equivalent to 1.6 x 10-19 joules. |
Fission | The process whereby a heavy nucleus is split into smaller nuclei. |
Gamma ray | Electromagnetic radiation which comes from the nucleus of an atom as a result of radioactive decay. |
Half-life | The time taken for half of the atoms of a radionuclide to undergo radioactive decay. |
Internal conversion | The process whereby excess energy from the nucleus is transferred to an orbital electron. The electron is then ejected from the atom. The electron vacancy is filled by an electron from an outer shell and results in the release of a characteristic x-ray. |
Ion bombardment | The process whereby high energy, charged particles are fired at a target. The particles are absorbed and the target becomes radioactive. |
Ionizing radiation | Any particle or ray which has sufficient energy to remove electrons from atoms. |
Isomeric transition | The process whereby a metastable radionuclide emits a gamma ray thereby removing excess energy from the nucleus. |
Metastable | A metastable radionuclide is one which has excess energy in the nucleus. |
Neutron | An uncharged particle in the nucleus of an atom composed of a proton and an electron. |
Neutron activation | The process whereby neutrons from a neutron source are absorbed by a stable atom thereby producing artificial radionuclides. |
Nucleus (pl. Nuclei) | The positively charged centre of an atom consisting of protons and neutrons. |
Parent | The original radionuclide before undergoing radioactive decay. |
Photon | A small packet of energy which is transmitted in the form of waves. |
Positron | A particle which is similar to a beta particle with the same mass but opposite charge. |
Primordial | Primordial radionuclides are naturally occurring in the Earth’s crust. |
Progeny | The more stable nuclide which results from radioactive decay. (See daughter). |
Radioactive decay | The change that takes place in the nucleus of an atom to make it more stable. |
Secular equilibrium | The situation reached when the activity of a long lived parent is the same as the activity of the much shorter lived progeny. |
Specific activity | The amount of activity per unit of mass or per unit volume. |
Terrestrial radiation | Radiation which comes from the rocks of the planet Earth. |
Transient equilibrium | The situation reached when the progeny radionuclide is decaying at the same rate as it is being produced. |
X-ray | Electromagnetic radiation which is produced when atomic electrons undergo a change in orbit. |
INTERNATIONAL ATOMIC ENERGY AGENCY AUSTRALIAN NUCLEAR SCIENCE AND TECHNOLOGY ORGANISATION |
DISTANCE LEARNING MATERIALS
RADIATION PROTECTION
Module – 1.4
Prepared by Safety and Radiation Science
Australian Nuclear Science and Technology Organisation
With the assistance of consultants in Australia and the United Kingdom, and IAEA experts from Korea, Mongolia, New Zealand, the Philippines and Thailand
Use of this material, acknowledging the IAEA and ANSTO as the source, is permitted for non-profit training
Acknowledgements
This material has been prepared by an extensive team of international experts from the fields of radiation protection, medicine and education. It is not possible to mention by name all those who have had an input to; the initial planning; writing modules and workbooks; preparing and marking final assignments; proof-reading and editing; using the material and providing valuable feedback; organizing and hosting review meetings; and general administrative support.
The support of ANSTO management in providing the resource and encouragement is gratefully acknowledged.
The enthusiastic support of IAEA Technical Officers has been vital to the success of this project
PART 1
BASIC KNOWLEDGE
MODULE 1.4
INTERACTION OF RADIATION WITH MATTER
CONTENTS
56.OVERVIEW
The interaction of photons with absorbing material will be discussed in terms of the photoelectric effect, Compton scattering and pair production. Finally, you will be introduced to the concepts of neutron interactions including elastic and inelastic scattering and neutron capture processes.
Note that the details for the practical activities are given in your workbook. You should contact your supervisor to arrange a suitable time to do this laboratory work. Full credit for this module will not be given until these activities are completed satisfactorily.
57.
TIME ALLOCATION
It is estimated that you will need to spend six to eight hours to complete this module (excluding the laboratory work) before commencing the assignment. This time estimate is for guidance only. Do not worry if you need more time to understand the module.
58.MATERIALS
You will need to have writing materials to take notes and answer questions in the module.
NOW YOU ARE READY TO START WORK
The type of radiation that is of prime concern to this distance learning course is ionizing radiation. As you have already learnt from Module 1.3 Ionizing Radiation and Radioactive Decay, ionizing radiation is defined as any particle or ray with sufficient energy to remove electrons from atoms or molecules. However, to fully understand the interaction of ionizing radiation with matter, it is important to understand the process of ionization itself.
As you already know from Module 1.1 Structure of Matter, atoms consist of a nucleus, which contains positively charged particles (protons) and particles having no charge (neutrons). Negatively charged particles (electrons) orbit the nucleus. An atom with no net charge has equal numbers of negative and positive charges and thus equal numbers of electrons and protons. When ionizing radiation interacts with atoms, it is possible for orbital electrons to receive extra energy. This extra energy allows some of them to overcome the attraction of the nucleus, break free of their orbits and leave the atom (see Figure 1).
Figure 9
The Process of Ionization
As the number of negatively charged electrons left in the atom is now less than the number of positively charged protons, the atom has an overall positive charge, and is referred to as a positive ion. The electron which left the atom is referred to as a negative ion and these oppositely charged ions are called an ion pair. The process which causes ions to be produced is called ionization, and the type of radiation which starts the process is called ionizing radiation. As you will remember from Module 1.3 Ionizing Radiation and Radioactive Decay, alpha and beta particles, gamma rays, x-rays and neutrons can all cause ionization and hence are classed as ionizing radiation.
It is important to note that the initial radiation (which caused the ionization in the first place) also loses energy in the interaction. If enough of these interactions occur, the energy of the ionizing radiation will eventually be absorbed by the material through which it travels.
Any type of ionizing radiation which carries electric charge is capable of exerting forces on the orbital electrons of atoms in material through which it passes. For example, alpha particles, which carry positive charge, are capable of attracting negatively charged electrons away from surrounding atoms to form a stable helium atom. In the case of beta particles, the force exerted on orbital electrons may be strong enough to repel them from the atom entirely. In each case, the electrons are removed from the atom by direct interaction of the ionizing radiation with the atoms themselves. Hence, any type of ionizing radiation which carries electric charge (such as alpha or beta particles) is referred to as directly ionizing radiation.
Types of radiation which do not carry an electric charge, such as x-rays, gamma rays and neutrons, are described as indirectly ionizing. Indirectly ionizing radiation moves through an absorbing medium without exerting any forces on the orbital electrons until by chance it collides with part of an atom. These interactions are described in more detail later in this module.
The term strongly ionizing is used to describe radiation which produces a high density of ions along its path. Alpha particles and other relatively heavy charged particles are strongly ionizing. Beta particles cause less ionization along their path than alpha particles but are still moderately ionizing.
X-rays and gamma rays produce the fewest ions as they move through material and are therefore considered to be weakly ionizing. Neutrons are a special case as they do not cause ionization directly. However, the products of their interactions with matter can range from weakly to strongly ionizing.
When radiation interacts with an atom, it is possible that the energy it transfers to the atom is not enough to cause ionization. An inner electron of an atom may receive enough energy to allow it to move into an excited state at a higher energy level but not enough to leave the atom completely. In this case excitation has occurred (see Figure 2).
Figure 10
The Process of Excitation
The energy gained by the absorber atom will be re-emitted as electromagnetic radiation when the electron returns to its original energy level. When we look at some of the methods of monitoring radiation in later modules, it will be important to know what we mean by excitation.
Compared with other particles, alpha particles are physically and electrically quite large, consisting of four nuclear particles and two positive charges. As alpha particles move through an absorbing material they exert electrical forces on the orbital electrons of the absorber. The orbital electrons will be pulled into higher energy shells or removed from the atom completely, thereby forming ion pairs.
An alpha particle can transfer large amounts of energy to the absorber over a short distance and produce a large number of ion pairs.For example, an alpha particle with an energy of 3.5 MeV will travel approximately 20 mm and produce roughly one hundred thousand ion pairs in air. The same energy alpha particle would travel approximately 0.03 mm (or 30 m) in tissue.
Alpha particles are the least penetrating of the radiations. The range of alpha particles will be important later when we look at problems encountered in monitoring for alpha radiation and when we consider how much of a hazard alpha particles are, both inside and outside the human body.
60.PRACTICAL ACTIVITY 1
Range of Alpha Particles in Air
This is a practical assignment in which you will measure how far alpha particles from a given source will travel in air. The details are found in your workbook. There are many errors involved in performing this experiment and your answer will not be a true value for the range of the alpha particles in air. However, it should give an appreciation of the range and also demonstrate the fact that alpha particles are monoenergetic (i.e. they have a single energy). You should contact your supervisor now to arrange a suitable time to complete this practical task.
60.14.1Direct Ionization
Compared with alpha particles, beta particles are very small. They have a single negative charge and almost negligible mass. In fact, they are identical to the orbital electrons of the absorber atom and their similarity in charge can cause direct ionization by repelling the orbital electrons from the atom.
Beta particles are less likely to cause direct ionization along their path than alpha particles and so will travel further than an alpha particle of the same energy. Hence, a 3.5 MeV beta particle will travel approximately 11 m in air and 17 mm in tissue. Low energy beta particles, however, do not travel very far in air or tissue (e.g. the 0.157 MeV beta particle emitted from carbon-14, travels only 300 mm in air and 0.8 mm in tissue).
60.24.2Bremsstrahlung Production
Some beta particles, particularly those with higher energy, may travel close to the positively charged nuclei of the absorber atoms. These particles will experience an attractive force which causes them to be deflected, thus losing energy which appears in the form of x-rays. This type of radiation is known as bremsstrahlung, a German term meaning ‘braking radiation’. Figure 3 shows a beta particle being deflected by the nucleus of a tungsten atom (atomic number 74) and x-rays being produced.
Figure 11
Bremsstrahlung Production
The production of bremsstrahlung radiation as a product of the interaction of beta particles with matter has important repercussions for radiation protection. As you will already know from having medical x-rays yourself, x-rays can travel through a large amount of material. This means that the bremsstrahlung produced during the absorption of beta radiation may pose more of a radiation problem than the initial beta radiation. To limit the amount of bremsstrahlung being produced, we need to understand its production in a little more detail.
Firstly, heavier nuclei (with higher atomic number and greater positive charge) are much more effective than lighter nuclei at producing bremsstrahlung radiation. This is because the force on the beta particle from the positively charged nucleus of heavier nuclei is much greater and hence, the deflection of the beta particle is also much greater. Secondly, during the production of bremsstrahlung all of the kinetic energy of the beta particle may be converted to x-ray radiation but usually only part of this energy is converted. In fact, the fraction of the incident beta energy converted into x-rays is directly proportional to both the maximum energy of the beta particles, and the atomic number of the absorber. This relationship may be written as shown in Equation 1.
F = 3.3 x 10-4ZEmax[1]
whereF = the fraction of the incident beta energy converted into X-rays
Z = the atomic number of the absorber
Emax = the maximum energy of the beta particle (in MeV)
From this equation, it is easy to see that interactions with low Z materials (such as water, Perspex or aluminium) produce the least bremsstrahlung, whereas high Z materials (such as lead) produce the most. An example of this is the case when beta radiation from phosphorus-32 (Emax = 1.7 MeV) passes through lead or perspex. In the case of lead (Z = 82), approximately 5% of the energy is converted to x-rays. However, if the absorbing material is Perspex (effectively Z = 7), then less than 0.5% is converted. You will learn later (in Module 2.2 Protection from External Radiation Hazards) how this information can be used in practice to design suitable shielding.
61.PRACTICAL ACTIVITY 2
Range of Beta Particles in a Medium
In this practical assignment you will measure the approximate range in air and other media of beta particles from a given source. Details are given in your workbook. You should contact your supervisor now to arrange a convenient time to complete the assignment.
62.SELF-CHECK 1
Now see how much you have understood by answering the following questions in your workbook:
Match the follow terms ionization, excitation, bremsstrahlung, ion pairs, ionizing radiation with the following descriptions:
Positively and negatively charged particles resulting from ionization.
X-ray radiation produced when beta particles are deflected by heavy atoms.
The process of removing an electron from an atom.
The type of radiation which can cause ionization in body tissue.
The process of giving an orbital electron enough energy to move into a higher energy level orbit.
Complete the following table
Type of Radiation
Ionizing Strength
Alpha
Beta
Gamma and x-ray
Neutron
Explain what is meant by the following terms and give examples of each:
directly ionizing radiation.
indirectly ionizing radiation.
a)Describe how bremsstrahlung radiation is produced.
b) Which two factors control the amount of bremsstrahlung radiation produced when beta radiation passes through an absorber?
c)List the following materials in order of their production of bremsstrahlung radiation for a phosphorous-32 source (Emax = 1.7 MeV) starting with the material which would produce the most bremsstrahlung radiation: steel (effective Z = 26), plastic (effective Z =12), perspex (effective Z = 7), aluminium (Z = 13), lead (Z = 82).
Now check your answers with the model answers in your workbook.
The way in which gamma rays and x-rays interact with material through which they pass is different to that of either alpha or beta radiation. Alpha and beta particles have definite ranges and they lose energy continuously until all of their energy has been transferred to the absorber. On the other hand, x-rays and gamma rays travel long distances between interactions and their energy cannot be completely absorbed, only reduced in intensity.
There are three principal ways in which gamma and x-rays interact with matter. These are as follows:
The photoelectric effect;
Compton scattering; and
Pair production.
Each of these produces ionization in the absorber and this is called primary ionization. The electrons produced in the primary ionization event then go on to ionize other atoms in the absorber. This is known as secondary ionization. A single primary ionization event can cause very many secondary ionizations and excitations. It is important to remember that it is the secondary interactions which will transfer most of the energy to the absorbing medium, and the way in which this occurs in human tissue will determine the potential for damage to tissue.
The interactions of x- and gamma rays with matter are a result of the particulate nature of electromagnetic radiation. Therefore the interactions will be described in terms of photons or packets of electromagnetic energy.
62.15.1The Photoelectric Effect
A photon of relatively low energy (less than 1 MeV) may transfer all its energy to a tightly bound electron in an inner shell, causing the electron to be ejected from the absorber atom (see Figure 4).
Figure 12
The Photoelectric Effect
The ejected electron, known as a photoelectron, will move through the absorber causing secondary ionization and excitation.
For typical photon energies, the most probable origin of the photoelectron is the innermost electron orbit or K shell. The absorber atom is left in an excited state with a vacancy in one of its inner shells. This vacancy is quickly filled by the capture of a free electron from the absorber, or by rearrangement of the electrons from other shells of the atom. In the latter case, electrons move from a higher energy shell to fill the vacancy; as they do so, energy is released in the form of characteristic x-rays. In a few cases, the x-rays produced by the above process will interact with an outer shell electron and cause it to be ejected from the atom. It has a low energy and is known as an auger electron. Figure 5 shows the production of auger electrons.
Figure 13
Auger Electron Production
Note that the photoelectric effect is most likely to occur in materials with a high atomic number, so a material such as lead (Z = 82) makes a useful shielding material for low energy photons. The photoelectric effect is relatively unimportant in low Z materials such as aluminium.
62.25.2Compton Scattering
Compton scattering involves a collision between a photon and an outer shell electron in which only part of the photon energy is transferred to the absorber atom. The electron is released from the atom (primary ionization) and will continue moving through the absorber causing secondary ionization and excitation. The photon is scattered with reduced energy and may also continue to interact with other absorber atoms. Figure 6 shows an incoming photon releasing an outer shell electron and being scattered with a reduced energy.
Figure 14
Compton Scattering
The angle at which the photon is scattered depends on its original energy and the energy transferred to the electron. Low energy photons transfer very little energy to the released electron and are scattered through large angles. However, high energy photons (10 to 100 MeV) transfer most of their energy to the released electrons and are not scattered very much.
Compton scattering is most important for photon energies between about 0.2 and 5.0 MeV, and predominates in absorbers with higher values of Z.
62.35.3Pair Production
Pair production takes place when a photon with energy greater than 1.02 MeV interacts with the strong electric field close to the heavy nucleus of an absorber atom and produces two particles, an electron and a positron. The energy value of 1.02 MeV is the energy equivalent of the total mass of the positron-electron pair and any photon energy in excess of this value provides kinetic energy to the electron and positron and may also cause the nucleus of the target atom to recoil.
The electron and positron then move off and lose kinetic energy through secondary ionization. A positron cannot exist without kinetic energy so when it has lost all its energy it will combine with an absorber atom electron in a process called annihilation. In this process, the two particles destroy each other and are converted into two annihilation photons, each of 0.51 MeV. These photons are emitted in opposite directions from each other.
Figure 7 shows the whole process of pair production and annihilation in the electric field around the nucleus of a lead atom.
Figure 15
Pair Production
For photons with energies above the threshold, the probability that pair production will take place increases with atomic number of the absorber. The effect also increases with photon energy, slowly from 1.02 to 5 MeV and more rapidly above that. Pair production is the most likely interaction for high energy photons in materials with a high atomic number.
62.45.4Summary of Photon Interactions
In practice, when a photon interacts with an absorber, a complicated series of events takes place. There may be thirty interactions or more before all the energy of the photon has been transferred to the absorber. Table 1 summarises the three most important interactions
Table 12
Photon Interactions
Photoelectric Effect | Compton Scattering | Pair Production | |
Part of atom involved | Inner shell electron | Outer shell electron | Nucleus |
Photon energies | Low (< 1 MeV) | Medium (0.2 to 5 MeV) | High (> 1.02 MeV) |
Z of absorber | Increases with Z | Independent of Z | Increases with Z |
Outcome | Inner shell electron (photoelectron) is ejected from atom. Characteristic x-rays produced. | Outer shell electron ejected from atom. Photon scattered with reduced energy. | Electron-positron pair produced. Positron undergoes annihilation to form two 0.51 MeV photons. |
Figure 8 shows how the probability of each interaction depends on the energy of the incident photon and the atomic number of the absorber. The energy of the incident photon is indicated (in MeV) on the x-axis as a logarithmic scale. The atomic number of the absorber, Z, is shown on the y-axis as a linear scale. Remember that this is only a diagrammatic way of showing what interactions might occur. It does not predict which interactions will occur.
Figure 16
Relative Importance of Three Major Types of Photon Interactions
63.SELF-CHECK 2
Now see how much you have understood by answering the following questions in your workbook:
a) Name the three principal photon interactions.
b) Chose one of these interactions and, with the aid of diagrams, describe the process in detail.
a) Which of the three processes can only take place with photons with energies over 1.02 MeV?
b) Which of these predominates for low energy photons?
c) Which process involves interaction of the photon with an outer shell electron?
d) Which of these results in the production of characteristic x-rays?
e) Which of these produces two annihilation photons?
Now check your answers with the model answers in your workbook.
Neutrons are one of the particles found in the nuclei of atoms and can be released by fission or nuclear reactions. All free neutrons start life as fast neutrons, with energies greater than about 0.10 MeV. Fast neutrons are slowed down and their energy reduced (or moderated) by collisions with nuclei of absorber atoms. The neutrons are then redefined as intermediate (from above 0.025 eV up to 0.10 MeV) or thermal (0.025 eV). (Note that the definitions of intermediate and fast neutrons are not exact and you will find that different books quote different energy ranges. The differences are not important in the descriptions of the interactions given in this module.)
Neutrons interact with matter in three ways and these are as follows:
Elastic scattering
Inelastic scattering
Neutron capture
Elastic and inelastic scattering serve as processes to slow down fast and intermediate neutrons. When neutrons attain thermal energies they are then captured by neutron capture processes.
63.16.1Elastic Scattering
Elastic scattering is the name given to the process whereby fast or intermediate neutrons undergo elastic collisions with the absorbing material and the neutron is deflected or scattered. (An elastic collision is one in which the total kinetic (or movement) energy of the particles is conserved i.e. it is the same after the collision as it was before the collision.) In the elastic collision, a fast or intermediate neutron collides with a nucleus of the absorbing medium and loses some of its initial kinetic energy. This energy is transferred to the target nucleus as kinetic energy and the target nucleus moves off. The neutron is then deflected or scattered (see Figure 9). Note that the direction of recoil of the target particle and the amount of scattering of the neutron depends on the amount of energy transferred.
Figure 17
Elastic Neutron Scattering
The most efficient way in which the kinetic energy of a neutron is transferred to an absorbing medium is for the neutron to strike something of about the same mass e.g. another neutron or a proton. If the neutron strikes a target very much larger than itself, it will bounce off the target, rather like a cricket ball bouncing off a cannon ball, and lose very little energy. Similarly if the neutron hits a target a lot smaller than itself, the target will be pushed out of the way, rather like a cricket ball pushing a table tennis ball out of the way, and very little energy is lost by the neutron. However, when a neutron collides with a proton or neutron, the energy of the incoming neutron is shared between the target particle and the neutron. In practical terms, this means that hydrogen-rich materials (such as water, concrete and paraffin) are particularly useful for neutron shielding because the single proton hydrogen atoms allow the energy of the incoming neutrons to be dissipated relatively quickly.
It is important to remember that recoiling nuclei resulting from elastic scattering of neutrons are heavy charged particles. They lose their energy by ionization and excitation at a high rate in the same way as alpha particles and are hence classed as strongly ionizing radiation. For this reason, and the fact that elastic scattering is the most likely interaction for fast neutrons in biological tissue, neutrons can be particularly damaging to the human body.
63.26.2Inelastic Scattering
A more complicated neutron interaction can take place where fast or intermediate neutrons collide with a target much larger than itself and do not bounce off (as is the case in elastic scattering), but are actually absorbed into the target nucleus. After a short time, the neutron is re-emitted with reduced energy, but the target nucleus is left in an excited state. The nucleus is then quickly de-excited by the emission of a gamma ray. As the total kinetic energy is not conserved in this collision (because some of the energy has been used to produce the gamma ray), this type of collision is known as an inelastic collision. The whole process is referred to as inelastic scattering (see Figure 10).
Figure 18
Inelastic Neutron Scattering
The probability of inelastic scattering taking place depends on the energy of the neutron, increasing as the neutron energy increases. Where this type of reaction is possible, the emission of gamma rays must be taken into account when shielding against neutrons.
63.36.3Neutron Capture
When fast and intermediate neutrons have been slowed down by elastic and inelastic collisions, they become thermal neutrons with energies in the order of 0.025 eV. Most thermal neutrons are captured and become part of the absorbing nucleus. The nucleus must then get rid of excess energy, usually by emitting a gamma ray (see Figure 11).
Figure 19
Neutron Capture
Neutron capture may also result in some of the following reactions:
In some light nuclei the capture of a neutron leads to the emission of a proton.
Neutron capture in boron or lithium leads to alpha emission.
Neutron capture in certain heavy nuclei such as uranium or plutonium can lead to fission.
Neutron capture may produce radioactive isotopes in a process known as neutron activation (see Module 1.3, Ionizing Radiation and Radioactive Decay). One example of neutron activation is the irradiation of stable iridium to produce iridium-192. (This isotope is a gamma/beta emitter which is used in industrial gamma radiography.)
The ability of an absorber to capture neutrons depends on a function called its capture cross section, which is measured in a unit called the barn. Cadmium, lithium and boron are particularly good absorbers of thermal neutrons but the neutron absorption in cadmium and boron produces gamma radiation which should be considered when planning neutron shielding. In fact, a combination of polyethylene and boron or lithium makes a good neutron shield. The hydrogen atoms in the polyethylene thermalize the neutrons which are then suitable for capture by the boron or lithium nuclei. The alpha particles produced by this absorption are quickly attenuated (reduced in intensity) and the remaining hazards are the 0.48 MeV gamma from the boron interaction, and possibly a 2.26 MeV gamma which results if the hydrogen nuclei absorb these neutrons. The absorption of thermal neutrons by hydrogen is not common as the capture cross sectionof hydrogen is relatively low.
63.46.4Summary of Neutron Interactions
Table 2 summarises the interactions between neutrons and matter.
Table 13
Neutron Interactions
Elastic Scattering | Inelastic Scattering | Neutron Capture | |
Neutron Energies | Fast | Fast | Thermal |
Z of Absorber | Low | High | Depends on capture cross-section |
Problems | Recoil nucleus is strongly ionizing. The most common interaction in biological tissue. | Recoil nucleus is strongly ionizing. Gamma rays are emitted and should be considered when designing shielding. | Possible high energy gamma rays produced. |
64.SELF-CHECK 3
Now see how much you have understood by answering the following questions in your workbook:
Give typical energy ranges of the following types of neutrons:
Thermal
Fast
Intermediate
Fill in the gaps with an appropriate word or phrase:
In _________ _________, the total kinetic energy before the collision is the same as after the collision. In this type of neutron interaction, a neutron collides with a _______ of the absorbing atom and _______ some of its initial energy.
In _________ _________, a neutron collides with a target much greater than itself and is __________ into the target nucleus. The neutron is then _________ with reduced energy and this is closely followed by the emission of a ________ ________. In this type of interaction the total kinetic energy is not conserved because _____________________________________________________.
When ________ and __________ neutrons have been slowed down through _________ and __________ scattering processes, they become ________ neutrons. These neutrons are then __________ and become part of the absorbing nucleus. The nucleus must then get rid of excess energy, usually by emitting a ________ ________.
a) Which type of neutron interaction is most important in relation to the human body?
b) Why is this so?
Now check your answers with the model answers in your workbook.
Table 3 provides a summary of the major ways in which ionizing radiation interacts with matter.
Table 14
Interaction of Radiation with Matter
Radiation | Process | Remarks |
Alpha | Inelastic collisions with bound electrons | Leads to excitation and ionization |
Beta |
|
|
|
| |
Gamma and X-Rays |
|
|
|
| |
|
| |
Neutron |
|
|
|
| |
|
|
65.KEY POINTS
Ionization is the process whereby electrons are removed from atoms and ion pairs are formed. Ionizing radiation (alpha particles, beta particles, gamma rays, x-rays and neutrons) is radiation with sufficient energy to cause ionization.
When excitation occurs, an electron is moved into a higher energy shell but is not completely removed from the atom.
Strongly ionizing radiation produces a high density of ions along its path e.g. alpha particles and other relatively heavy charged particles
Beta particles cause less ionization along their path than alpha particles but are still moderately ionizing.
X-rays and gamma rays produce the fewest ions as they move through material and are therefore considered to be weakly ionizing.
The products of neutron interactions can range from weakly to strongly ionizing.
Any type of ionizing radiation which carries electric charge (such as alpha or beta particles) is referred to as directly ionizing radiation.
Types of radiation which do not carry an electric charge, such as x-rays, gamma rays and neutrons, are indirectly ionizing.
Alpha particles have a very short range in air.
Beta particles have a moderate range in air.
X-rays and gamma rays are reduced in intensity when passing through matter and have a high penetrating ability
When beta particles interact with matter, they may be deflected and produce x rays called bremsstrahlung radiation.
The fraction of the incident beta energy converted into bremsstrahlung x-rays is directly proportional to both the maximum energy of the beta particles and the atomic number of the absorber.
X-rays and gamma rays interact with matter by the photoelectric effect, Compton scattering and pair production. The interaction is dependent on the energy of radiation and the material through which the radiation passes.
In the photoelectric effect, a photon of relatively low energy (less than 1 MeV) may transfer all its energy to a tightly bound electron in an inner shell, causing the electron to be ejected from the absorber atom and a characteristic x-ray to be produced.
In some cases, the x-rays produced by the photoelectric effect will interact will an outer shell electron and cause it to be ejected from the atom. This electron is known as an Auger electron.
The photoelectric effect predominates in material of high atomic number and with photons of relatively low energy (less than 1 MeV).
Compton scattering involves a collision between a photon and an outer shell electron. The electron is ejected from the atom and may go on to cause secondary ionization. The photon is scattered with reduced energy.
Compton scattering predominates in absorbers with higher atomic number and for photon energies between 0.2 and 5.0 MeV.
Pair production occurs when photons with energy greater than 1.02 MeV interact with the strong electric field close to the heavy nucleus of an absorber atom. An electron-positron pair is produced.
The electron and positron produced from pair production will lose kinetic energy through secondary ionization. As a positron cannot exist without kinetic energy, when it has lost all its energy it will combine with an absorber atom electron in a process called annihilation.
During annihilation, the two particles (positron and absorber electron) destroy each other and are converted into two annihilation photons, each of 0.51 MeV. These photons are emitted in opposite directions from each other.
Pair production predominates for high energy photons (greater than 1.02 MeV) in materials with high atomic number.
Neutrons are classified as fast, intermediate or thermal depending on energy.
Fast neutrons have energies greater than 0.1 MeV
Intermediate neutrons have energies between 0.025 eV and 0.1 MeV.
Thermal neutrons have energies of approximately 0.025 eV.
Fast and intermediate neutrons are slowed by elastic and inelastic scattering to from thermal neutrons.
Thermal neutrons may then be captured by target atoms.
An elasticcollision is one in which the total kinetic energy of the particles is conserved.
Elastic scattering is the name given to the process whereby fast or intermediate neutrons undergo elastic collisions with the absorbing material and the neutron is deflected or scattered.
Elastic scattering of concern in the human body as it is the most predominant interaction with body tissues and the recoiling nuclei are strongly ionizing and may go on to cause secondary ionization.
An inelasticcollision is one in which the total kinetic energy of the particles is not conserved.
Inelastic scattering occurs when fast or intermediate neutrons collide with a target much larger than itself and are absorbed into the target nucleus. After a short time, the neutron is re-emitted with reduced energy, but the target nucleus is left in an excited state. The nucleus is then quickly de-excited by the emission of a gamma ray.
When fast and intermediate neutrons have been slowed down by elastic and inelastic collisions, they become thermal neutrons. Most thermal neutrons are captured and become part of the absorbing nucleus. The nucleus must then get rid of excess energy, usually by emitting a gamma ray.
66.FINAL ASSIGNMENT
This assignment is to be completed under test conditions, so spend some time now studying this module. Then contact your supervisor to arrange a suitable time to complete the assignment. Remember that laboratory work must also be completed satisfactorily before you receive full credit for this module.
67.GLOSSARY OF TERMS
Annihilation | The process whereby a positron with no energy combines with an electron to produce two annihilation photons each of energy 0.51 MeV. In the process, the positron and electron are destroyed and the resultant photons travel in opposite directions from each other. |
Auger electron | An electron that is sometimes produced subsequent to the photoelectric effect. It occurs when X-rays (produced from higher energy electrons dropping to lower energy states) interact with an outer shell electron and cause it to be ejected from the atom. |
Bremsstrahlung | The X-ray radiation which is produced when beta particles are deflected by positively charged nuclei. This is known as braking radiation. |
Capture cross section | The probability that a neutron will be captured by absorber atoms. |
Compton scattering | An elastic collision between a photon and an electron in which only part of the photon energy is transferred to the absorber atom. |
Directly ionizing | Radiation which carries electric charge and which therefore exerts electrical forces on the orbital electrons of the material through which it passes. |
Elastic collision | A collision in which the total kinetic energy of the particles is the same after the collision as it was before the collision. |
Elastic scattering | The result of an elastic collision between a neutron and a nucleus of an absorbing medium which causes the target nucleus to gain kinetic energy and the neutron to be deflected or scattered. |
Excitation | When an inner electron of an atom receives enough energy to raise it to a higher energy level but not enough to leave the atom completely. |
Fast neutron | A neutron with an energy greater than 0.1 MeV. |
Indirectly ionizing | Radiation which carries no electric charge but which can cause ionization by colliding with part of an atom. |
Inelastic collision | A collision in which the total kinetic energy of the particles is less after the collision than it was before the collision. |
Inelastic scattering | The result of an inelastic collision between a neutron and a target much larger than itself which causes the neutron to be absorbed into the target nucleus and then re-emitted with a reduced energy. The total kinetic energy after the collision is not the same as before because some of the energy appears as an accompanying gamma ray and which is emitted from the excited target nucleus. |
Intermediate neutron | A neutron with an energy in the range 0.025 eV to 0.1 MeV. |
Kinetic energy | The energy which causes things to move. |
Ion pair | The combination of a positive and negative ion. |
Ionizaton | The complete removal of electrons from atoms. |
Ionizing radiation | Any particle or ray which has sufficient energy to cause ionization. |
Monoenergetic | Particles or rays which all have the same energy. |
Neutron activation | The process whereby neutrons from a neutron source are absorbed by a stable atom thereby producing artificial radionuclides. |
Neutron capture | The process whereby thermal neutrons are captured by, and become part of, the absorbing nucleus. The excess energy is usually released by emitting a gamma ray. |
Pair production | The process whereby a photon of energy greater than 1.02 MeV interacts with a strong electric field close to the heavy nucleus of an absorber atom and produces two particles, an electron and a positron. |
Photoelectric effect | The process whereby a photon of relatively low energy (less than 1 MeV) transfers all its energy to a tightly bound electron in an inner shell. This electron is then ejected from the atom. |
Photoelectron | An electron produced as the result of the photoelectric effect. |
Photon | A small packet of energy transmitted in the form of waves. |
Primary ionization | The initial ionization which occurs as the result of ionizing radiation interacting with matter. |
Secondary ionization | The process whereby the electrons produced from primary ionization then go on to ionize other atoms in the absorber. |
Strongly ionizing | Radiation which produces a high density of ionization along its path. |
Thermal neutron | A fast neutron that has been slowed down by a series of elastic and inelastic collisions. The energy is usually of the order of 0.025 eV. |
Weakly ionizing | Radiation which produces a low density of ionization along its path. |
INTERNATIONAL ATOMIC ENERGY AGENCY AUSTRALIAN NUCLEAR SCIENCE AND TECHNOLOGY ORGANISATION |
DISTANCE LEARNING MATERIALS
RADIATION PROTECTION
Module – 1.5
Prepared by Safety and Radiation Science
Australian Nuclear Science and Technology Organisation
With the assistance of consultants in Australia and the United Kingdom, and IAEA experts from Korea, Mongolia, New Zealand, the Philippines and Thailand
Use of this material, acknowledging the IAEA and ANSTO as the source, is permitted for non-profit training
Acknowledgements
This material has been prepared by an extensive team of international experts from the fields of radiation protection, medicine and education. It is not possible to mention by name all those who have had an input to; the initial planning; writing modules and workbooks; preparing and marking final assignments; proof-reading and editing; using the material and providing valuable feedback; organizing and hosting review meetings; and general administrative support.
The support of ANSTO management in providing the resource and encouragement is gratefully acknowledged.
The enthusiastic support of IAEA Technical Officers has been vital to the success of this project
PART 1
BASIC KNOWLEDGE
MODULE 1.5
METHODS OF RADIATION DETECTION
CONTENTS
Before studying this module, it is important that you have read and understood the information in the previous four modules. In particular, you will need to have a good understanding of the information in Module 1.4 Interaction of Radiation with Matter.
An understanding of how the different types of detectors work will also assist you in your choice of detector and its method of use. Hence, this module provides the background information necessary to understand the later module, Module 2.4 Use of Radiation Monitoring Instrumentation. It is therefore important that you understand the information in this module before continuing with the course.
There is one practical activity associated with this module. You will find the relevant information in your workbook. Remember that this practical activity must be completed before you can gain full credit for this course. You should therefore make sure that you arrange a suitable time with your supervisor for doing this practical work.
TIME ALLOCATIONIt is estimated that you will need to spend eight to ten hours to complete this module before commencing the assignment. This time estimate is for guidance only. Do not worry if you need more time to understand the module.
You will need to have writing materials to take notes and answer questions and assignments in the module.
When you have completed this module you will be able to do the following:
|
NOW YOU ARE READY TO START WORK
Since ionizing radiation cannot be detected by our bodies’ senses we rely on the detection of changes produced by the radiation when it interacts with materials. Radiation detectors operate by detecting a change in the absorbing medium that is caused by the transfer of energy from the ionizing radiation to this medium. There are several effects caused by ionizing radiation which allow us to detect and measure the radiation and these are as follows:
Ionization;
Scintillation;
Thermoluminescence;
Chemical mechanisms;
Heating; and
Biological mechanisms.
Ionization is caused directly by alpha and beta radiation and indirectly by x rays, gamma and neutron radiation. The ion pairs which are produced can be collected, and the number of ion pairs collected can be related to the amount of radiation causing the ionization. Many radiation monitoring instruments use ionization as the detection mechanism.
Scintillation is the production of light following the movement of electrons from high energy levels orbits to lower energy levels within an absorbing material. The electrons have moved into higher energy orbits by the process of excitation. (Remember from module 1.4 Interaction of Radiation with Matter that excitation occurs when the energy from ionizing radiation causes electrons to move into higher energy levels temporarily). The light released can be converted to an electrical signal. The size of the electrical signal depends on the number of electrons moved into higher energy orbits and can therefore be related to the amount of radiation causing the scintillation. Scintillation is a very important detection mechanism for radiation monitoring and detectors which use this mechanism are known as scintillation detectors.
When electrons in certain materials absorb energy they will move into higher energy levels or ‘forbidden bands’. They remain trapped in these bands until the material is heated to a certain temperature. The heat energy releases the electrons and the material emits light as the electrons move back to their original level. The light is converted to an electrical signal which can be related to the amount of incident radiation. Thermoluminescent materials are used for monitoring personal doses (i.e. dose to individual people) and will be discussed further in Module 2.5 Personal Dosimetry.
Ionizing radiation can cause chemical changes. This effect is observed in the use of photographic film for personal dosimetry, medical x-rays and industrial radiography. In some cases, ionizing radiation increases the rate at which chemical reactions occur and this mechanism can be used for measuring high doses during the irradiation of medical equipment.
Ionizing radiation can increase the temperature of the absorbing medium and careful measurement of this increase can give a radiation dose measurement. This technique (known as calorimetry) is not suitable for routine measuring equipment in radiation protection as high doses are needed to cause even small temperature rises. It is however used as a primary standard for instrument calibration (see Module 2.4 Use of Radiation Monitoring Instruments).
High doses of radiation can cause biological changes in living cells. This will be discussed further in Module 1.6 Biological Effects of Ionizing Radiation. Biological changes are only used for dose estimation in extreme circumstances where personnel are suspected of having accidentally received a high dose.
Table 1 summarizes the mechanisms which can be used to detect ionizing radiation.
Table 15
Summary of the Mechanisms Used for Radiation Detection
Mechanism | Main Use | Type of Instrument | Detector |
Ionization | Radiation monitoring instruments | 1. Ion chamber 2. Proportional counter 3. Geiger-Müller counter 4. Solid state |
|
Scintillation | Radiation monitoring instruments | Scintillation counter | Crystal or liquid |
Thermoluminescence | Personal dosimetry | Thermoluminescent Dosimeter (TLD) | Crystal |
Chemical | Personal dosimetry | Photographic film | Photographic emulsion |
Heating | Primary standard and instrument calibration | Calorimeter | Solid or liquid |
Biological | Accident situations | Biological tissue | Biological tissue |
Now see how much you have understood by answering the following questions in your workbook:
Why do we need to monitor ionizing radiation?
How do radiation detectors operate?
a) List the six mechanisms of radiation detection.
b) Which of these are important for radiation monitoring instruments?
c) Which of these are important for monitoring personal dose?
Now check your answers with the model answers in your workbook.
As already mentioned, many radiation monitoring instruments use the ionization as the detection mechanism, and the two types of detectors which are most commonly used are gas-filled detectors and solid state conductivity detectors.
Gas-filled detectors consist of a chamber filled with a gas (often air) and two voltage plates known as electrodes. The positive electrode is called the anode and is often in the centre of the chamber. It is electrically insulated from the outer casing. The outer casing of the chamber is often the negative electrode or cathode. Figure 1 shows a simple diagram of a gas-filled detector.
Figure 20
A Simple Gas-Filled Detector
Incoming radiation interacts with the walls of the chamber or the gas particles and produces ion pairs. When a voltage is applied between the electrodes, positive ions are attracted towards the negatively charged cathode, and the electrons are attracted towards the positively charged anode. A charge builds up on the anode, causing a voltage change in the circuit. This change in voltage is referred to as a pulse, and the presence of this pulse causes a current to flow in the external circuit. By detecting either this pulse or current, we can detect the presence of ionizing radiation.
The size of the pulse depends on the number of electrons collected by the anode and this can depend on the amount of ionizing radiation entering the chamber as well as its type and energy.
In addition, the size of the pulse is also a function of the voltage applied between the cathode and the anode. Figure 2 shows how the pulse size (or height) varies as the applied voltage is increased.
Figure 21
The Variation of Pulse Height with Voltage for a Gas-filled Detector
As you can see from Figure 2, this variation in pulse height with voltage shows a number of clearly defined regions. These regions are known as the recombination, ion chamber, proportional, Geiger-Müller and continuous discharge regions.
When the voltage on the chamber is quite low, the force on the ions (which attracts them to the electrodes) is also quite low. In this situation, there are two processes which are competing for the ions. One of these is ion collection and the other is ion recombination. This means that, after an ion has been formed, it may recombine to become neutral again before it can be collected by the electrodes. Hence, the pulse in the external circuit depends on the outcome between these two processes.
As the voltage across the electrodes is increased, more of the ions reach the electrodes and the pulse size increases (see Figure 2). However, recombination of ions is still significant and so this region is known as the recombination region. Gas-filled detectors are not normally operated in this region as the recombination of ions makes it very difficult to measure the quantity of incoming radiation.
When the voltage is large enough, almost all the ions generated will reach the electrodes and the loss of ions through recombination is negligible. In this region nearly all the ions are being collected and the pulse size no longer increases with applied voltage. Instead, it levels out to a plateau known as the ion chamber region (see Figure 2).
The current flowing in the circuit also reaches a maximum value known as the saturation current. This saturation current is proportional to the amount of radiation entering the chamber and if the amount of radiation is increased, then the saturation current is also increased.
As the voltage is increased past the ion chamber region, the pulse size starts to increase again. We can explain why the pulse size increases if we consider what is happening to the ions. As the applied voltage is increased, the ions not only gain enough energy to reach the electrodes, but they also gain enough energy to be accelerated. This acceleration causes more ion pairs to be produced through secondary ionization of the particles in the gas. This process is known as gas multiplication and it results in the collection of more ions and therefore a larger pulse.
Figure 3 shows a single electron being accelerated towards the anode and producing an avalanche of ions.
Figure 22
Gas Multiplication in the Proportional Region
The increase in the number of ions collected is a function of the applied voltage. However, the total pulse size that results is also proportional to the initial number of ions produced in the gas. For this reason, the region of a gas-filled detector where this occurs is known as the proportional region.
If the voltage is increased still further, the gas multiplication is so great that a single ionizing particle produces multiple avalanches along the length of the anode, resulting in a very large pulse. The region where this occurs is known as the Geiger-Müller(G-M) region and in this region, the size of the pulse is the same, regardless of the quantity of energy originally deposited. Instead, the pulse size is controlled more by the external circuit than by the gas-filled chamber, and the pulse height shows a very small rise as the voltage is increased (see Figure 2).
If the voltage is increased beyond the Geiger-Müller plateau, then the voltage is high enough to ionize the gas molecules directly and a large signal is generated even when the radiation field is removed. This is called the continuous discharge region and as the readings can be misleading, radiation detectors should not be operated in this region.
!
Radiation detectors must not be operated in the continuous discharge region.
Now see how much you have understood by answering the following questions in your workbook:
What is the basic detection mechanism on which all gas-filled detectors depend?
Fill in the gaps with a suitable word or phrase:
Gas-filled detectors consist of a chamber filled with a ____ and two voltage plates known as __________. The positive electrode is called the _______ and the negative electrode is called the __________. Incoming radiation interacts with the walls of the chamber or the gas particles and produces ____ _______. When a voltage is applied between the electrodes, the _________ _____ are attracted towards the negatively charged electrode, and the _________ are attracted towards the positively charged electrode. A charge builds up, causing a voltage change in the circuit. This change in voltage is referred to as a__________, and this causes a current to flow in the external circuit. By detecting either this voltage change or current, we can detect the presence of ionizing radiation.
3.a)List the five regions of a gas-filled detector.
b)Complete the following table by matching the different regions with their descriptions.
Region
Description
1.
a) The region where the applied voltage is large enough to cause acceleration of ions.
2.
b) The region where almost all ions are being collected and the current reaches a constant value known as the saturation current.
3.
c) The region where many ions do not reach the electrodes.
4.
d) The region where the voltage is high enough to ionize the gas molecules directly.
5.
e) The region where the size of the pulse is the same regardless of the amount of energy deposited.
4.Which of these regions are used for detecting ionizing radiation?
Now check your answers with the model answers in your workbook.
Before considering the operation of the different types of gas-filled detectors, it is important to understand the concepts of dead time, recovery time and resolving time. This is because if resolving time of a detector is too long, at high counting rates the pulses from the detector may be spaced so closely in time that a lot of the information is lost. This means that the total counts may then be grossly underestimated.
The resolving time of a detector is defined as the minimum amount of time which must separate two events in order that they are recorded as two separate processes. The resolving time depends on the following factors:
The dead time of the detector (i.e. length of time for the signal or pulse to build up sufficiently for it to be detected); and
The recovery time (i.e. length of time for the detector to recover from an ionization event and return to its original condition).
Figure 4 shows how the dead time and recovery time for a Geiger-Müller detector combine to give resolving time.
Figure 23
Resolving Time for a G-M Tube
The detector resolving time will depend on what interactions are taking place in the detector. However, the overall resolving time of a whole instrument will also depend on the dead times associated with electronic components of the counting system.
In practice, the terms dead time and resolving time are used interchangeably. Whichever term is used, the quoted value is taken to be a measure of the ability of the instrument to distinguish two separate events which occur very close together in time. Manufacturers’ specifications often use the term dead time to describe the combined behaviour of the detector-counting system.
In the following section we will look at the three types of gas-filled detectors used in radiation monitoring instruments. The three types are as follows:
Ionization chambers;
Proportional counters; and
Geiger-Müller counters.
Ionization chambers (more commonly known as ion chambers) are designed to operate at saturation current in the ion chamber region shown in Figure 2. The average current output is measured and is proportional to the amount of radiation to which the chamber has been exposed. Since the output is not dependent on the voltage, there is no need for a highly stable power supply. However, it is important that the voltage is steady enough to ensure that saturation current is maintained.
To prevent the ion chamber from operating in the proportional region, the applied voltage is limited to less than that required to cause secondary ionization of the gas molecules. If a 25V power supply is used, the energy gained by an electron accelerating between the electrodes cannot be greater than 25 eV. This energy is not enough to cause further ionization.
The currents produced in ion chambers are very small, typically in the order of 10-12 A, and so must be amplified for measurement purposes. Hence instruments which incorporate ion chamber detectors require quite complex solid state circuitry to amplify these extremely small direct currents.
The design of ion chambers and the choice of filling gas depend on the particular application of the instrument. In portable radiation monitoring instruments, the chamber is usually air-filled and constructed of low atomic number materials. If the instrument is to be used to measure alpha or beta radiation, the chamber must have thin walls or a thin end window. The only way that this type of detector can be used to discriminate between the types of radiation is by placing a shield over the thin end window to prevent the alphas or betas from entering the chamber.
A typical beta/gamma portable radiation monitoring instrument containing a ion chamber detector is shown in Figure 5. Note the sliding metal plate which is incorporated into the design of the instrument. By sliding this plate over the end window of the ion chamber, you can distinguish between beta and gamma radiation.
Front View Rear View
Figure 24
A Typical Beta Gamma Radiation Monitoring Instrument Incorporating an Ion Chamber Detector
Note that ion chambers may also be incorporated in other instruments to distinguish between the different energies of the incoming radiation. This process is known as spectroscopy
A proportional counter operates in the proportional region as shown in Figure 2. The effect of the gas multiplication may increase the number of ions produced by 104. This means that for each electron produced by the original ionization event, there may be ten thousand additional electrons produced. Therefore each ionization event can be distinguished and counted.
The output from a proportional counter is a series of pulses which are counted by a counting circuit. In general, the resolving time is generally very short for these counters (less than a microsecond) so high pulse rates can be counted. However, the amplitude of each pulse is very small (of the order of millivolts) and pre-amplification is required before the pulses can be counted.
Have another look at Figure 2. You will notice that the slope of the graph in the proportional region is quite steep. This means that a slight variation in the applied voltage will have an effect on the pulse height. It is therefore important that a stable high voltage supply is used as this will ensure that any change in output is related to the change in incoming radiation rather than a change in the applied voltage.
As noted earlier, the total pulse size is proportional to the energy deposited by the radiation. Hence, proportional counters can be used with a pulse height discrimination circuit to distinguish between the types of radiation on the basis of their ionizing ability. For example, if the instrument is exposed to both alpha and beta radiation of about the same energy, the alpha radiation will produce a much greater number of ion pairs for the same path length so the pulse height will be much larger. If different external circuits are used, proportional counters can also be used to distinguish between the different energies of the incoming radiation (i.e perform spectroscopy)
Gas flow proportional counters are often used for counting samples (see Figure 6). The counting chamber has a very thin end window to allow alpha and beta particles to enter the chamber. The term gas flow is used because there must be a continuous flow of gas into the chamber to replace the gas that has diffused out through the thin end window. The type of gas used is usually a mixture of one of the inert gases with a hydrocarbon. For example, the gas commonly known as P-10 is frequently used. This gas consists of 90% argon and 10% methane.
Figure 25
A Gas Flow Proportional Counter
Geiger-Müllercounters operate in the Geiger-Müller (G-M) region shown in Figure 2 and use a filling gas such as the P-10 used in proportional counters. The height of the output pulse is independent of the energy of the ionizing particle. This means that it is not possible to distinguish electronically between alpha and beta radiation. Nor is it possible to measure or discriminate between the energies of the incoming radiation.
In the Geiger-Müller region, a discharge takes place all along the anode. This discharge must be quenched to prevent it from continuing by itself and to prevent multiple pulses forming. Use of an appropriate gas such as organic gases (e.g. ethyl alcohol) or halogens (e.g. chlorine, bromine) in addition to the filling gas will provide this quenching. Organic gases are used up during the quenching process, therefore organically quenched tubes have a limited useful lifetime of about 109 counts. Halogens have the advantage of not being used up in the quenching process so halogen-filled tubes have a much longer lifetime and are more useful in high count rate situations.
Geiger-Müller counters can be made in a variety of shapes and sizes. For the majority of applications, the counter is cylindrical and is known as a GM tube (see Figure 7).
Figure 26
A Radiation Monitoring Instrument with A Geiger-Müller Tube
A small G-M tube can be sufficiently sensitive to measure low dose rates whereas an ionization chamber with similar sensitivity would need to be much larger. If the counter is to be used to detect alpha and beta radiation, it must have a thin window to let the radiation enter the tube.
A G-M counter usually counts pulses in the same way as the proportional counter. However, it can be modified to measure average current as done by the ionization chamber. One advantage of G-M counters is that the output pulse is in the order of a few volts, so the signal does not require pre-amplification and the circuitry can be kept simple. This means that Geiger-Müller counters are very rugged and are therefore commonly used in the workplace for monitoring gamma radiation.
If G-M detectors are to be used as dose or dose rate meters, they must have a response similar to human tissue over a wide energy range. As G-M tubes over-respond at energies below about 200 keV, they are usually encased in suitable filtration material to ensure that the energy response is as linear as possible. This is called energy compensation.
One of the disadvantages of a G-M counter is their long resolving time. This is usually of the order of 100 to 300 microseconds which means that this counter is not suitable for high counting rates where pulses are forming very quickly. A condition called foldback can occur in high radiation fields where the pulses are being produced so quickly that they attach themselves to the tail of the previous pulse before the anode has been cleared of charge. Pulses following the initial pulse are therefore too small to be registered. If an instrument is turned on in a high radiation field, it will initially show a rise in reading, but this rapidly falls back to zero wrongly indicating that the field is safe.
!
A G-M counter may read zero in an area of high dose rate because of foldback.Additional circuitry can be built into the detector to prevent this potentially hazardous situation. Unless the instrument specifications provided by the manufacturer clearly state that foldback will not occur, you should always assume that it may be a problem.
Many portable radiation monitoring instruments use gas-filled detectors. Table 2 summarizes their properties and characteristics. Remember that it is important to consider the thickness of the window through which the radiation enters the detector if you are hoping to detect alpha or beta radiation.
Table 16
Summary of Gas-filled Detectors
Detector | Type of Radiation | Efficiency | Comments |
Ionization Chambers | Alpha | High (with suitably thin end window) | Used for counting and spectroscopy. |
Beta | Moderate (with suitably thin end window) | Used in portable radiation monitoring instruments. | |
Gamma | <0.1% | Used in portable radiation monitoring instruments. | |
X-rays | Depends on window thickness | Useful for most energies encountered in radiation protection. | |
Proportional Counters | Alpha | High (with suitably thin end window) | Used for counting and spectroscopy. |
Beta | Moderate (with suitably thin end window) | Used for counting all energies. Can be used for spectroscopy with energies <200 keV. | |
Gamma | <1% | ||
X-rays | Depends on window thickness | ||
Geiger-Müller Counters | Alpha | Moderate (with suitably thin end window) | Cannot discriminate between energies. |
Beta | Moderate (with suitably thin end window) | Cannot discriminate between energies. | |
Gamma | <1% | Cannot discriminate between energies but used (with suitable energy compensation) in portable radiation monitoring instruments | |
X-rays | Depends on window thickness | Cannot discriminate between energies but used (with suitable energy compensation) in portable radiation monitoring instruments |
Operational Characteristics of a Geiger-MüllerDetector
This is a practical assignment in which you will learn how to set up a G-M tube so that it will operate correctly and give consistent results. The details are found in your workbook. Contact your supervisor to arrange a convenient time to complete this practical task.
Now see how much you have understood by answering the following questions in your workbook.
a) Match the following terms with their descriptions:
Term
Description
1. Resolving time
a) The minimum amount of time which must separate two events in order that they are recorded as two separate processes.
2. Dead time
b) The length of time for the detector to recover from an ionization event and return to its original condition.
3. Recovery time
c) The length of time for the signal or pulse to build up sufficiently for it to be detected.
b) Why is it important to consider the resolving time of a gas-filled detector?
Which two types of gas-filled detectors require current amplification?
a) Which type of gas-filled detector requires a stable high voltage power supply?
b) Why is this so?
Which type of gas-filled detector can be used with a pulse height discriminator circuit to distinguish between the types of ionizing radiation?
Which types of detectors require thin end windows to discriminate between different radiation types?
a) Which type of detector is commonly used to detect gamma radiation in the workplace?
b) Why is this so?
a) Explain the term foldback in relation to Geiger-Müller counters.
b) Why is it important to consider the possibility of foldback?
Now check your answers with the model answers in your workbook.
Conductivity refers to the ability of a material to conduct an electric current and materials which have good conductivity (e.g. metals), are known as conductors. Materials which have poor conductivity (e.g. wood) are known as insulators. A semiconductor is a material with properties somewhere in between these two extremes, and although there are a number of substances with semiconducting properties, the ones most commonly used for radiation detection are the crystalline solids of silicon and germanium.
Solid state conductivity detectors are so named because they consist of semiconducting crystalline solids. When ionizing radiation interacts with these solids, the overall conductivity of the material is increased. If this increase is then measured, it can be related to the amount of incident radiation.
To understand how solid state conductivity detectors work we need to consider the interaction of ionizing radiation with semiconducting materials on a microscopic scale. As you may remember for Module 1.1 Structure of Matter, electrons can only exist in definite energy levels. In solids, these energy levels are referred to as energybands. These energy bands are separated by areas known as forbidden bands, and the highest energy band in which electrons usually exist is known as the valence band.
Ionizing radiation can give enough energy to an electron in a semiconducting crystalline solid to move it from its usual energy level (in the valence band) through normally forbidden levels (in the forbidden band) and up into a higher energy state (known as the conduction band). As it does so it leaves a vacancy (or hole) in the valence band (see Figure 8).
Figure 27
The Formation of an Electron-Hole Pair by Ionizing Radiation
The raising of the electron to the conduction band is known as ionization and the resulting electron-hole pair can be compared to the ion pair in a gas-filled detector. In the same way as positive and negative ions move between electrodes in a gas-filled detector, the ion pair will ‘move’ in a solid state detector when a voltage is applied. This movement results in a pulse in the external circuit which can be measured.
Note that in reality, the positively charged material cannot move in a crystalline solid. What actually happens is that holes are filled by neighbouring electrons which move across and leave another hole behind. In this way, the holes appear to move.
Solid state conductivity detectors consist of semiconductors which have had their conductivity enhanced. In general, the conductivity is improved by introducing impurities to the semiconductor material. This process is known as doping and the introduced impurities provide either extra electrons or extra holes. If the impurity provides extra electrons to the valence band (e.g. in the case of arsenic or phosphorus doping), then these loosely bound electrons can move to the conduction band with only a small amount of energy being deposited in the material. In this way, the main conduction mechanism is the movement of negative charges and the material is known as an ntypesemiconductor. If the impurity provides extra holes to the valence band (e.g. in the case of boron or gallium doping), then the main conduction mechanism is the movement of positive holes and the material is known as a p typesemiconductor.
Solid state conductivity detectors actually consist of p and n type material joined together. An electric voltage is applied across the junction so that the holes and electrons move away from the junction. The area around the junction is free of holes and electrons and is known as the depletion layer. This depletion layer is the part of the material which will detect any incident radiation (see Figure 9).
Figure 28
The Basis of a Solid State Conductivity Detector
When ionizing radiation passes through the depletion layer, it forms electron-hole pairs. The electron-hole pairs move apart causing a pulse in the external circuit. This pulse can then be measured. In this way, the depletion layer forms the sensitive volume of the solid state detector and it is equivalent to the chamber in a gas-filled detector.
There are many different types of solid state conductivity detectors available for detecting ionizing radiation. The types of solid state conductivity detectors considered in this module are:
Diffused junction diodes;
Surface barrier detectors;
Ion implantation detectors;
Lithium drifted detectors; and
High purity germanium detectors.
In diffused junctiondiodes the p type impurity has been allowed to diffuse or spread into the n type material. This creates a depletion region just below the crystal surface (typically about 1m below the surface) as shown in Figure 10. The surface layer represents a dead layer or window through which the radiation must pass before entering the sensitive volume.
Figure 29
The Basis of a Diffused Junction Diode
This window can be a disadvantage in charged particle spectroscopy because some of the lower energy particles may not be detected. To avoid this disadvantage, diffused junction diodes have been replaced in many charged particle spectroscopy applications by surface barrier detectors (see Section 2.2.2.2). However, diffused junction diodes (made of either silicon or germanium) are still used for charged particle detection as they are more rugged than surface barrier detectors.
Another practical use of silicon diffused junction diodes has recently been discovered. These diodes (often referred to as silicon PIN photodiodes) can be incorporated in electronic dosimeters (see Figure 11) to measure the amount of gamma radiation being received by a person over time (i.e. to measure personal gamma dose).
Figure 30
An Electronic Dosimeter Incorporating a Silicon PIN Photodiode
Note that electronic dosimeters are also manufactured with G-M detectors. The main advantage of using a solid state detector is that the instrument is lighter in weight.
Surface barrier detectors have a very thin layer of p type material deposited on n type material (see Figure 12). Again the incident radiation needs pass through this layer to reach the sensitive volume but due to the thinness of this layer in this type of detector, charged particles can easily be detected.
Figure 31
The Basis of a Surface Barrier Detector
As well as being extremely efficient at detecting charged particles, surface barrier detectors are also very good at separating out the different energies of the incoming radiation (i.e. they have very good energy resolution). For example, surface barrier detectors can separate the three families of alpha particles from Am-241 with energies of 5.486, 5.443 and 5.389 MeV.
One of the main problems with surface barrier detectors is that the crystal surface must be kept very clean and free from oil or other foreign material. They are also very sensitive to light because light photons can reach the sensitive volume and create electron-hole pairs.
An alternative method of introducing impurities at the surface of a semiconductor is to expose the surface to a beam of ions produced by an accelerator. For example, a silicon crystal exposed to boron ions will have a layer of p type material formed close to the surface. This method of doping is called ion implantation and it gives a much more stable crystal which is less likely to be affected by environmental conditions. In fact, these type of detectors are very rugged, and they can be manufactured with thin end windows for alpha and beta detection.
Ion implantation detectors have a wide variety of applications including alpha spectroscopy, low energy beta detection and heavy ion detection.
Surface barrier and ion implantation detectors are very good for the spectroscopy of charged particles but, due to inherent impurities in the semiconductor crystals, they do not have a large enough sensitive volume for photon (i.e. gamma ray and x-ray) spectroscopy. To counteract the effects due to these impurities, semiconductors can have lithium added to them to create a bigger sensitive volume. The area between the p type and n type materialsis then known as the lithium drifted or intrinsic region and the size of this intrinsic region determines the sensitive volume of the detector (see Figure 13).
Note that, although adding lithium to a semiconductor is considered to provide a much bigger sensitive volume, in real terms, the size of the whole detector is actually very small. This means that one advantage of this type of solid state conductivity detector is that the detector dimensions can be kept much smaller than the equivalent gas-filled detector.
Figure 32
The Basis of a Lithium Drifted Detector
When lithium is added to a germanium crystal, the detector is called a lithium drifted germanium (or Ge(Li)) detector. At room temperature the lithium atoms will continue to move through the germanium crystal changing the nature of the intrinsic region, so it is important that a Ge(Li) detector is always kept at a very low temperature (using liquid nitrogen), even when not being used. Lithium drifted germanium detectors are efficient detectors of gamma radiation and have excellent energy resolution.
Lithium drifted silicon (or Si(Li)) detectors, as their name suggests, consist of a lithium drifted silicon crystal. These Si(Li) detectors are very similar to the Ge(Li) detectors but have the advantage that they can be stored at room temperature without any damage to the crystal. They can be operated at room temperature but their performance is greatly improved if they are cooled by liquid nitrogen before use. Silicon has a much lower atomic number that germanium so it is less likely to interact with gamma radiation. Lithium drifted silicondetectors are therefore not as efficient at detecting gamma radiation as Ge(Li) detectors. However, they make good detectors for very low energy gamma rays (less than about 150 keV), x-rays, and beta particles.
Pure germanium has a high efficiency for the detection of gamma radiation. Hence if the impurities in a germanium crystal are kept low, it is possible to obtain depletion layers (sensitive volumes) that are comparable with those in a Ge(Li) detector. This type of detector is called a high purity germanium (or HPGe) detector (see Figure 14).
Figure 33
A Typical High Purity Germanium Detector (HPGe) Arrangement
Like the Ge(Li) detector, the HPGe detector acts as an efficient gamma detector with excellent energy resolution. Similarly, both detectors require cooling with liquid nitrogen for efficient operation but one advantage of the HPGe detector is that it may be stored at room temperature when not in use.
Table 3 summarizes the properties of the various solid state conductivity detectors.
Table 17
Summary of Solid State Conductivity Detectors
Detector | Main Uses | Advantages | Disadvantages |
Diffused Junction Diode | Charged particle detection |
|
|
Silicon PIN Photodiode | Photon detection |
| |
Surface Barrier | Alpha and beta spectroscopy |
|
|
Ion Implantation | Alpha spectroscopy Low energy beta monitoring |
| |
Lithium Drifted Germanium Ge(Li) | Gamma spectroscopy |
|
|
Lithium Drifted Silicon Si(Li) | Beta, gamma and x-ray spectroscopy |
|
|
High Purity Germanium (HPGe) | Gamma spectroscopy |
|
|
Solid state detectors have a number of advantages over gas-filled detectors and these are as follows:
Solid state conductivity detectors are much smaller.
They have much better energy resolution for all radiation types.
They have much higher efficiency for gamma radiation.
The sensitive volume of the detector can be chosen to suit the application.
The main disadvantages of solid state detectors are that:
They may need to be cooled to liquid nitrogen temperatures for operation.
They are sometimes less portable than gas-filled detectors.
Now see how much you have understood by answering the following questions in your workbook:
Fill in the gaps with a suitable word:
A material which has poor electrical conductivity is known as an ____________.
A material which has medium conductivity is known as a ____________.
A material which has good conductivity is known as a ____________.
Name the two semiconductor materials commonly used in solid state conductivity detectors.
a) What is doping?
b) Why are semiconductor materials doped?
In what way are semiconductor detectors like gas-filled detectors?
Explain the term energy resolution.
Which type of solid state conductivity detector would be best for detecting the following types of radiation?
Alpha particles.
Beta particles.
Low energy gamma and x- rays.
Medium and high energy gamma rays.
7.What are the advantages of solid state conductivity detectors over gas-filled detectors?
Now check your answers with the model answers in your workbook.
Scintillation detectors rely on the fact that some materials (known as phosphors) will emit visible light when electrons change energy levels. If you remember from Module 1.4, Interaction of Radiation with Matter, ionizing radiation can give electrons sufficient energy to move into a higher energy shell. In a phosphor, these electrons do not remain in the higher energy level for very long. Instead, they fall back to their original level and, as they do so, they emit photons of visible light (see Figure 15)
Figure 34
The Scintillation Process
The number of photons of light emitted, and therefore the intensity of the light, is proportional to the energy of the incoming radiation. Hence, scintillation detectors can be used not only to detect radiation but also to separate out the energies (i.e they can be used for spectroscopy purposes).
The phosphors which can be used in radiation detectors must have certain properties, as follows:
They must convert a large fraction of the absorbed energy into light energy.
The time between the excitation of the electron and the emission of the light photon must be short.
They must allow the light photons produced to pass through the material.
The emitted light must be able to be converted easily and efficiently to an electrical signal.
A variety of materials meet these criteria and these make up the basis of scintillation detectors. The types of scintillation detectors discussed in this module are as follows:
Zinc sulphide detectors;
Sodium iodide detectors;
Plastic organic scintillators; and
Liquid organic scintillators.
Some of these phosphors may have small quantities of impurities (called activators) added to control the way in which the electrons move back to the lower energy levels. This ensures that the photons emitted will be visible light photons.
Zinc sulphide (ZnS) detectors commonly have atoms of silver added as activators. These type of detectors, known as ZnS(Ag) detectors, are very efficient for detecting ionizing radiation. However, as this type of material does not allow the visible light photons to pass through it very easily, it can only be used in thin layers (see Figure 16). Although this means that these detectors are useful for detecting alpha particles and heavy ions, the main disadvantage is that the thin layer can easily be pierced by sharp objects.
Figure 35
A Zinc Sulphide Detector
Sodium iodide detectors with thallium atoms added NaI(Tl) are very efficient for the detection of gamma radiation, even more so than solid state conductivity detectors. However, the crystal will absorb moisture from the atmosphere and deteriorate very rapidly. It is therefore ‘canned’ in an air-tight container. The container is often made of aluminium (see Figure 17) and may have a thin end window.
Figure 36
A Portable Sodium Iodide Detector Used for Gamma Ray Detection
The NaI(Tl) crystals can be made in various thicknesses. A thin crystal of thickness 3 mm is very efficient for detecting gamma radiation up to about 150 keV. A thicker crystal is needed for maintaining a high efficiency for higher energy gammas. A NaI(Tl) detector is easier to use in the work environment than a solid state conductivity detector because it does not need to be cooled. It also has a much better measuring efficiency, particularly at higher energies. However, its energy resolution is poor when compared with a solid state detector.
Figure 18 shows a typical sodium iodide detector with the related circuitry for gamma spectroscopy.
Figure 37
A Typical Sodium Iodide Detector for Gamma Spectroscopy
Plastic organic scintillators are cheap and can be manufactured in a variety of different shapes and sizes. They are often used in conjunction with ZnS(Ag) detectors for monitoring alpha and beta radiation.
Liquid organic scintillators have a special use for monitoring alpha and beta radiation, particularly low energy beta radiation such as carbon-14 and tritium. Use of a liquid scintillator allows the contaminant of interest to be mixed directly with the scintillant and can lead to very high detection efficiency.
Table 4 summarizes the properties of the various scintillation detectors.
Table 18
Summary of Scintillation Detectors
Detector | Main Uses | Advantages | Disadvantages |
Zinc Sulphide | Detection of alpha particles and heavy ions |
|
|
Sodium Iodide | Gamma spectroscopy Gamma detection |
|
|
Plastic Organic | Monitoring alpha and beta radiation |
| |
Liquid Organic | Monitoring alpha and low energy beta radiation |
|
Photomultiplier (or PM) tubes are necessary in scintillation circuits to convert photons of light from the scintillator into electrical pulses. They are also used to increase the size of the initial signal. Although, strictly speaking, PM tubes are really part of the electronic system rather than the detection mechanism, they are included in this section because they are of specific use with scintillation detectors and are not part of general counting circuits.
Firstly, the incident radiation interacts with the phosphor to produce a light photon. This light photon then hits a surface coated with light-sensitive material known as a photocathode. The energy from this light photon is absorbed by an electron in the light sensitive material and this electron gains enough energy to leave the photocathode. The ejected electron forms the basis of the electrical signal but, in practical terms, the signal must be amplified by a series of dynodes. Each dynode is basically an anode which releases about four electrons for every electron it collects. The dynode system requires a very stable high voltage power supply in order to operate consistently. Figure 19 shows how the energy is transferred from the original scintillation event to the external electrical circuit.
Figure 38
A Scintillation Detector Arrangement Incorporating a Photomultiplier Tube
Now see how much you have understood by answering the following questions in your workbook:
Fill in the gaps with a suitable word or phrase:
Scintillation detectors rely on the fact that some materials (known as _______) will emit visible light when electrons change _______ _____. When ionizing radiation interacts with the electrons in this type of material, they are given enough energy to move to a _______ energy shell. These electrons do not remain in here for very long. Instead, they fall back to their original level and, as they do so, they emit _______ ______.
Can scintillation detectors be used for spectroscopy purposes? Explain your answer.
Which type of scintillator would you use for detecting alpha particles and heavy ions?
Which type of scintillator would be best for detecting gamma radiation?
Which type of scintillator would be best for detecting tritium?
a) Give two advantages of using a sodium iodide detector compared with a germanium detector.
b) What is the major disadvantage of sodium iodide detectors?
Why are photomultiplier tubes needed for scintillation detection systems?
Now check your answers with the model answers in your workbook.
Neutrons are uncharged particles and so do not cause ionization directly. However, when they interact with material they produce secondary ionizing particles and it is the detection of these particles which allows us to detect neutrons.
The most common interactions used in neutron detectors are;
the reaction with boron-10, which produces alpha radiation;
the reaction with helium-3, which produces a proton; and
elastic scattering by hydrogen nuclei.
The first two interactions are most likely to occur for neutrons with energies up to about 0.5 eV. These neutrons are at the bottom of the intermediate neutron range and in the thermal neutron (0.025 eV) range. Elastic scattering can be used to detect fast neutrons.
There are several factors to be taken into account when designing a suitable neutron detector:
Moderating material must be used to slow down fast neutrons (without absorbing them) so that they will interact with the detector material.
The detector material must have a high cross section (i.e. a high possibility) for the particular reaction to occur so that detectors can be built which are not too large.
The heavy charged particles formed during the interaction with the detecting material must all be stopped within the active volume of the detector.
Four types of neutron detectors which fit this criteria are as follows:
Boron trifluoride proportional counters
Helium proportional counters
Gas recoil proportional counters
Bubble detectors
Boron trifluoride proportional counters consist of a gas-filled proportional counter filled with boron-10 enriched boron trifluoride (BF3). This gas provides the filling gas for the detector as well as the target for incoming thermal neutrons. The nuclear reaction which occurs in the detector is given by Equation 1:
10B + n 7Li + 1
This reaction is often written as 10B(n,)7Li.
The lithium nucleus and the alpha particle both have sufficient energy to cause secondary ionization in the filling gas, and these secondary ionization events can then be detected. Note that, some neutron interactions produce a 0.48 MeV gamma ray. Hence, a suitable discrimination circuit is necessary to distinguish between the incoming neutrons and resultant gamma rays.
Boron trifluoride proportional counters can also be used to detect intermediate and fast neutrons (up to 10 MeV). However, in this case, the detector must be surrounded by a moderating material such as polyethylene to slow down the neutrons before capture (see Figure 20). Cadmium filters are used to provide a uniform energy response.
Figure 39
A Boron Trifluoride Counter
As well as being good detectors for thermal, intermediate and fast neutrons, boron trifluoride proportional counters can be used for neutron spectroscopy purposes.
Helium proportional counters are similar in many respects to boron trifluoride proportional counters. The main detection mechanism involves thermal neutron capture, but if a moderator is used, helium proportional counters can be used to detect intermediate and fast neutrons.
As the name suggests, helium proportional counters use helium as both the target and filling gas. The important reaction is given in Equation 2:
3He + n 3H + p[2]
This is often written as 3He(n,p)3H.
In this reaction, a tritium nucleus and proton are formed and it is these charged particles which produce the secondary ionization.
Again, helium proportional counters can be used for neutron spectroscopy purposes.
Gas recoil proportional counters use elastic scattering with hydrogen nuclei as their mechanism of detection. In these counters, neutrons with energies greater than about 500 keV are detected using a proportional counter filled with a hydrogen-rich gas such as methane. A fast neutron will collide with a hydrogen nucleus (which is just a single proton) giving it energy. This nucleus will then go on to produce secondary ionization.
In some gas recoil proportional counters the hydrogen atoms may be supplied by using material such as polyethylene in the walls of the counter. The counter is enclosed in a thin sheet of cadmium which absorbs thermal neutrons.
Bubble detectors contain microscopic liquid drops suspended in a gel-like material. Incoming neutrons transfer enough energy to the liquid drops to make them suddenly boil and change into a bubble. These bubbles are visible to the eye and can be counted (see Figure 21).
Figure 40
Bubble Detectors Before (left) and After (right) Neutron Exposure
The actual neutron dose is proportional to the density of bubbles, and these remain fixed in the material until the dosimeter is reset.
Bubble dosimeters are mainly used for personal dosimetry. However, they can also be used for environmental monitoring.
Table 5 summarizes the properties of the various neutron detectors
Table 19
Summary of Neutron Detectors
Detector | Main Uses | Comments |
Boron trifluoride proportional counters |
|
|
Helium proportional counters |
|
|
Gas recoil proportional counters |
| |
Bubble detectors |
|
Now see how much you have understood by answering the following questions in your workbook:
Why can’t neutrons be detected using the detectors learnt about in previous sections?
a) What modifications are needed to proportional counters to allow them to detect neutrons?
b) Why is a material such as polyethylene often used to surround the detector tube?
Which type of neutrons are most likely to interact with boron or helium?
Which type of neutrons are most likely to undergo elastic collisions with hydrogen nuclei?
Which type of neutron detector can be used for personal dosimetry?
Now check your answers with the model answers in your workbook.
So far in this module we have been considering different types of detectors. Once the energy of the ionizing radiation has been converted to an electrical signal, various electronic components must be added to the detection system to provide a meaningful reading.
The electrical signals produced by detectors are of two types – direct current (as in the ion chamber) and pulse. If the signal is measured as a direct current, the average current over many interactions is recorded and the circuit is said to be operating in current mode. If the signal is measured as a change or drop in voltage, individual interactions are recorded and the size of the pulse is dependent on the number of electrons collected. This is known as pulse mode.
Direct current output is measured by a direct current amplifier whereas a pulsed output is measured in a counting circuit. Figure 22 shows the components of a general counting circuit.
Figure 41
A General Counting Circuit
In this section we will look briefly at the functions of a direct current amplifier and the different components of a counting circuit. Remember that in a field instrument all components are usually built into the instrument, which may limit the capabilities of the instrument. A laboratory instrument can have more functional components attached.
A stable direct voltage supply is necessary to supply the operating potential for the detector. Field instruments are dependent on batteries to supply the voltage. The level of the high voltage and the degree of stability required depends on the type of detector. The voltage supply is known traditionally as the HV (high voltage) supply.
A direct current amplifier increases a very low current, in the order of 10-12 A, to a current which can be measured by an ammeter, in the order of 10-3 A. This requires a high gain. (The gain of an amplifier is the ratio of the size of the output pulse to the size of the input pulse.) Since the necessary gain is so high, any slight change in the input signal can have a large effect on the output measurements. For this reason high standards of insulation and cleanliness must be maintained. Direct current amplifiers are mainly used with ion chambers and some semiconductor detectors operating in current mode.
The output from most detectors is so small that it must be amplified before going to the main amplifier. The pre-amplifier (pre-amp) is often built into the detector housing. In the case of scintillation detectors, it forms part of the photomultiplier system. The pre-amplifier must be capable of amplifying the signal without causing additional noise. Electronic noise consists of signals which tend to hide the signal coming from the detector and can be due to such events as the thermal movement of electrons.
The amplifier shapes the pulse and increases it to a level which is suitable for the counting equipment being used. The gain which needs to be provided by the amplifier depends on the size of the pulse coming from the detector.
A discriminator allows us to discard pulses which are either too large or too small. A low level discriminator ignores pulses below a set level which is very useful for eliminating unwanted noise. If both a low level and an upper level discriminator are used and set close together, the instrument will operate as a single channel analyser (SCA) and only accept pulses of a narrow range. Discriminators provide a standard size pulse for counting equipment when the pulse falls within the set range.
There are three types of counting devices:
A scaler which gives a visual display of the counts which have accumulated in the counting time. It will usually include a timing device so that a count time can be preset. Scalers are most frequently used in laboratory equipment for counting samples.
A rate meter which gives a continuous indication of the rate of arrival of pulses and is the normal counting device for field instruments. The reading on the meter will be constantly changing as pulses are counted. The reading can be smoothed out electronically but too much smoothing can result in a slow response to a changing pulse rate which can be unsatisfactory for workplace monitoring.
A pulse height analyser (PHA) or multi-channel analyser (MCA) whichis used when the pulse height depends on the energy of the ionizing radiation. It separates the pulses into different channels according to their heights. The number of pulses counted in each channel is shown on a visual display and provides information about the energy spectrum of the radiation.
Now see how much you have understood by answering the following questions in your workbook:
What type of detector would require a direct current amplifier?
List the components of a general counting circuit.
What is the main function of the following equipment?
a) The pre-amplifier.
b) The pulse amplifier.
c) The discriminator.
Name the three types of counting devices. Which of these is normally used in field instruments?
Which counting device would you use with an HPGe, Ge(Li) or NaI(Tl) detector if you were attempting to identify a mixture of different radionuclides?
Now check your answers with the model answers in your workbook.
The six basic methods of radiation detection are: ionization, scintillation, thermoluminescence, chemical mechanisms, heating and biological mechanisms.
Radiation detectors which rely on ionization consist of gas-filled detectors and solid state conductivity detectors.
The three types of gas-filled radiation detectors are ionization chambers, proportional counters and Geiger-Müller counters.
The resolving time of a detector is defined as the minimum amount of time which must separate two events in order that they are recorded as two separate processes.
The dead time of the detector is the length of time for the signal or pulse to build up sufficiently for it to be detected).
The recovery time is the length of time for the detector to recover from an ionization event and return to its original condition.
Ionization chambers operate at saturation current and are used for counting and spectroscopy.
The average current output from an ionization chamber is proportional to the amount of incident radiation. The output is very small and must be amplified.
Ionization chambers do not need a stable high voltage supply.
If ionization chambers are used to measure beta radiation, they must have a thin end window.
In proportional counters, the total pulse size is proportional to the energy deposited by the radiation.
The total pulse size in proportional counters is very small and requires amplification.
Proportional counters require a stable high voltage supply.
Proportional counters are used for counting and spectroscopy.
Geiger-Müller detectors cannot distinguish between types and energies of incident radiation.
G-M detectors must be quenched to prevent the discharge continuing by itself.
G-M detectors do not require amplification.
G-M detectors have long resolving times and hence foldback can occur in high radiation fields.
G-M tubes require energy compensation.
Solid state conductivity detectors consist of n type and p type semiconductors. These semiconductors may also be doped.
Solid state conductivity detectors include surface barrier detectors, diffused junction diodes, ion implantation detectors, lithium drifted detectors and high purity germanium detectors.
Surface barrier detectors have very good energy resolution and can be used for charged particle spectroscopy.
Diffused junction diodes may not detect low energy particles because of their dead layer.
Silicon PIN photodiodes can be used for gamma ray detection in electronic dosimeters.
Ion implantation detectors are quite rugged and can be used for alpha spectroscopy and low energy beta detection.
Lithium drifted detectors have lithium added to them counteract the impurities in the semiconductor crystals. This creates a bigger sensitive volume for photon spectroscopy.
Ge(Li) detectors must be kept at very low temperatures at all times.
Si(Li) detectors are not as efficient as Ge(Li) detectors but they may be stored at room temperature when not in use.
HPGe detectors have the highest efficiency for photon detection and they may be stored at room temperature when not in use.
Solid state conductivity detectors are much smaller than gas-filled detectors.
Scintillation detectors consist of phosphors which emit visible light when excited electrons move back to lower energy levels.
Typical scintillation detectors are: ZnS(Ag) detectors, NaI(Tl) detectors, plastic organic scintillators and liquid organic scintillators.
ZnS(Ag) detectors exist as thin layers and can be used for detecting alpha particles and heavy ions.
NaI(Tl) detectors are efficient scintillation detectors for x- and gamma radiation but have poor energy resolution.
Plastic organic scintillators can be used for monitoring alpha and beta radiation.
Liquid scintillators can be used for detection of low energy beta particles.
Scintillation detectors require photomultiplier tubes to collect and amplify the signal.
Neutron detectors require secondary ionization to take place before the neutron can be detected.
Gas-filled proportional counters with boron-10 (boron trifluoride proportional counters) or helium (helium proportional counters) can be used to detect neutrons. A moderating material is needed to slow down fast and intermediate neutrons.
Fast neutrons can be measured using a gas recoil proportional counter.
Bubble dosimeters can be used for personal dosimetry and environmental monitoring.
Direct current amplifiers are needed for detectors operating in the current mode.
A general counting circuit contains a pre-amplifier, a pulse amplifier, a discriminator and a counting device.
Scalers, rate meters and pulse height analysers are all types of counting devices.
This assignment is to be completed under test conditions, so spend some time now studying this module. Then contact your supervisor to arrange a suitable time to complete the assignment.
Activator | An impurity added to phosphors to ensure that only visible light photons are emitted from excited electrons returning to lower energy levels. |
Anode | A positively charged electrode. |
Avalanche | The process in which a free electron produces more free electrons, which in turn produce more free electrons and so on. |
Cathode | A negatively charged electrode. |
Conductor | A material that allows electrical current to pass through it. |
Current mode | An electrical signal measured as a current. |
Dead time | The length of time for a signal or pulse to build up sufficiently for it to be detected. |
Depletion layer | The area at the junction of n-type and p-type semiconductors which is free of electrons and holes. |
Doping | The process whereby semiconductors such as germanium and silicon have impurities introduced to improve their conductivity. |
Dynode | A positively charged electrode which multiplies the number of electrons in a photomultiplier tube. |
Electrode | A metal plate to which an electric voltage is applied. |
Energy compensation | A method of ensuring that a detector responds to all photon energies in the same way. |
Energy resolution | The ability to separate measurements of particles or photons with different energies. |
Foldback | An effect which gives an apparent zero reading on a detector in a high radiation field. |
Gas multiplication | The increase in the number of ion pairs formed in a gas-filled detector. |
Insulator | A material that does not allow electric current to pass through it. |
Intrinsic region | The region in a silicon or germanium detector that has had lithium added. This creates a thick sensitive volume of material suitable for the collection of electron-hole pairs created by incident radiation. |
Ionization | The process whereby electrons are removed from atoms or molecules thus producing ion pairs. |
n-type semiconductor | A material which has been doped with an impurity that provides extra electrons. In this material conduction is improved by the movement of negative charges. |
Photocathode | An electrode coated with light sensitive material from which electrons are emitted. |
p-type semiconductor | A material which has been doped with an impurity that provides extra holes. In this material conduction is improved by the effective movement of positive charges. |
Pulse mode | An electrical signal measured as a change or drop in voltage. |
Quenching | The suppression of an electrical signal in a gas-filled detector. |
Recombination region | The low voltage region of a gas-filled detector in which recombination of ions occurs. |
Recovery time | The length of time for a detector to recover from an ionization event and to return to its original conditions. |
Resolving time | The minimum amount of time which must separate two events to ensure that they are recorded as two separate processes. |
Saturation current | The constant current which occurs when almost all ions generated in the chamber of a gas-filled detector reach the electrodes. |
Scintillation | The production of light accompanying the movement of electrons from high energy orbits to lower energy levels within an absorbing material. |
Semiconductor | A material which allows an electric current to pass through it better than an insulator but not as well as a conductor. |
Sensitive volume | The part of a detector which detects radiation. |
Spectroscopy | The process whereby detectors separate out the energies of radiation so as to identify the radionuclides present in the radioactive material. |
Thermoluminescence | The release of energy in the form of visible light when previously excited electrons return to lower energy levels. For this to occur the thermoluminescent materials must be heated in order to release the electrons trapped in higher energy levels. |
INTERNATIONAL ATOMIC ENERGY AGENCY AUSTRALIAN NUCLEAR SCIENCE AND TECHNOLOGY ORGANISATION |
DISTANCE LEARNING MATERIALS
RADIATION PROTECTION
Module – 1.6
Prepared by Safety and Radiation Science
Australian Nuclear Science and Technology Organisation
With the assistance of consultants in Australia and the United Kingdom, and IAEA experts from Korea, Mongolia, New Zealand, the Philippines and Thailand
Use of this material, acknowledging the IAEA and ANSTO as the source, is permitted for non-profit training
Acknowledgements
This material has been prepared by an extensive team of international experts from the fields of radiation protection, medicine and education. It is not possible to mention by name all those who have had an input to; the initial planning; writing modules and workbooks; preparing and marking final assignments; proof-reading and editing; using the material and providing valuable feedback; organizing and hosting review meetings; and general administrative support.
The support of ANSTO management in providing the resource and encouragement is gratefully acknowledged.
The enthusiastic support of IAEA Technical Officers has been vital to the success of this project.
PART 1
BASIC KNOWLEDGE
MODULE 1.6
BIOLOGICAL EFFECTS OF EXPOSURE TO IONIZING RADIATION
CONTENTS
68.OVERVIEW
As an introduction to this module, you will be given a basic understanding of how the human body works. The module goes on to discuss the effects of ionizing radiation on a cellular level and the resulting effects to the total body. You will then learn about the terms used to describe these types of effects.
69.
TIME ALLOCATION
It is estimated that you will need to spend six to eight hours to complete this module before commencing the assignment. This time estimate is for guidance only and if you would like to spend more time on the module to understand it more fully, then by all means do so.
70.MATERIALS
You will need to have writing materials to take notes and answer questions and assignments in the module.
NOW YOU ARE READY TO START WORK
The human body is affected by ionizing radiation from sources outside the body (an external source) and from radioactive materials which have entered the body (internal contamination). This is illustrated by Figure 1.
Figure 42
External and Internal Radiation Hazards
For external sources to cause harm they must be able to penetrate the body and affect our cells. As alpha particles and low energy beta particles cannot penetrate the skin (unless through an open wound or through chemical absorption), only high energy beta particles, gamma rays, x-rays and neutrons present an external radiation hazard. This will be further explained in Module 2.2 Protection from External Radiation Hazards.
If radioactive materials are taken into the body either by inhalation, ingestion, through an open wound or through chemical absorption, they are in direct contact with cells and can therefore irradiate all of the cells surrounding them. In this case, alpha and beta particles are of most concern as they both have short ranges in biological tissue and will dissipate their energy in a small volume. This will be further explained in Module 2.3 Protection from Internal Radiation Hazards. However, when considering sources inside the body, it is important to have some idea of how they human body works and how radionuclides can become deposited in the various parts of the body.
The human body is based around a bony structure called a skeleton, and consists of a number of functional units known as organs. The skin covers and protects the body and also helps to control body temperature and fluid balance. Within the body there are systems for the intake of air, food and water, the transport of material and removal of wastes. Knowledge of these systems is important as they are the means by which radionuclides may enter, be transported around and finally leave the body. These body systems are known as the respiratory, digestive, circulatory, lymphatic and urinary systems.
The function of the respiratory system is to bring air close enough to the circulatory system so that oxygen can enter the blood and carbon dioxide can leave. The respiratory system consists of the nose, trachea, breathing bronchi and the lungs. The lung is full of small air sacs called alveoli which are surrounded by a network of blood capillaries (see Figure 2). This is where the exchange of gases occurs.
Figure 43
The Respiratory System
In radiation protection we are concerned about airborne radioactive materials (especially particulates) entering the body through inhalation and affecting the lungs and other organs. The overall effect of the radioactive material is dependent on the chemical and physical characteristics of the inhaled material, particularly the size of the particles and how easily they can be dissolved.
If we now consider the whole process of inhalation and exchange of gases, we can see how the radioactive materials can become deposited in the body. Firstly, particles of dust can enter the body with the air we breath. If the dust particles are large (>10m in diameter) most of them will be trapped in the upper parts of the respiratory system (e.g. the hairs in the nose) and do not enter the lungs. However, smaller dust particles are more likely to travel further into the respiratory system (see Figure 44).
The Process of Inhalation of Particulates
The dust particles will remain in the respiratory system until removed either physically by the sweeping action of fine hairs (cilia) lining the bronchi (aided by coughing) or chemically (e.g. by being dissolved). The removal of dust particles from the lungs by movement of the cilia and coughing is usually followed by swallowing. This means that inhaled material may end up in the digestive system.
If the dust particles are soluble they will dissolve in the alveoli. The dissolved material enters the bloodstream and is transported to other areas of the body. Insoluble material will remain in the lungs or adjacent lymph nodes.
The digestive system is the means by which food and water are taken into the body and changed so that they can be absorbed into the bloodstream. The digestive system is a continuous tube consisting of the mouth, oesophagus, stomach, small intestine and large intestine (see Figure 45).
The Digestive System
During digestion, food is broken down into simple chemical compounds which are absorbed from the small intestine into the bloodstream and transferred via the liver to body tissues. The unabsorbed food has most of the water removed as it passes through the large intestine and is passed out of the body as solid waste (faeces).
The digestive system is also a major route by which radionuclides may enter the body. Soluble radionuclides in food, water and other material entering the mouth (e.g. by chewing fingernails) will be absorbed into the bloodstream and transported to body tissue. Insoluble radioactive material will pass through the digestive system and be excreted in the faeces. The amount of radioactive material which enters the circulatory system depends on many factors including the chemical and physical characteristics of the ingested material.
The circulatory system is the means by which material is transported throughout the body. The circulatory system consists of the heart and anetwork of arteries, capillaries and veins which carry blood throughout the human body. Red and white blood cells and a liquid called plasma are the main components of blood.
The circulatory system carries oxygen and essential nutrients to all places in the body and takes waste products away for removal from the body. The circulatory system also is important for the body’s protection from infection as it carries the defensive and repair units to the source of the infection.
The circulatory system is the major mechanism by which radionuclides may be transported within the body. Radionuclides may enter the circulatory system directly (i.e. if the skin is broken due either to wounds or injection) or indirectly (via the respiratory or digestive systems). The part of the body to which radionuclides are transported depends on the chemical properties of the radionuclide. For example, calcium is extracted from our food and deposited in bone tissue. Elements which have similar chemical properties to calcium (e.g. strontium, barium and radium) will also go to the bones whether the atoms are radioactive or not. Iodine is required by the thyroid gland in the neck so any intake of iodine will go to the thyroid. In fact, this aspect of radionuclide deposition is very useful for medical imaging and therapy purposes as particular radionuclides may be attached to a special chemicals so that they are transported to the region of interest in the body. Such substances are known as radiopharmaceuticals.
The lymphatic system is really a part of the circulatory system. It consists of a fluid, called the lymph, which fills all the spaces in body tissue, lymph vessels and numerous lymph glands or nodes (such as in the groin and under the arm). The lymphatic system has no central pump but relies on body movement to move fluid around. It is responsible for the transfer of material between the circulatory system and all cells of the body. It also plays an important part in protecting the body. Lymph nodes filter out substances like bacteria, small particles and even cancerous cells, preventing them from entering the blood system and spreading to other areas of the body.
If the skin is broken, the lymphatic system is one of the means by which the radionuclide may be taken up by the body. The lymphatic system will transport the radionuclide within the local area of the wound prior to being taken into the blood and transported within the circulatory system.
The urinary system is the primary means by which soluble radionuclides are removed from the body. The urinary system consists of the kidneys, the ureters, the bladder and the urethra (see Figure 5).
Figure 46
The Urinary System
The urinary system filters out the soluble waste products produced within the body, including radionuclides, and disposes of them in the urine. If a person has taken a large amount of a radionuclide into their body, such as during medical procedures, the urine may need to be handled as a radioactive substance.
The following table summarizes information about the body systems. Knowledge of the respiratory and digestive systems helps us understand how radioactive materials can enter the body. Knowledge of the circulatory and lymphatic systems helps us understand how radioactive materials may be transported around the body to different organs. The urinary system explains how soluble radioactive materials may be excreted.
Table 20
Summary of Body Systems
Respiratory System | Digestive System | Circulatory System | Urinary System | Lymphatic System | |
Major Organs | Lungs | Stomach Intestines | Heart Arteries Veins | Kidneys Bladder | Lymph Lymph nodes |
Major Function | Exchange of gases | Process food | Transport | Excretion of soluble waste | Transport |
Radiological Significance | Inhalation pathway | Ingestion pathway | Transport of radionuclides | Excretion | Transport of radionuclides |
72.SELF-CHECK 1
Now see how much you have understood by answering the following questions in your workbook:
Which body system (or systems) is responsible for each of the following functions?
a)Transporting material around the body.
b)Gas exchange between the air and the blood.
c)Filtering the blood to remove waste.
Processing food.
Explain briefly, using the names of the body systems, how the following radionuclides may enter the body and be deposited in body organs:
a)Iodine-131 in milk.
b)Uranium ore dust in the air. (Assume that the dust is not very soluble.)
c)A solution of phosphorus-32 on a needle.
Now check your answers with the model answers in your workbook.
The different parts of the human body are made up of microscopic building blocks called cells. Cells which have the same function are grouped together to form tissue e.g. muscle tissue. Different tissues can group together to form an organ e.g. the heart. Organs group together to form body systems such as the systems considered in the previous sections.
Most body cells have three main parts:
the cell membrane which forms the boundary of the cell. Materials move in and out of the cell through the cell membrane.
the nucleus whichcontrols the functions of the cell, particularly growth and division; and
the cytoplasm which is a fluid-like substance within the cell and contains many of its functional parts. Most of the chemical changes taking place in a cell occur in the cytoplasm.
The basic structure of a body cell is shown in Figure 6.
Figure 47
Basic Structure of a Body Cell
The nucleus in the human body contains 46 chromosomes which each consist of fine fibrous strands made up of genes. These genes are composed of proteins and molecules of deoxyribonucleic acid (DNA). This DNA carries all the genetic information about the physical and mental characteristics of a person. It also enables this information to be passed from one generation of cells to the next.
The different parts of human body cells are summarized in Table 2.
Table 21
Summary of Cell Structure
Cell Part | Description |
Cell membrane | Allows the movement of material in and out of the cell. |
Cytoplasm | Where most chemical processes occur. |
Nucleus | Controls the cell. |
Chromosomes | Consist of fibrous strands of genes. |
Genes | Consist of proteins and DNA. |
DNA | Carries genetic information. |
A feature of most body cells is that they pass through a stage of reproduction during which they divide and form exact copies of themselves. Each cell divides to form two new ones and it is the chromosomes in the nucleus that are the main participants. Red blood cells do not have a nucleus and so are unable to divide. This means that new red blood cells must continuously be manufactured, a process that occurs in the bone marrow.
Cell division is a continuous process in some parts of the body such as the lining of the digestive tract. For adults cell division may take hours or even days. For a child or unborn baby it is more rapid and can be as short as about 20 minutes. If radiation damage to cells occurs during cell division the damage is likely to be more extensive. Hence young children and the unborn, because of more rapid cell division, are considered to be more at risk from the effects of radiation. For the same reason, cancerous tumours (rapidly dividing cells) are also more likely to be damaged by radiation than normal tissue.
Both male and females carry reproductive cells. In males these are known as sperm and in females they are known as the ova. They are manufactured in the reproductive organs or gonads (the testes in a male and the ovaries in a female). These cells only contain half the number of chromosomes (23 instead of 46) and during sexual reproduction, a sperm and ovum are joined to create a cell with 46 chromosomes. The reproductive cells are important as they pass inherited characteristics onto the next generation.
Radiation damage occurs when ionizing radiation interferes with the normal operation of a cell causing direct and indirect damage to the cell.
Direct damage occurs when radiation strikes a critical area of the cell (such as the DNA) and causes direct ionization in the molecule itself.
Indirect damage occurs as the result of the formation of very chemically reactive atom groups, called free radicals, within the cell. About 80% of the cell is water. When radiation ionizes water molecules the ions formed interact with other water molecules. Two of the products formed, H (hydrogen atom) and OH (hydroxyl group) are very reactive because they have unpaired electrons. Another reaction product in the cell is hydrogen peroxide (H2O2) which is also very reactive. These reactive atom groups can interfere with normal cellular processes by breaking chemical bonds such as the bonds between carbon atoms in the DNA molecule. This will result in a break in the DNA molecule which may prevent the cell from dividing. Free radicals may also cause damage to enzymes (chemicals which are important for the functioning of the cell) or to membranes (affecting transport of materials). This sequence of events is summarized in Figure 7.
Figure 48
The Process of Indirect Damage to Cells
Radiation damage to individual cells results almost entirely from the damage to the DNA. The three main consequences of this damage can be summarized as follows:
the cell may die;
changes may occur in the cell which might lead to abnormal cell division; or
the genetic material of the cell may change and the change is passed on to new cells.
Note that ionizing radiation does not cause any damage to cells that could not be caused by other agents such as chemicals and viruses.
Cells have a very efficient repair mechanism and can recover from damage caused by a variety of different agents, including radiation. If the rate at which cells are being damaged is relatively slow (i.e. exposure to low radiation doses over a long period of time), then the chances of the cells recovering is high. This situation, where radiation exposure occurs regularly over a long time period (e.g. months or years), is known as chronic exposure. It is the most common type of radiation exposure for members of the public (from natural radiation) and for radiation workers.
Conversely, if the rate at which cells are being damaged is relatively fast (i.e. exposure to high radiation doses over a short period of time), then the cells have less time to recover and the probability of cell repair is much lower. This situation, where radiation exposure occurs over a short time period (e.g. within hours or days), is known as acute exposure. This type of exposure could occur in accident situations.
This mechanism of cell repair is an important concept in the radiation therapy of cancer patients. In this case, high total doses to a small volume of tissue are delivered in fractions, rather than as a single dose. This is because the healthy tissue, adjacent to the tumour, then has time to recover whereas the cancerous tissue, which has much greater cell damage, will not recover as easily.
73.SELF-CHECK 2
Now see how much you have understood by answering the following questions in your workbook:
Which part of the cell:
a) is the control centre of the cell?
b) is the place where cellular processes occur?
is composed of fibrous strands of genes?
allows the movement of material in and out of the cell?
contains proteins and DNA?
carries genetic information?
Fill in the gaps with a suitable word or phrase:
Radiation damage occurs when radiation interacts with the normal operation of cells. ________ damage occurs when radiation strikes a critical area of the cell (e.g. the DNA) and causes ___________ in the molecule itself. ________ damage occurs as the result of the formation free radicals within the cell.
a) What are free radicals?
b) How are they formed?
How do they interfere with normal cell processes?
What are the three main consequences of radiation damage to cells?
a) What is the difference between chronic and acute exposures?
b) Which type of exposure is most likely for radiation workers?
Which type of exposure could occur in accident situations?
Explain why radiation damage to cells does not always result in permanent biological damage.
Now check your answers with the model answers in your workbook.
As you have already learnt, ionizing radiation acts on the cells of the human body. If the cells do not repair themselves, permanent effects of radiation damage can be seen as biological changes in tissues and organs. These changes may be manifested as medical symptoms which are classified into deterministic or stochastic effects. These effects are of particular concern in the case of the developing foetus.
The most common result of radiation damage is for the cell to die. If only a few cells are affected, it is not usually a problem as there are many cells in the body and new cells will replace the dead cells. However, as the amount of radiation absorbed (i.e. the dose) increases, a point will be reached where sufficient cells are killed to affect the overall operation of the organ. The result of this is a loss of organ function which will become more serious as the number of affected cells is increased.
The different types of radiation damage resulting from the loss of organ function are known as deterministic effects. These effects are characterized by having a threshold dose (below which there is no observable effect) followed by a response where the severity of the effect increases with increasing radiation dose (see Figure 8).
Figure 49
Deterministic Dose Response Curve
An example of a deterministic effect is erythema or skin reddening. Exposure to a low dose of ionizing radiation, below the threshold dose, will not cause the skin to redden. If the dose is increased to a value just above the threshold dose the skin will redden, in the same way that fair skinned people experience mild sunburn. If the dose is increased further, blistering will occur (like severe sunburn) and higher doses will result in death of the skin tissue and ulceration. Other deterministic effects results from irradiation of a particular organ include sterility (temporary or permanent) and cataracts.
Note that the effect of radiation dose on a particular person depends on biological factors (e.g. age and general health) as well as on chemical factors (e.g. the amount of oxygen present in tissue). Therefore in any population there will be a range of sensitivity to radiation. Hence, the threshold dose in a given tissue will be reached at lower doses in more sensitive individuals. As the dose increases more individuals will show the effect, up to a dose above which all exposed people will show the effect.
Deterministic effects are most often seen in cases of high doses of radiation delivered in a short period of time (i.e. in the case of acute exposure). Other than for controlled medical exposure, high doses are not usual in the workplace. Hence deterministic effects are only seen in accident situations and do not occur routinely in the workplace.
Deterministic effects do not occur routinely in the workplace. They are the result of accident situations.
Table 3 shows the deterministic effects to specific organs which occur following an acute exposure. Note that the doses in the table are given in units of millisieverts (mSv). You do not need to understand these units at present as the numbers are given for comparison only. The actual definition of these dose units will be explained in detail in Module 2.5 Personal Dosimetry.
Table 22
Effects of Acute Exposures to Specific Organs
Dose (mSv) | Organ | Effect |
3 500 | Testes | Permanent sterility |
3 500 | Eye | Later cataract formation |
3 000 | Ovaries | Sterility |
2 500+ | Skin | Skin reddening (erythema) and possible permanent hair loss |
500 | Bone marrow | Reduced blood cell formation |
150+ | Testes | Temporary sterility |
60 | Foetus | Probable minimum dose causing effect (possible malformation) |
Most of the effects shown in Table 3 are classed as early effects as they are normally observed within a few days or weeks of exposure. The exception to this is the formation of cataracts following irradiation of the eye. This effect takes several years to develop and is therefore classified as a late effect. It is still a deterministic effect because there is a threshold dose below which cataracts will not occur.
The severity of the deterministic effects mentioned in Table 3 depends on the size of the dose and the period over which the dose was received. In fact, if the dose is received over several weeks rather than all at once, the threshold dose at which the effect occurs increases considerably, usually by about 100%.
Very high doses of radiation to the whole body can cause sufficient damage to the organs to stop their function and this may ultimately cause death. Radiation sickness (nausea, vomiting diarrhoea) is an early deterministic effect resulting from an acute high dose to the whole body. Other effects resulting from acute exposure to the whole body are shown in Table 4.
Table 23
Effects of Acute Whole Body Exposure to Radiation
Dose (mSv) | Effect |
50 000+ | Severe damage to central nervous system rapidly lethal. |
8 000 - 50 000 | Destruction of lining of intestine and white blood cells death within two weeks. |
4 000 | Fatal for half those irradiated within 30 days without medical treatment. |
2 000 - 8 000 | Damage to white blood cells and gut lining. Death may result from secondary infection but can be avoided in many cases with special medical treatment. |
1 000 - 2 000 | Possible radiation sickness nausea, vomiting, diarrhoea not lethal. |
Sometimes, the effect of radiation is not to kill the cell but to alter it in some way. In most cases this alteration will not affect the cell significantly so there will be no observable effect. However there is a possibility that the injury might affect the control system of the cell, subsequently causing it to divide more rapidly than normal. If the affected cell does begin to divide in this way, an increasing number of abnormal daughter cells will be produced. If these abnormal cells invade normal tissue they are called malignant cells and this results in cancer.
The type of cancer formed is dependent on the type of the original cell which was altered. Cancers do not appear immediately after radiation exposure but appear after a latency period in which no effects are observable. The latency period is dependent on the type of cancer but can vary from two years for leukemia to thirty years or possibly longer for some solid cancers. Hence, cancer is classified as a late effect.
Unlike deterministic effects, the amount of radiation exposure does not change the severity of the cancer but it does alter the chance of getting cancer. In other words, exposure to a high dose can increase the risk of getting a cancer but if cancer occurs (whether it be at low or high dose) the severity of the cancer is the same. This is rather like a lottery prize in that even a single ticket could win the first prize but the more tickets you buy the more chance you have of winning. However, the value of the prize does not change. Effects of ionizing radiation which rely on chance are referred to as stochasticeffects.
For the purposes of radiation protection, it is assumed that the probability of a stochastic effect increases linearly as the dose increases and that there is no threshold dose (see Figure 9). If there is no threshold dose then it is considered that even small doses of radiation might cause cancer.
Figure 50
Stochastic Dose Response Curve
Stochastic effects are the only effects possible at low doses. The risk of stochastic effects is the primary reason for limiting doses to both the public and radiation workers.
Stochastic effects are the only effects possible at low doses and hence, radiation protection is aimed at preventing deterministic effects and reducing the chances of stochastic effects occurring.
If one of the reproductive cells (either the sperm or the ovum) is damaged by ionizing radiation, there is a chance that this damage may affect either the immediate child or subsequent generations. This type of effect is therefore known as a hereditary effect. Hereditary effects are based on chance and hence are stochastic. However, the risk of hereditary effects is much lower than the risk of cancer.
Experimental studies on plants and animals have shown that hereditary effects can occur after exposure to large doses of radiation. However, there have been no cases identified in humans where radiation has resulted in hereditary effects.
Hereditary effects from exposure to ionizing radiation have not been identified in humans.
Some organs or tissue are more sensitive to radiation than others and will have an increased probability of developing stochastic effects. Also some cancers are more likely to result in death or serious problems than others. Hence, when determining the overall effect of ionizing radiation on humans, a factor known as the tissue weighting factor (wT) is applied. Basically, this factor takes into account the varying radiosensitivity of organs and tissues and the severity of the resulting cancer.
The values for radiation weighting factors given in Table 5 have been recommended internationally. The higher the value of the weighting factor, the greater is the probability of serious stochastic effects occurring following a specific exposure. Although different people respond to radiation doses differently the radiation weighting factors are approximated so that they can be applied to everybody. Note that the total of all radiation weighting factors for all tissues and organs adds up to give a whole body exposure factor of 1.
Table 24
Weighting Factors for Human Tissues and Organs
Tissue or Organ | Weighting Factor wT |
Gonads | 0.20 |
Red bone marrow | 0.12 |
Colon | 0.12 |
Lung | 0.12 |
Stomach | 0.12 |
Bladder | 0.05 |
Breast | 0.05 |
Liver | 0.05 |
Oesophagus | 0.05 |
Thyroid | 0.05 |
Skin | 0.01 |
Bone surface | 0.01 |
Remainder | 0.05 |
The above values imply that the lung is nearly two and a half times as sensitive to radiation as the thyroid (0.12 divided by 0.05 equals 2.4). In Module 2.5 Personal Dosimetry, you will learn how the radiation weighting factor can be used to convert an organ dose to a whole body dose.
In a foetus, or unborn child, the number of cells is less than in the adult and the cells are rapidly dividing. As radiation damage is more extensive on dividing cells, the foetus is particularly sensitive to radiation damage and exposure to high doses could result in possible malformation or even death. For this reason and because it is possible that exposure to radiation at any time in pregnancy may increase the probability of cancer in the child, special radiation protection measures are necessary to protect the foetus (see Module 2.1 Principles of Radiation Protection).
Research on the biological effects of ionizing radiation on developing foetus has mainly concentrated on the Hiroshima and Nagasaki bomb victims as well as the Chernobyl accident in 1986. These studies have indicated that exposure to radiation during the first two weeks of pregnancy has not resulted in deterministic or stochastic effects to the child. Between weeks two and twenty four of pregnancy, high doses to the mother can cause major organ damage to the developing foetus. The central nervous system could also be severely damaged resulting in mental retardation. At very high doses, effects such as spontaneous abortion, malformation and reduction in intelligence have been observed, the frequency and severity of these effects varying with both dose and stage of foetal development.
Several new terms have been introduced in this section and Figure 51 shows how all these terms are related. Remember that acute exposures may lead to early or late effects which may be either stochastic or deterministic. High level chronic exposures could lead to late effects which may be either deterministic or stochastic. In Figure 51, deterministic effects are shown in bold type and stochastic effects are shown in normal type.
* Never observed in humans
Summary of Radiation Effects
74.SELF-CHECK 3
Now see how much you have understood by answering the following questions in your workbook:
a) What is the most likely type of radiation effect (deterministic or stochastic) arising from whole body doses of radiation received regularly over a long period of time?
b) Is this an early or late effect?
What is the most likely type of radiation effect (deterministic or stochastic) arising from a high whole body dose of radiation which is received over a short period of time?
b) Is this an early or late effect?
Explain why cataract formation as a result of radiation exposure is classified as late deterministic effect.
Why are special radiation protection procedures needed for the foetus?
List the following organs and tissues in order of increasing sensitivity: thyroid, bladder, gonads, skin, red bone marrow.
Now check your answers with the model answers in your workbook.
75.KEY POINTS
The major systems in the body are the respiratory, digestive, circulatory, lymphatic and urinary systems.
Through various processes, inhaled and ingested materials may eventually be deposited in body organs. From this position they can irradiate nearby organs and tissues.
The human body is made up of small building blocks called cells which are grouped to form tissues and organs.
Each cell has a cell membrane, nucleus and cytoplasm.
The nucleus consists of 46 chromosomes.
Chromosomes consist of genes made up of proteins and molecules of DNA.
DNA carries genetic material concerning the physical and mental characteristics of a person.
Cells divide to produce more cells and during division the cell is more sensitive to radiation.
Ionizing radiation can damage a cell directly or indirectly by creating free radicals.
Free radicals can break the chemical bonds in the DNA molecule, damage the enzymes or damage the membranes of a cell.
Radiation damage may result in cell death, abnormal cell division or cell modification.
Radiation exposure may be acute (over a short period of time) or chronic (over a long period of time).
Radiation effects may be early effects or late effects.
Deterministic effects have a threshold below which there is no effect and above which the severity of the effect increases with dose. Deterministic effects are associated with high doses and dose rates.
Stochastic effects depend on chance and have a latency period before the effect occurs. There is thought to be no threshold for stochastic effects, and the chance of an effect increases as the dose increases. The severity of the effect is not dependent on the size of the dose.
Hereditary affects may occur if a reproductive cell is changed by radiation and this may be passed to future generations. Hereditary effects have not been observed in humans.
Stochastic effects are the only possible effects at low doses.
Radiation protection is aimed at preventing deterministic effects and reducing the chances of stochastic effects occurring.
Different organs within the body have different responses to radiation. Weighting factors are used to allow for the different radiosensitivities of the various organs.
The unborn child is very sensitive to radiation and special protective measures are required to protect the foetus.
76.FINAL ASSIGNMENT
This assignment is to be completed under test conditions, so spend some time now studying this module. Then contact your supervisor to arrange a suitable time to complete the assignment.
77.GLOSSARY OF TERMS
Acute exposure | Exposure to radiation over a short time period (a few hours or less). |
Chronic exposure | Exposure to radiation over a long time period (months or years). |
Cell membrane | The boundary of the cell. |
Chromosomes | Fine fibrous strands of genes. |
Cytoplasm | The fluid-like substance within a cell which contains many functional part of the cell. |
Deterministic effect | An effect of radiation (eg. skin reddening) which is characterised by having a threshold dose. |
Deoxyribonucleic acid (DNA) | A molecule which carries all the genetic material concerning the physical and mental characteristics of a human being. |
Dose | The amount of ionizing radiation absorbed by a human being. |
Early effect | A radiation effect which occurs within a few days or weeks of exposure. |
Foetus | An unborn child. |
Free radical | A chemically reactive atom group which may be formed by the ionization of water in the cell. |
Gene | The part of a chromosome consisting of proteins and DNA molecules. |
Hereditary effect | An effect of radiation which could be passed on to future generations. |
Late effect | A radiation effect which occurs years after exposure. |
Nucleus | The part of a cell which controls the functions of a cell. |
Stochastic effect | An effect of radiation (eg. cancer) where the probability of the effect is proportional to the dose received. The severity of the effect is, however, independent of the dose. |
Threshold dose | The dose of radiation below which there is no observable radiation injury. |
Tissue weighting factor | A factor which considers the differences in probability of fatal cancer for different organs and tissues. |