Area of Study 1

NUCLEAR PHYSICSAND RADIOACTIVITY

1UNIT

On completion of this area of study, you should be able to explain and model relevant physics ideas to describe the sources and uses of nuclear reactions and radioactivity and their effects on living things, the environment and in industry.

outcome

Nuclear physics and radioactivityMany people think that they never come into contact with

radioactive materials or the radiation that such materials produce. They are wrong to think this way. Human beings

have always been exposed to radiation from a variety of natural sources. The ground that we walk on is radioactive. Every time we inhale, we take minute quantities of radioactive radon into our lungs. Even the food we eat and the water we drink contain trace amounts of radioactive isotopes. It is now accepted that exposure to higher than normal levels of high-energy radiation leads to the development of cancerous tumours and leukaemia. However, radiation and radioactive elements can also be used in a variety of applications that are of real benefit to people in industry and in medicine, for example:

• Radioactive substances are used in the diagnosis and treatment of cancer. The photograph shows an image taken with a gamma ray camera. Technetium-99m (a radioactive isotope) was injected into the bloodstream of a patient. This allows the blood-flow patterns within the brain to be studied.

• Smoke detectors usually contain a small sample of the radioactive element americium-241.

• Geologists and archaeologists determine the age of rocks, artefacts and fossils by analysing the radioactive elements in them.

In this chapter, we will examine radioactivity and discuss the associated dangers and benefits of its many applications. An understanding of this topic will help you to develop an informed opinion on this important issue.

1CHAPTER

you will have covered material from the study of nuclear physics and radioactivity including:

• the origin, nature and properties of α, β and γ radiation

• the detection of α, β and γ radiation

• stable, unstable, natural and artifi cial isotopes

• production of artifi cial radioisotopes

• the half-life of a radioactive isotope

• radiation doses from internal and external sources

• effects of α, β and γ radiation on humans and other organisms

• nuclear transformations and decay series.

by the end of this chapter

Chapter 1 Nuclear physics and radioactivity 3

Atoms, isotopes and radioisotopes1.1

AtomsIn order to understand radioactivity, it is necessary to be familiar with the structure of the atom. The central part of an atom, the nucleus, consists of particles known as protons and neutrons. Collectively, these particles are called nucleons and are almost identical in mass and size. However, they have very different electrical properties. Protons have a positive charge, whereas neutrons are electrically neutral and have no charge. The nucleus contains nearly all of the mass of the atom, but accounts for less than a million-millionth (10−12) of its volume. Most of the atom is empty space that is only occupied by negatively charged particles called electrons. These are much smaller and lighter than protons or neutrons and they have various amounts of energy.

The simplest atom is hydrogen. It consists of just a single proton with a single electron. Compare this with a uranium-238 atom. Its nucleus contains 92 protons and 146 neutrons. Its 92 electrons occupy the region around the nucleus. Uranium-238 is the heaviest atom found in the Earth’s crust.

A particular atom can be identified by using the following format:

mass number

A

Z X element symbol

atomic number

The atomic number defines the element. Atoms with the same number of protons will all belong to the same element. For example, if an atom has six protons in its nucleus (i.e. Z = 6) then it is the element carbon. Any atom containing six protons is the element carbon, regardless of the number of neutrons.

In an electrically neutral atom, the number of electrons is equal to the number of protons. Any neutral atom of uranium (Z = 92) has 92 protons and 92 electrons.

The complete list of elements is shown in the periodic table in Figure 1.6.

IsotopesAll atoms of a particular element will have the same number of protons, but may have a different number of neutrons. For example, lithium exists naturally in two different forms. One type of lithium atom has three protons and three neutrons. The other type has three protons and four neutrons. These different forms of lithium are isotopes of lithium. Isotopes are chemically identical to each other. They react and bond with other atoms in precisely the same way. The number of neutrons in the nucleus does not influence the way in which an atom interacts with other atoms. The

Two important terms that are used to describe the nucleus of an atom are its:• ATOMIC NUMB…R (Z)—the number of protons in the nucleus of an atom.• MASS NUMB…R (A)—the total number of protons and neutrons in the nucleus.

i

To gain an idea of the emptiness of atoms and matter, consider this example. If the nucleus of an atom was the size of a pea and this was placed in the centre of the MCG, the electrons would exist in a three-dimensional space that would extend into the grandstands.

Physics file

Figure 1.2 (a) Hydrogen is the simplest atom. It consists of just one proton and one electron. (b) Uranium-238 is the heaviest naturally occurring atom. Its nucleus contains 238 nucleons—92 protons and 146 neutrons.

Figure 1.1 The nucleus of an atom occupies about 10−12 of the volume of the atom, yet it contains more than 99% of its mass. Atoms are mostly empty space!

(a)

(b)

nucleus consisting

protons ( )of neutrons ( ) and

cloud of electrons

Nuclear physics and radioactivity4

difference between isotopes lies in their physical properties. More neutrons in the nucleus will mean that these atoms have a higher density.

When referring to a particular nucleus, we talk about a nuclide. In this case, we ignore the presence of the electrons. For example, the nuclide lithium-6 has three protons and three neutrons. Stable isotopes can be found for most of the elements and, in all, there are about 270 stable isotopes in nature. Tin (Z = 50) has ten stable isotopes, while aluminium (Z = 13) has just one.

RadioisotopesMost of the atoms that make up the world around us are stable. Their nuclei have not altered in the billions of years since they were formed and, on their own, they will not change in the years to come.

However, there are also naturally occurring isotopes that are unstable. An unstable nucleus may spontaneously lose energy by emitting a particle and so change into a different element or isotope. Unstable atoms are radioactive and an individual radioactive isotope is known as a radioisotope. By way of illustration, carbon has two stable isotopes, carbon-12 and carbon-13, and one isotope in nature that is not stable. This is carbon-14. The nucleus of a radioactive carbon-14 atom may spontaneously decay, emitting high-energy particles that can be dangerous. If you look at the periodic table in Figure 1.6, you will see that every isotope of every element with atomic mass greater than that of bismuth (Z = 83) is radioactive.

Most of the elements found on Earth have naturally occurring radioisotopes; there are about 200 of these in all. As well as these, about 2000 radioisotopes have been manufactured. During the 20th century, an enormous number of radioisotopes were produced in a process known as artificial transmutation.

Artificial transmutation: how radioisotopes are manufacturedNatural radioisotopes were used in the early days of research into radiation. Today, most of the radioisotopes that are used in industrial and medical applications are synthesised by artificial transmutation. There are now more than 2000 such artificial radioisotopes. In the periodic table, every element with an atomic number greater than 92 (i.e. past uranium) is radioactive and is produced in this way.

One of the ways that artificial radioisotopes are manufactured is by neutron absorption. (In Australia, this is done at the Lucas Heights reactor near Sydney.) In this method, a sample of a stable isotope is placed inside a nuclear reactor and bombarded with neutrons. When one of the bombarding, or irradiating, neutrons collides with a nucleus of the stable isotope, the neutron is absorbed into the nucleus. This creates an unstable isotope of the sample element.

ISOTOP…S are atoms that have the same number of protons but different numbers of neutrons. Isotopes have the same chemical properties but different physical properties.

i

Figure 1.3 Isotopes of lithium. (a) The nucleus of a lithium-6 atom contains three protons and three neutrons. (b) The nucleus of a lithium-7 atom contains three protons and four neutrons.

Figure 1.4 This symbol is used to label and identify a radioactive source.

Figure 1.5 Artificial radioisotopes for medical and industrial uses are manufactured in the core of the Lucas Heights reactor in Sydney. This is Australia’s only nuclear reactor facility and has been operating since 1958. The original reactor was replaced by the OPAL (Open Pool Australian Light-water) reactor in 2007.

(a)

(b)

5Chapter 1 Nuclear physics and radioactivity

This is how the radioisotope cobalt-60 (widely used for cancer treatment) is manufactured. A sample of the naturally occurring and stable isotope cobalt-59 is irradiated with neutrons. Some of the cobalt-59 nuclei absorb neutrons and this results in a quantity of cobalt-60 being produced: 10n + 59

27Co → 6027Co. This nuclear transformation is illustrated in Figure 1.7.

Figure 1.6 The periodic table of elements.

Figure 1.7 The artificial radioisotope cobalt-60 is used extensively in the treatment of cancer. It is produced by bombarding a sample of cobalt-59 with neutrons.

Group

Period 1

Group

2

3

4

5

6

7

Lanthanides

Actinides

Every isotope of theseelements is radioactive

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2

H He 1.01 4.00 3 4 5 6 7 8 9 10

Li Be B C N O F Ne 6.94 9.01 10.81 12.01 14.01 16.00 19.00 20.18 11 12 13 14 15 16 17 18

Na Mg Al Si P S Cl Ar 22.99 24.31 26.98 28.09 30.97 32.06 35.45 39.95 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 39.10 40.08 44.96 47.90 50.94 52.00 54.94 55.85 58.93 58.71 63.54 65.37 69.72 72.59 74.92 78.96 79.91 83.80 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 85.47 87.62 88.91 91.22 92.91 95.94 (99) 101.07 102.91 106.4 107.87 112.40 114.82 118.69 121.75 127.60 126.90 131.30 55 56 57 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 132.91 137.34 138.91 178.49 180.95 183.85 186.2 190.2 192.2 195.09 196.97 200.59 204.37 207.19 208.98 (210) (210) (222) 87 88 89 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118

Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Rg Cn Uut Uuq Uup Uuh Uus Uuo (223) (226) (227) (261) (262) (263) (264) (277) (268) (271) (272) (277) (289) (289) (292) (293)

58 59 60 61 62 63 64 65 66 67 68 69 70 71

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu 140.12 140.91 144.24 (145) 150.35 151.96 157.25 158.92 162.50 164.93 167.26 168.93 173.04 174.97

90 91 92 93 94 95 96 97 98 99 100 101 102 103

Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr 232.04 (231) 238.03 (237) (242) (243) (247) (247) (249) (254) (253) (256) (254) (257)

cobalt-59: stable cobalt-60: radioactive

The heaviest stable isotope in the universe is 209

83Bi. Every isotope of every element with more than 83 protons, i.e. beyond bismuth in the periodic table, is radioactive. For example, every isotope of uranium (Z = 92) is radioactive. Technetium (Z = 43) and promethium (Z = 61) are the only elements with an atomic number below bismuth (Z = 83) that do not have any stable isotopes. Uranium is the heaviest element that occurs naturally on Earth. All the elements with atomic numbers greater than 92 have been artificially manufactured.

Physics file

Nuclear physics and radioactivity6

Worked example 1.1A Use the periodic table in Figure 1.6 to determine:a the symbol for element 95

42X

b the number of protons, nucleons and neutrons in this isotope.

Solution a From the periodic table, the element with an atomic number of 42 is Mo, molybdenum.b The lower number is the atomic number, so this isotope has 42 protons. The upper

number is the mass number. This indicates the number of particles in the nucleus, i.e. the number of nucleons, so this atom has 95 nucleons. The number of neutrons can be found by subtracting 42 from the mass number. This isotope has 53 neutrons.

Our understanding of the atom has changed greatly in the past 100 years. It was once thought that atoms were like miniature billiard balls: solid and indivisible. The word ‘atom’ comes from the Greek ‘atomos’ meaning indivisible. That idea was changed forever when the first subatomic particles—the electron, the proton and then the neutron—were discovered in the period from 1897 to 1932.

Since World War II, further research has uncovered about 300 other subatomic particles! Examples of these include pi-mesons, mu-mesons, kaons, tau leptons and neutrinos. For many years, physicists found it difficult to make sense of this array of subatomic particles. It was known that one family of particles called the leptons had six members: electron, electron-neutrino, muon, muon-neutrino, tau and tau-neutrino.

Then in 1964 Murray Gell-Mann put forward a simple theory. He suggested that most subatomic particles were themselves composed of a number of more fundamental particles called quarks. Currently, it is accepted that there are six different quarks, each with different properties (and strange names!): up, down, charmed, strange, top and bottom. The latest quark to be identified was the top quark, whose existence was confirmed in 1995. The proton consists of two up quarks and one down quark, while neutrons consist of one up quark and two down quarks. Subatomic particles that consist of quarks are known as hadrons. Leptons are indivisible point particles; they are not composed of quarks.

A significant amount of effort and money has been directed to testing Gell-Mann’s theory—both theoretically and experimentally. This has involved the construction of larger and larger particle accelerators such as Fermilab in Chicago and CERN in Geneva. Australia built its own particle accelerator—a synchrotron—next to Monash University. This began operating in 2007.

While the current theory suggests that quarks and leptons are the ultimate fundamental particles that cannot be further divided, the nature of scientific theories and models is such that they can change as new experimental data are obtained. Are quarks and leptons made of smaller particles again? Time will tell!

Quarks and other subatomic particles!Physics in action

Figure 1.8 This particle accelerator is at the CERN European centre for high-energy physics. It accelerates protons from rest to 99.99995% of the speed of light in under 20 seconds!

7Chapter 1 Nuclear physics and radioactivity

• The nucleus of an atom consists of positively charged protons and neutral neutrons. Collectively, protons and neutrons are known as nucleons. Negatively charged electrons surround the nucleus.

• The atomic number, Z, is the number of protons in the nucleus. The mass number, A, is the number of nucleons in the nucleus, i.e. the combined number of protons and neutrons.

• Isotopes of an element have the same number of protons but a different number of neutrons. Isotopes

of an element are chemically identical to each other, but have different physical properties.

• An unstable isotope—a radioisotope—may spon tan-eously decay by emitting a particle from the nucleus.

• Artificial radioisotopes are manufactured in a process called artificial transmutation. This commonly takes place as a result of neutron bombardment in the core of a nuclear reactor.

Atoms, isotopes and radioisotopes1.1 summary

1 1 How many protons, neutrons and nucleons are in the following nuclides? a 45

20Cab 197

79Auc 235

92Ud 230

90Th

2 2 How many protons and neutrons are in these atoms? Use the periodic table to answer this question.a cobalt-60b plutonium-239c carbon-14

3 3 What is the difference between a stable isotope and a radioisotope? Give three examples of stable isotopes.

4 4 Can a natural isotope be radioactive? If so, give an example of such an isotope.

5 5 Which of these atoms are definitely radioactive?

2412Mg, 59

27Co, 19578Pt, 210

84Po, 23892U

Explain how you made your choice.

6 Radium was discovered by Marie and Pierre Curie in 1898. Two isotopes of radium are Ra-226 and Ra-228. Use the periodic table to answer this question.a How many protons, neutrons and nucleons are in

a nucleus of radium-226?b How many protons, neutrons and nucleons are in

a nucleus of radium-228?

c A geologist is examining a small lump of radium-226 and a small lump of radium-228. The samples contain exactly the same numbers of atoms as each other. Is it possible for the geologist to determine which isotope is which? Explain.

7 7 The nucleus of a gold atom has a radius of 6.2 × 10−15 m while the atom itself has a radius of 1.3 × 10−10 m. Given that the volume of a sphere is V = 4

3 πr3, determine the value of the fraction:

volume of nucleus volume of atom

8 8 As part of a science project, a student wanted to make a scale model of a gold atom using a marble of radius 1.0 cm as the nucleus. Calculate the radius of the sphere to be occupied by the electrons in this model. Use the information in Question 7 to assist your calculations.

9 9 Krypton-84 is stable but krypton-89 is radioactive. a Discuss any differences in how these atoms would

interact chemically with other atoms.b Describe the difference in the composition of these

two atoms.

10 10 A particular artificial radioisotope is manufactured by bombarding the stable isotope 27Al with neutrons. The radioisotope is produced when each atom of 27Al absorbs one neutron into the nucleus. Identify the radioisotope that is produced as a result of this process.

Atoms, isotopes and radioisotopes1.1 questions

Worked Solutions

Nuclear physics and radioactivity8

Radioactivity and how it is detected1.2

Through the Middle Ages, alchemists tried without success to change lead into gold. They thought that it would be possible to devise a chemical process that would change one element into another. We now know that it is extremely difficult to change one element into another and that chemistry is not the way to do it. About 100 years ago, Ernest Rutherford and Paul Villard discovered that there were three different types of emission from radioactive substances. They named these alpha, beta and gamma radiation. Further experiments showed that the alpha and beta emissions were actually particles expelled from the nucleus. Gamma radiation was found to be high-energy electromagnetic radiation, also emanating from the nucleus. When these radioactive decays occur, the original atom spontaneously changes into an atom of a different element. Nature was already doing what the alchemists had so fruitlessly tried to do!

Scientists such as Ernest Rutherford quickly made use of these new particles to investigate the nature of matter. Later on, scientists also used them to create new isotopes.

Alpha decay 42α

When a heavy nucleus undergoes radioactive decay, it may eject an alpha particle. An alpha particle is a positively charged chunk of matter. It consists of two protons and two neutrons that have been ejected from the nucleus of a radioactive atom. An alpha particle is identical to a helium nucleus and can also be written as 42He2+, α2+, 42 α or simply α.

Uranium-238 is radioactive and may decay by emitting an alpha particle from its nucleus. This can be represented in a nuclear equation in which the changes occurring in the nuclei can be seen. Electrons are not considered in these equations—only nucleons. The equation for the alpha decay of uranium-238 is:

23892U → 234

90Th + 42α + energyor

23892U α→ 234

90ThIn the decay process, the parent nucleus 238

92U has spontaneously emitted an alpha particle (α) and has changed into a completely different element, 234

90Th. Thorium-234 is called the daughter nucleus. The energy released is mostly kinetic energy carried by the fast-moving alpha particle.

When an atom changes into a different element, it is said to undergo a nuclear transmutation. In nuclear transmutations, electric charge is conserved—seen as a conservation of atomic number. In the above example 92 = 90 + 2. The number of nucleons is also conserved: 238 = 234 + 4.

Figure 1.9 Marie Curie performed pioneering work on radioactive materials. In fact, Marie Curie coined the term ‘radioactivity’ and is one of only four scientists to have been awarded two Nobel prizes. She received one for chemistry and one for physics.

Figure 1.10 Ernest Rutherford was born in New Zealand and is considered to be one of the greatest experimental physicists who ever lived. He used the newly discovered alpha particles to investigate the nature of matter. His discoveries form the foundation of nuclear physics.

Figure 1.11 When the nucleus of uranium-238 decays, it will spontaneously eject a high-speed alpha particle that consists of two protons and two neutrons. The remaining nucleus is thorium-234. Kinetic energy, carried by the thorium-234 and alpha particles, is released as a result of this decay.

alpha particle

thorium-234uranium-238: unstable

9Chapter 1 Nuclear physics and radioactivity

Beta decay –1

0βBeta particles are electrons, but they are electrons that have originated from the nucleus of a radioactive atom, not from the electron cloud. A beta particle can be written as −1

0e, β, β− or −10β. The atomic number of −1 indicates

that it has a single negative charge, and the mass number of zero indicates that its mass is far less than that of a proton or a neutron.

Beta decay occurs in nuclei in which there is an imbalance of neutrons to protons. Typically, if a light nucleus has too many neutrons to be stable, a neutron will spontaneously change into a proton, and an electron and an uncharged massless particle called an antineutrino ( ν– ) are ejected to restore the nucleus to a more stable state.

Consider the isotopes of carbon: 126C, 13

6C and 146C. Carbon-12 and

carbon-13 are both stable, but carbon-14 is unstable. It has more neutrons and so undergoes a beta decay to become stable. In this process one of the neutrons changes into a proton. As a result, the proton number increases to seven, and so the product is not carbon. Nitrogen-14 is formed and energy is released.

The nuclear equation for this decay is: 14

6C → 147N + −1

0β + ν– + energyThe transformation taking place inside the nucleus is:

10n → 11p + −1

0e + ν–

Once again, notice that in all these equations the atomic and mass numbers are conserved. (The antineutrino has no charge and has so little mass that both its atomic and mass numbers are zero.)

Gamma decay γGenerally, after a radioisotope has emitted an alpha or beta particle, the daughter nucleus holds an excess of energy. The protons and neutrons in the daughter nucleus then rearrange slightly and off-load this excess energy by releasing gamma radiation (high-frequency electromagnetic radiation). Gamma rays—like all light—have no mass and are uncharged and so their symbol is 00γ. Being a form of light, gamma rays travel at the speed of light.

A common example of a gamma ray emitter is iodine-131. Iodine-131 decays by beta and gamma emission to form xenon-131 as shown in Figure 1.13.

In any nuclear reaction, including radioactive decay, atomic and mass numbers are conserved. Energy is released during these decays.

i

Figure 1.12 The nucleus of carbon-14 is unstable. In order to achieve stability, one neutron transforms into a proton, and an electron and antineutrino are emitted in the process. The emitted electron is a beta particle, and it travels at nearly the speed of light.

carbon-14:unstable

nitrogen-14:stable

beta particle –10β

antineutrino ν–A different form of beta decay occurs in atoms that have too many protons. An example of this is the radioactive decay of unstable nitrogen-12. There are seven protons and five neutrons in the nucleus, and a proton may spontaneously change into a neutron and emit a neutrino (ν) and a positively charged beta particle. This is known as a β+ (beta-positive) decay and the positively charged beta particle is called a positron.

The equation for this decay is:

127N → 12

6C + +10e + ν + energy

Positrons, +10β, have the same

properties as electrons, but their electrical charge is positive rather than negative. Positrons are an example of antimatter.

Physics file

Nuclear physics and radioactivity10

The equation for this decay is:

13153I → 131

54Xe + −10e + γ

or131

53I β, γ

→ 13154Xe

Since gamma rays carry no charge and have almost no mass, they have no effect when balancing the atomic or mass numbers in a nuclear equation.

The chart in Figure 1.14 identifies the 272 stable nuclides, as well as some radionuclides and decay modes.

Worked example 1.2A Strontium-90 decays by radioactive emission to form yttrium-90. The equation is:

9038

Sr → 90

39Y

+ X

Determine the atomic and mass numbers for X and identify the type of radiation that is emitted during this decay.

Solution By balancing the equation, it is found that X has a mass number of zero and an atomic number of −1. X is an electron and so this must be beta decay. The full equation is 9038

Sr → 9039

Y + −1

0e.

Worked example 1.2B Iodine-131, a radioisotope that is used in the treatment of thyroid cancer, is produced in a two-stage process. First, tellurium-130 (130

52Te) is bombarded with neutrons inside the core

of a nuclear reactor. This results in the formation of the very unstable tellurium-131 and a gamma ray.a Write down the balanced nuclear equation for this process.b Tellurium-131 decays by beta emission to produce a daughter nuclide and an

antineutrino. Identify the daughter nuclide.

Solution a 130

52 Te + 1

0n → 131

52 Te + γ

b Both the atomic and mass number of the antineutrino are zero. The beta particle has a mass number of zero and an atomic number of –1.

13152

Te → 13153

X + −1

0β + ν–

Balancing the nuclear equation gives the unknown element an atomic number of 53 and a mass number of 131. The periodic table reveals the daughter nuclide to be iodine-131.

Figure 1.13 In the beta decay of iodine-131, a high-energy gamma ray photon is also emitted. This high-energy electromagnetic radiation has no electric charge—just energy. The beta particle and xenon nucleus also carry energy.

iodine-131:unstable

xenon-131gamma ray 00

beta particle –10

Gamma decay alone occurs when a nucleus is left in an energised or excited state following an alpha or beta decay. This excited state is known as a metastable state and it usually only lasts for a short time. An example of this is the radioactive decay of iodine-131, usually a two-stage process.

First, a beta particle is emitted and the excited nuclide xenon-131m is formed. Then, the nucleus undergoes a second decay by emitting a gamma ray:

The ‘m’ denotes an unstable or metastable state. Cobalt-60 and technetium-99 also exist in metastable states.

I → 13153

Xe + 131m54

e 0–1

Xe → 131m54

Xe + 13154

γ

Physics file

11Chapter 1 Nuclear physics and radioactivity

Figure 1.14 From this table of stable isotopes and radioisotopes, it is evident that for larger nuclei there is a distinct imbalance between the number of protons and neutrons. The ‘line of stability’ of the stable nuclides can be seen as a line that curves away from the N = Z line. Notice that every element, up to and including bismuth, has stable isotopes, except for technetium and promethium. Also notice that every isotope of every element beyond bismuth is radioactive.

− − − + +− − − − − − +

− − − − + +− − − − − + + +

− − − + + + +− − − − + + + +

− + + + + + +− − −− − −− −

− −− −

− − −− − − −

− − − − −− − − −

− − − − − −

− − − − − − − + +− − − − − − − − +

− − − − − − − + + +− − − − − − − + + +− − − − − + + + + +− − − − − − + + + +− − − − + + + + + +− − − + + − − − − −

+ + + + + + + + + + + + + + + + + +

−−−

− −− − − −− − − −

− − − − −− − − − − − − − −− − − − − − − − +− − − − − − − − −

− − − − − + + + + +− − − − − + + + + +− − − − + + + + + +− − − + + + + + + +− − + + + + + + + +− − + + + + + + + +− + + + + + + + + +− + + + + + + + + ++ + + + + + + + + +

+ + + + + + + + +

− −− −

− − −− − −

− − − −− − − −

− − − + +− − − − − − +− − − + + + +

− − − − − − − + + +

+ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + +

− − − − − − − − − +− − − − − − − − − +− − − − − − − + + +− − − − − − − + + +− − − − − + + + + +− − − − − − + + + +− − − − + + + + + +− − − + + + + + + +− − − + + + + + + +− − + + + + + + + +

+ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + +

− − − − − − − + + +− − − − − − − + + +− − − − − + + + + +− − − − − + + + + +− − − − + + + + + +− − − − + + + + + +− − + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + +

− − − −− − − −

− − − − −− − − − −

− − − − − −− − − − − − −− − − − − − −

− − − − − − − −− − − − − − − −− − − − − − − −

− − − − − − − − − −− − − − −

− − − − − −− − − − − − − −− − − − − − − −

− − − − − − − − −− − − − − − − − − −− − − − − − − − − −− − − − − − − − − −

− − − − + + + + +− − − − − + + + + +− − − + + + + + + +− − − + + + + + + +− − − + + + + + + +− − − + + + + + + ++ + + + + + + + + ++ + + + + + + + + α+ + + + + + + + + ++ + + + + + + α α α

+ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + +

− − − −− − − −

− − − − −− − − − −

− − − − − −− − − − − − −− − − − − − −

− − −− − −− − −

−−−−

− − −− − −− − −

− − − −− − − −− − − −

+ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + +

− − − − − − − + + +− − − − − − − + + +− − − − + + + + + +− − − − + + + + + +− − − − + + + + + +− − − − + + + + + +− − + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + +

− − − − − − − − − − − − −− − − − − − −− − − − − − −

− − − − − − − −− − − − − − − − −

− − − − − − − − − −− − − − − − − − − −− − − − − − − + + +− − − − − − − + + +

− − − + + + + + + +− − − − + + α + + +− − − + + + + + + α− − + + α + + α + α− + + + + + α α α α+ + α + α α α α α α+ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + +

+ α α α α + + + + ++ α α α α + α + + ++ α α α α + + + + αα α α α α + + α + αα α α α α + α α α αα α α α α α α α α α+ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + + + +

− − − − − − − − − − − − −− − − − − − −− − − − − − −

− − − − − − − −− − − − − − − − −

− − − − − − − − − −− − − − − − − − − −− − − − − − − − − −

− − − − − −

− − − − − − − − +− − − − − − − − − +− − − − − − − + + +− − − − − − − + + +− − − − − − − + + +− − − − − − − + + +− − − − − + + + + +− − − − − + + + + +− − − − − + + + + +− − − − − + + + + +

+ + + + + + + α α α+ + + + + + + α α α+ + + + + + + α α α+ + + + + + + α α α+ + + + + + α α α α+ + + + + + α α α α+ + + + + + α α α α+ + + + + + + + + ++ + + + + + + + + ++ + + + α + + + + +

− − − − − − − − − − − − −

−−

− −− −

− − −− − −

− − − −− − − −

+ + + α α α+ α α α+ + + α + + + α α α+ + + α + + + α α α+ + + α + + + α α α+ + + + + + α α α α+ + + + + + α α α α+ + + + + + α α α α+ + + + + + + + + ++ + + + + + + + + ++ + + + α + + + + +

αααα

− − − −− − − −

− − − − +− − − − +

− − − − + +− − − − − +

− − − − + + +− − − − − + α +− − − − − + + +− − − − + + + +

+ + + + + + + α α α+ + + + + + + α α α+ + + + + + α α α α+ + + + α α α α α α+ + + + α α α α α α+ + + + α α α α α α+ + + + α α α α α α+ + + + α α α α α α+ + + + α α α α α α+ + + α α α α α α α

− − − − − − − − − − − − −

−−

− −− −

− − −− − −

− − − −− − − −

− − − − α α α α α α− − − α α α α α α α− − − − α α α α α α− − − − α + α α α α− − − + α + α α α α− − − + α + α α α α+ + + + + + + α α α+ + + + + + + α α α+ + + + + + + α α α+ + + + + + + α α α

αααα αα ααα

− − − −− − α −− − − −α α α αα α α α

α α α α α αα α α α α α

− − α α α α α α − − α α α α α α− − α α α α α α

αα − αα − αα α α αα α αα α αα αα αα αα

αα − αα − αα α α αα α αα α αα α αα α αα α αα α α−

‘Line of stability’

+ + ++ + ++ + ++

N = Z

−−−

− −− − − −− − − −

− − − − −− − − − − − − − −

−−

−−−

− −− − − −− − − −

− − − − −− − − − − − − − −

−−

− − − −− − − −

− − − − −− − − − −

− − − − − −− − − − − − −− − − − − − −

− − −− − −− − −

αα

− − α α α α α α αα

+ + + + + + + α α α+

+ + + + + + + + α α

+ + + + ++ + + ++

++ + + + + + ++ + + ++

+ + + +

+ + + + + + + + ++++

+ + + +− − + + +

+ + + + + +

+ + + + + + + + +− − − − − − − − −−

+ + +− − − − − −

−−−−−

+

−−−

−

++++

+

−−−−−−−

L

++++++++

++++

−−−−−+

−−−

i

++++++

+++++

−−

++

−−

+++ααα

+

++++++++++

−−−

ααα

++++++αααα

+

++++++++++

+

−−

+

ααααααα

α

αααααααααα

α

α

+ + + + α ++ + + + + +− − − −− +− − − − − − +

α+ + + + + + + α α α α−−− − α

+++++

+++

+

−−−−−−++

−−−−

+

α α αα140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

Num

ber

of n

eutr

ons

(N)

0 10 20 30 40 50 60 70 80 90 100

Atomic number (Z)

Bismuth, Z = 83

Promethium, Z = 61

Technetium, Z = 43

stable nuclide− β− emitter+ β+ emitterα emitter

Key

α

Nuclear physics and radioactivity12

Why radioactive nuclei are unstableInside the nucleus there are two completely different forces acting. The first is an electric force of repulsion between the protons. On its own, this would blow the nucleus apart, so clearly a second force must act to bind the nucleus together. This is the nuclear force, a strong force of attraction between nucleons, which acts only over a very short range.

In a stable nucleus, there is a delicate balance between the repulsive electric force and the attractive nuclear force. For example, bismuth-209, the heaviest stable isotope, has 83 protons and 126 neutrons, and the forces between the nucleons balance to make the nucleus stable. Compare this with bismuth-211. It has two extra neutrons and this upsets the balance between forces. The nucleus of 211Bi is unstable and it ejects an alpha particle in an attempt to attain nuclear stability.

Figure 1.14 shows all the stable nuclei with their proton and neutron numbers. It is evident that there is a ‘line of stability’ along which the nuclei tend to cluster. Nuclei away from this line are radioactive. For small nuclei with atomic numbers up to about 20, the ratio of neutrons to protons is close to one. However, as the nuclei become bigger, so too does the ratio of neutrons to protons. Zirconium (Z = 40) has a neutron to proton ratio of about 1.25, while for mercury (Z = 80) the ratio is close to 1.66. This indicates that for higher numbers of protons, nuclei must have even more neutrons to remain stable. These neutrons dilute the repelling forces that act between the extra protons. Elements with more protons than bismuth (Z = 83) simply have too much repulsive charge and additional neutrons are unable to stabilise their nuclei. All of these atoms are radioactive.

How radiation is detectedOur bodies cannot detect alpha, beta or gamma radiation. Therefore a number of devices have been developed to detect and measure radiation.

A common detector is the Geiger counter. These are used:• by geologists searching for radioactive minerals such as uranium• to monitor radiation levels in mines• to measure the level of radiation after a nuclear accident such as the

accident at Fukushima, Japan, in 2011• to check the safety of nuclear reactors• to monitor radiation levels in hospitals and factories.

A Geiger counter consists of a Geiger–Muller tube filled with argon gas as shown in Figure 1.15. A voltage of about 400 V is maintained between the positively charged central electrode and the negatively charged aluminium tube. When radiation enters the tube through the thin mica window, the argon gas becomes ionised and releases electrons. These electrons are attracted towards the central electrode and ionise more argon atoms along the way. For an instant, the gas between the electrodes becomes ionised enough to conduct a pulse of current between the electrodes. This pulse is registered as a count. The counter is often connected to a small loudspeaker so that the count is heard as a ‘click’.

People who work where there is a risk of continuing exposure to low-level radiation usually pin a small radiation-monitoring device to their clothing.

Neutrinos are particles with the lowest mass in nature, and they permeate the universe. Neutrinos have no charge and their mass has only recently been discovered to be about one-billionth that of a proton, i.e. about 10−36 kg. While you have been reading these sentences, billions of neutrinos have passed right through your body, and continued on to pass right through the Earth! Fortunately neutrinos interact with matter very rarely and so are harmless. It has been estimated that if neutrinos passed through a piece of lead 8 light-years thick, they would still have only a 50% chance of being absorbed!

Physics file

Figure 1.15 A radioactive emission that enters the tube in a Geiger counter will ionise the argon gas and cause a pulse of electrons to flow between the electrodes. This pulse registers as a count on a meter.

+

–

thin micawindow

positively chargedelectrode

argongas

negatively chargedaluminium tube

Interactive

13Chapter 1 Nuclear physics and radioactivity

This could be either a film badge or a TLD (thermoluminescent dosimeter). These devices are used by personnel in nuclear power plants, hospitals, airports, dental laboratories and uranium mines to check their daily exposure to radiation. When astronauts go on space missions, they wear monitoring badges to check their exposure to damaging cosmic rays.

Film badges contain photographic film in a lightproof holder. The holder contains several filters of varying thickness and materials covering a piece of film. After being worn for a few weeks, the film is developed. Analysis of the film enables the type and amount of radiation to which the person has been exposed to be determined.

Thermoluminescent dosimeters are more commonly used than film badges. TLDs contain a disk of lithium fluoride encased in plastic. Lithium fluoride can detect beta and gamma radiation as well as X-rays and neutrons. Thermoluminescent dosimeters are a cheap and reliable method for measuring radiation doses.

Figure 1.16 Thermoluminescent dosimeters are used by doctors, radiologists, dentists and technicians who work with radiation, to monitor their exposure levels.

Technetium-99m is the most widely used radioisotope in nuclear medicine. It is used for diagnosing and treating cancer. However, this radioisotope decays relatively quickly and so usually needs to be produced close to where it is to be used. Technetium-99m is produced in small nuclear generators that are located in hospitals around the country. In this process, the radioisotope molybdenum-99, obtained from Lucas Heights, is used as the parent nuclide. Molybdenum-99 decays by beta emission to form a relatively stable (or metastable) isotope of technetium, technetium-99m, as shown below:

9942Mo → 99m

43Tc + −10β + ν–

Technetium-99m is flushed from the generator using a saline solution. The radioisotope is then diluted and attached to an appropriate chemical compound before being administered to the patient as a tracer. Technetium-99m is purely a gamma emitter. This makes it very useful as a diagnostic tool for locating and treating cancer. Its decay equation is:

99m43Tc → 99

43Tc + γ

How technetium is producedPhysics in action

Figure 1.17 Technetium generators are used in hospitals that require radioisotopes. The generator has a thick lead shield that absorbs the beta and gamma radiation.

SPARKlab Risk AssessmentPrac 1

Nuclear physics and radioactivity14

• Radioactive isotopes may decay, emitting alpha, beta and gamma radiation from their nuclei.

• An alpha particle, α, consists of two protons and two neutrons. It is identical to a helium nucleus and can be written as 42α, α2+ or 42He.

• A beta particle, β, is an electron, −10e, that has been

emit ted from the nucleus of a radioactive atom as a result of a neutron transmuting into a proton.

• A gamma ray, γ, is high-energy electromagnetic

radiation that is emitted from the nuclei of radioactive atoms. Gamma rays usually accompany an alpha or beta emission.

• In any nuclear reaction, both atomic and mass numbers are conserved.

• Radiation can be detected using a device such as a Geiger counter. People can monitor their exposure to radiation with film badges and thermoluminescent dosimeters.

Radioactivity and how it is detected1.2 summary

1 From which part of a radioisotope, the nucleus or the electron cloud, are the following particles emitted?a alpha particles b beta particles c gamma rays

2 2 Discuss the physical differences between α, β and γ radiation.

3 3 Identify each of these particles.a −1

0A b 11B c 4

2C d 10D

4 4 Determine the atomic and mass numbers for the unknown elements, X, in these decay equations, then use the periodic table to identify the elements.a 218

84Po → X + α + γ b 23592U

α, γ→ X

c 22888Ra → X + β + γ d 198

79Au β, γ→ X

5 5 Determine the mode of radioactive decay for each of the following transmutations.a 218

86Rn → 21484Po + X + γ b 234

91Pa x, γ→ 234

92Uc 214

82Pb → 21483Bi + X + γ d 239

94Pu x, γ→ 235

92Ue 60m

27 Co → 6027Co + X

6 6 When the stable isotope boron-10 is bombarded with neutrons, it transmutes by neutron capture into a different element X and emits alpha particles. The equation for this reaction is:

105B + 10n → X + 42He.

Identify the final element formed.

7 7 Identify the unknown particles in these nuclear transmutations.a 14

7N + α → 178O + X b 27

13Al + X → 2712Mg + 11H

c 147N + X → 14

6C + 11p d 2311Na + X → 26

12Mg + 11H

8 8 Carbon-14 decays by beta emission to form nitrogen-14. The equation for this is 14

6C → 147 N + −1

0e + ν–. It can be seen that the carbon nucleus initially has six protons and eight neutrons.

a List the particles that comprise the decay side of this equation.

b Analyse the particles and determine which particle from the parent nucleus has decayed.

c Write an equation that describes the nature of this decay.

d Energy is released during this decay. In what form does this energy exist?

9 9 Use the chart in Figure 1.14 to answer these questions.a List all the stable nuclides of calcium, Z = 20.b How many stable nuclides does niobium, Z = 41,

have?c 48

19K has a large imbalance of neutrons over protons and so is radioactive. Find potassium-48 on the chart and determine whether it is an alpha or beta emitter.

d Write the decay equation for potassium-48 and determine whether the daughter nucleus is itself stable or radioactive.

e Calculate the ratio of neutrons to protons for each of potassium-48 and its daughter nucleus.

f 21787Fr is a radioisotope. Is it an alpha or beta

emitter?g Determine the decay processes that francium-217

undergoes before it becomes a stable nuclide; identify this nuclide.

10 10 Gold has only one naturally occurring isotope, 197Au. If a piece of gold foil is irradiated with neutrons, neutron capture will occur and a radioactive isotope of gold will be produced. This radioisotope is a beta emitter. Write an equation that describes the:a neutron absorption processb decay process.

Radioactivity and how it is detected1.2 questions

Worked Solutions

Chapter 1 Nuclear physics and radioactivity 15

Properties of alpha, beta and gamma radiation1.3

Alpha particles, beta particles and gamma rays all originate from the same place—the nucleus of a radioisotope. Each type of radiation has enough energy to dislodge electrons from the atoms and molecules that they smash into. This property is what makes radiation dangerous, but it also enables it to be detected. The properties of alpha, beta and gamma radiation are distinctly different from each other. During early investigations of radioactivity, the emissions from a sample of radium were directed through a magnetic field. As shown in Figure 1.18, the emissions followed three distinct paths, suggesting that there were three different forms of radiation being emitted.

Alpha particlesAlpha particles, α, consist of two protons and two neutrons. Because an alpha particle contains four nucleons, it is relatively heavy and slow moving. It is emitted from the nucleus at speeds of up to 20 000 km s−1 (2.0 × 107 m s−1), just less than 10% of the speed of light.

Alpha particles have a double positive charge. This, combined with their relatively slow speed, makes them very easy to stop. They only travel a few centimetres in air before losing their energy, and will be completely absorbed by thin card. They have a poor penetrating ability.

Beta particlesBeta particles, β, are fast-moving electrons, created when a neutron decays into three parts—a proton, an electron (the beta particle) and an antineutrino. Beta particles are much lighter than alpha particles, and so they leave the nucleus with far higher speeds—up to 90% of the speed of light.

Figure 1.18 When radiation from radium passes through a magnetic field, the radiation splits up and takes three different paths. One path is undeflected. The other two paths deviate in opposite directions and to different extents. This suggests that there are three different forms of radiation being emitted from radium.

Figure 1.20 Gamma rays can pass through human tissue and sheets of aluminium quite readily. A 5 cm thick sheet of lead is needed to stop 97% of the gamma rays in a beam. By comparison, alpha particles are not capable of penetrating through a sheet of paper or beyond the skin of a person.

Figure 1.19 The relative speeds of alpha, beta and gamma radiation. (a) Alpha particles are the slowest of the radioactive emissions. Typically they are emitted from the nucleus at up to 10% of the speed of light. (b) Beta particles are emitted from the nucleus at speeds up to 90% of the speed of light. (c) Gamma radiation, being high-energy light, travels at the speed of light (3.0 × 108 m s−1).

N

SRamagnet α

γβ

α

β

γ

aluminium lead

c

~0.1c

~0.9c

42α

–10β

00γ ray

(a)

(b)

(c)

Interactive Risk AssessmentPrac 1

Nuclear physics and radioactivity16

Beta particles are more penetrating than alpha particles, being faster and with a smaller charge. They will travel a few metres through air but, typically, a sheet of aluminium about 1 mm thick will stop them.

Gamma raysGamma rays, γ, being electromagnetic radiation with a very high frequency, have no rest mass and travel at the speed of light—3.0 × 108 m s−1 or 300 000 km s−1. They have no electric charge. Their high energy and uncharged nature make them a very penetrating form of radiation. Gamma rays can travel an almost unlimited distance through air and even a few centimetres of lead or a metre of concrete would not completely absorb a beam of gamma rays.

The ionising abilities of alpha, beta and gamma radiationWhen an alpha particle travels through air, its slow speed and double positive charge cause it to interact with just about every atom that it encounters. The alpha particle dislodges electrons from many thousands of these atoms, turning them into ions. Each interaction slows it down a little, and eventually it will be able to pick up some loose electrons to become a helium atom. This takes place within a centimetre or two in air. As a consequence, the air becomes quite ionised, and the alpha particles are said to have a high ionising ability. Since the alpha particles don’t get very far in the air, they have a poor penetrating ability.

Beta particles have a negative charge and are repelled by the electron clouds of the atoms they interact with. This means that when a beta particle travels through matter, it experiences a large number of glancing collisions and loses less energy per collision than an alpha particle. As a result, beta particles do not ionise as readily and will be more penetrating.

Gamma rays have no charge and move at the speed of light, and so are the most highly penetrating form of radiation. Gamma rays interact with matter infrequently, when they collide directly with a nucleus or electron. The low density of an atom makes this a relatively unlikely occurrence. Gamma rays pass through matter very easily—they have a very poor ionising ability but a high penetrating ability.

The energy of alpha, beta and gamma radiationThe energy of moving objects such as cars and tennis balls is measured in joules. However, alpha, beta and gamma radiation have such small amounts of energy that the joule is inappropriate. The energy of radioactive emissions is usually expressed in electronvolts (eV). An electronvolt is the energy that an electron would gain if it were accelerated by a voltage of 1 volt.

One …L…CTRONVOLT is an extremely small quantity of energy equal to 1.6 × 10−19 J, i.e. 1 eV = 1.6 × 10−19 J.

i

Some types of radiation, such as radio waves, are harmless. Other types, however, are dangerous to humans. Known as ionising radiation, these interact with atoms, having enough energy to remove outer-shell electrons and create ions. Alpha particles, beta particles and gamma rays are all ionising. So too is electromagnetic radiation with a frequency above 2 × 1016 Hz. Thus, X-rays and ultraviolet-B radiation are ionising. When ionising radiation interacts with human tissue, it is the ions it produces that are harmful and that lead to the development of cancerous tumours.

Lower-energy electromagnetic radiation such as radio waves, microwaves, infrared, visible light and ultraviolet-A are non-ionising. We are exposed to significant amounts of such radiation each day with no serious consequences. Non-ionising radiation does not have enough energy to change the chemistry of the atoms and molecules that make up our body cells.

Physics file

X-rays and gamma rays are ionising radiation. They are both high-energy forms of electromagnetic radiation (released as high-energy photons), but gamma rays usually have higher energies. This means that gamma rays are usually more highly penetrating than X-rays. The defining distinction between X-rays and gamma rays is the method of production.

X-rays are created from electron transitions within the electron cloud, whereas gamma rays are emitted from the nuclei of radioactive atoms. Gamma rays and X-rays have similar properties, but X-rays are not the result of radioactive decay.

Physics file

Prac 3 Risk Assessment

17Chapter 1 Nuclear physics and radioactivity

Alpha and beta particles are ejected from unstable nuclei with a wide range of energies. Alpha particles typically have energies of 5–10 million electronvolts (5–10 MeV). This corresponds to speeds of about 16 000 km s−1, about 5–10% of the speed of light.

Beta particles are usually ejected with energies up to a few million electronvolts. For example, sodium-24 emits beta particles with a maximum energy of 1.4 MeV. This is equivalent to 2.24 × 10−13 J. These particles are travelling at speeds quite close to the speed of light.

Gamma rays normally have less than a million electronvolts of energy. They may even have energy as low as 100 000 electronvolts. For example, the gamma rays emitted by the radioactive isotope gold-198 have a maximum energy of 412 000 eV (412 keV) or 6.6 × 10−14 J. Increasing the energy of a gamma ray does not increase its speed; it increases the frequency of the radiation.

Table 1.1 The properties of alpha, beta and gamma radiation

Property α particle β particle γ ray

Mass heavy light none

Charge +2 −1 none

Typical energy ∼5 MeV ∼1 MeV ∼0.1 MeV

Range in air a few cm 1 or 2 m many metres

Penetration in matter ∼10−2 mm a few mm high

Ionising ability high reasonable poor

Worked example 1.3A Uranium-238 emits alpha particles with a maximum energy of 4.2 MeV. a Explain why a sample of this radioisotope encased in plastic is quite safe to handle yet,

if inhaled as dust, would be considered very dangerous. b Calculate the energy of one of these alpha particles in joules.

Solution a The alpha particles have a poor penetrating ability and so would be unable to pass

through the plastic casing. However, if the radioactive uranium was on a dust particle and was inhaled, the alpha-emitting nuclei would be in direct contact with lung tissue and the alpha particles would damage this tissue.

b 4.2 MeV = 4.2 × 106 eV = 4.2 × 106 × 1.6 × 10−19 J = 6.7 × 10−13 J

The energy released during any nuclear reaction (including radioactive decay) is many times greater than that released in a typical chemical reaction. For example the chemical reaction of a sodium ion capturing an electron releases about 1 eV of energy.

Na+ + e− → Na + 1 eV

Nuclear reactions such as alpha, beta and gamma decays typically release energies of the order of megaelectronvolts, MeV, i.e. nuclear reactions release about a million times more energy than chemical reactions.

Physics file

Nuclear physics and radioactivity18

Each year, dozens of people in Australia die as a result of domestic fires. Evidence has shown that the installation of a smoke detector can reduce the risk of dying in a house fire by about 60%. For this reason, new houses are required to contain at least one smoke detector. There are two common types of smoke detector: ionisation and photoelectric. Ionisation smoke detectors were invented by NASA in the 1970s to protect astronauts on Skylab and contain a small radioactive source. The radioisotope most commonly used is americium-241, an artificial isotope which is produced in the core of a nuclear reactor. Americium-241 emits alpha particles and low-energy gamma rays. The penetrating ability of the alpha particles is so poor that they are stopped by the case of the detector. Some gamma rays will escape into the room, but they have such low energy (~60 keV) that exposure to them is insignificant when compared with the level of background radiation. As well as this, the detectors are usually located in the ceiling, some distance from people, and this distance further reduces the intensity of the radiation.

An ionisation smoke detector contains a pair of oppositely charged low-voltage metal electrodes. When the alpha particles pass between these electrodes, they ionise the air molecules that are present. These ions are then attracted to the electrodes. However, when smoke (or steam) is present, the ions attach themselves to the smoke particles. The flow of charges to the electrodes reduces greatly because these charged smoke (or steam) particles are much bigger and so much less mobile than the ionised air molecules. It is this reduction in the flow of charges reaching the electrodes that triggers the alarm.

Beta particles can be used to monitor the thickness of rolled sheets of metal and plastic during manufacture. A beta particle source is placed under the newly rolled sheet and a detector is placed on the other side. If the sheet is being made too thick, fewer beta particles will penetrate and the detector count will fall. This information is instantaneously fed back to the rollers and the pressure is increased until the correct reading is achieved, and hence the right thickness is attained.

Would alpha particles or gamma rays be appropriate for this task? Alpha particles have a very poor penetrating ability, so none of them would pass through the metal. Gamma rays usually have a high penetrating ability and so a thin metal sheet would not stop them. Workers would also need to be shielded from gamma radiation. You can see that the penetrating properties of beta rays make them ideal for this job. The thickness of photographic film and coatings on metal surfaces are also monitored in this way.

Smoke detectorsPhysics in action

Monitoring the thickness of sheet metalPhysics in action

Figure 1.21 Ionisation smoke detectors contain a small quantity of radioactive material. When used correctly, they greatly reduce the chances of being killed or injured in a house fire.

Figure 1.22 The thickness of a sheet of metal is monitored using a strontium-90 isotope. A beam of beta particles is directed into the metal and those penetrating the metal sheet are counted by a detector on the other side. This count gives an indication of the thickness of the metal sheet. The thicker the sheet, the lower the count in any given time period.

control box

β source

rollers

Geigercounter

19Chapter 1 Nuclear physics and radioactivity

• Alpha particles are ejected with a speed of about 5–10% of the speed of light. Alpha particles have a double positive electrical charge and are relatively heavy. They are a highly ionising form of radiation, but their penetrating ability is poor.

• Beta particles have a single negative electrical charge and are much lighter than alpha particles. They are a moderately ionising and penetrating form of radiation.

• Gamma rays are high-energy electromagnetic radiation and so have no electrical charge. They have a high penetrating ability, but a weak ionising ability.

• The energy of alpha, beta and gamma radiation is usually measured in electronvolts (eV).

• 1 eV = 1.6 × 10−19 J

Properties of alpha, beta and gamma radiation1.3 summary

1 1 As part of an experiment, a scientist fires a beam of alpha, beta and gamma radiation at a brick. If the three radiation types are of equal energy, arrange them in order of:a increasing penetrating abilityb increasing ionising ability.

2 2 Which one of the following correctly explains how penetrating ability relates to the ionising ability of a radioactive emission?A Emissions with more ionising ability have greater

penetrating ability.B Emissions with less ionising ability have more

penetrating ability.C There is no relationship between the ionising

ability and penetrating ability of a radioactive emission.

3 3 An external source of radiation is used to treat a brain tumour. Which type of radioactive emission is best suited for this treatment?

4 4 A radiographer inserts a radioactive wire into a breast cancer with the intention of destroying the cancerous cells in close proximity to the wire. Should this wire be an alpha, beta or gamma emitter? Explain your reasoning.

5 Calculate the energy in electronvolts of:a an alpha particle with 8.5 × 10–12 J of energyb a beta particle with 6.4 × 10–11 J of energyc a gamma ray with 4.7 × 10–11 J of energy.

6 6 Calculate the energy in joules of:a an alpha particle with 8.8 MeV of energy b a beta particle with 0.42 MeV of energyc a gamma ray with 500 keV of energy.

7 7 Alpha particles travelling through air ionise about 100 000 atoms each centimetre. Each time they ionise an atom, the alpha particles lose about 34 eV of energy. a How much energy will alpha particles lose as they

pass through 1 cm of air?b Calculate the approximate distance that an alpha

particle with 5.6 MeV will travel in air before it loses all of its energy.

8 8 Which one of the following has the greatest penetrating ability?A an alpha particle with 5.3 MeV of energyB a beta particle with 1.2 MeV of energyC a gamma ray with 700 keV of energyD a gamma ray with 0.81 MeV of energy

9 9 Which radiation identified in Question 8 will be the most damaging to human tissue should irradiation occur?

10 10 A radioactive sample is emitting alpha, beta and gamma radiation into the air. A Geiger counter held about 20 centimetres from the sample would be most likely to detect:A alpha, beta and gamma radiationB gamma radiation onlyC alpha radiation onlyD beta and gamma radiation only.

Properties of alpha, beta and gamma radiation1.3 questions

Worked Solutions

Nuclear physics and radioactivity20

Half-life and activity of radioisotopes1.4

Different radioisotopes will emit radiation and decay at very different rates. For example, a Geiger counter held close to a small sample of polonium-218 will initially detect a significant amount of radiation, but the activity will not last for very long. After half an hour or so, there will hardly be any radiation detected at all.

Compare this with a similar sample of radium-226. A Geiger counter directed at the radium will show a sustained but low count rate—much lower than that of the polonium-218 sample. Furthermore, the activity will remain relatively steady for a very long time. In fact, no change in the count rate would be noticed for decades!

To explain this, you need to know that radionuclides are unstable but to different degrees. Consider again the sample of polonium-218. If the sample initially contains 100 million undecayed polonium-218 nuclei, as shown in Figure 1.24, after 3 minutes about half of these will have decayed, leaving just 50 million polonium-218 nuclei. A further 3 minutes later, half of these remaining polonium-218 nuclei will decay, leaving approximately 25 million of the original radioactive nuclei, and so on.

The time that it takes for half of the nuclei of a radioisotope to decay is known as the half-life of that radioisotope. The half-life of polonium-218 is 3 minutes.

As time passes, a smaller and smaller proportion of the original radio-isotope remains in the sample. The graph in Figure 1.25 shows this.

It is important to appreciate that although the behaviour of a large sample of nuclei can be predicted, it is impossible to predict when any one particular nucleus will decay. The decay of the individual nuclei in a sample is random. It is rather like throwing dice. If 60 dice are thrown, on average 10 of them will roll up ‘6’. You just don’t know which ones!

Furthermore, the half-life of a radioisotope is constant and is largely unaf fected by any external conditions such as temperature, magnetic field or the chemical environment. It is related only to the instability of the nucleus of the radioisotope.

The decay rate of a radioisotope is measured in terms of its half-life (t1/2

). The HALF-LIF… of a radioisotope is the time that it takes for half of the nuclei of the sample radioisotope to decay spontaneously.

i

Figure 1.25 The amount of the original isotope halves as each half-life passes. This is an exponential relationship and the mathematical relationship that describes it is shown.

Figure 1.23 (a) The emissions from polonium-218 only last for a relatively short time. Its activity decreases very rapidly. (b) The emissions from a sample of radium-226 remain steady for a very long time. Its activity does not change significantly.

Figure 1.24 During one half-life, the number of nuclei of the radioisotope sample decreases by half (i.e. by 50%). After two half-lives, only one-quarter (25%) of the original radioisotope nuclei will remain.

30 minutes later

10 years later

Ra Ra

Po Po

(a)

(b)

Per

cent

age

rem

aini

ng

0Number of half-lives

100

N = N0( )n1

2

50

25

12.5

1 2 3

where n = no. of half-lives N0 = original amount N = final amount

Initially:100 million

218Po nuclei

After 3 minutes:~ 50 million218Po nuclei

After 6 minutes:~ 25 million218Po nuclei

Key: 1 million 218Po nucleiPrac 4

21Chapter 1 Nuclear physics and radioactivity

Look at Figure 1.23 once again. It is evident that radium-226 has a very long half-life when compared with polonium-218. In fact, the half-life of radium-226 is about 1600 years. Clearly, a sample of radium-226 will emit particles and decay for centuries. The half-lives of some common radioisotopes are shown in Table 1.2. This table also illustrates that the half-life of a radioisotope is a factor in its application. For example, most medical applications using a radioisotope as a tracer require a short half-life. This is so that radioactivity does not remain in the body any longer than necessary. On the other hand, the radioisotope used in a smoke detector is chosen because of its long half-life. The detector can continue to function for a very long time, as long as the battery is replaced each year.

Table 1.2 Some common radioisotopes and their half-lives

Isotope Emission Half-life Application

Natural

Polonium-214 α 0.00016 seconds Nothing at this time.

Strontium-90 β 28.8 years Cancer therapy

Radium-226 α 1630 years Once used in luminous paints

Carbon-14 β 5730 years Carbon dating of fossils

Uranium-235 α 700 000 years Nuclear fuel, rock dating

Uranium-238 α 4.5 billion years Nuclear fuel, rock dating

Thorium-232 α 14 billion years Fossil dating, nuclear fuel

Artificial

Technetium-99m γ 6 hours Medical tracer

Sodium-24 γ 15 hours Medical tracer

Iodine-131 γ 8 days Medical tracer

Phosphorus-32 β 14.3 days Medical tracer

Cobalt-60 γ 5.3 years Radiation therapy

Americium-241 α 460 years Smoke detectors

Plutonium-239 α 24 000 years Nuclear fuel, rock dating

ActivityA Geiger counter records the number of radioactive decays occurring in a sample each second. This is the activity of the sample.

Over time, the activity of any sample of a radioisotope will decrease. This is because more and more of the radioactive nuclei have decayed and will no longer emit radiation. So, over one half-life, the activity of any sample will be reduced by half. If the sample of polonium-218, discussed previously, has an initial activity of 2000 Bq, then after one half-life (i.e. 3 minutes) its activity will be 1000 Bq. After 6 minutes, the activity of the sample will have reduced to 500 Bq and so on.

ACTIVITY is measured in becquerels, Bq.1 Bq = 1 disintegration per second

i

On 11 March 2011, a catastrophic earthquake and tsunami hit Japan, killing tens of thousands of people and severely damaging the nuclear power station at Fukushima, causing a release of radioactive materials. Two of the radioactive isotopes released were caesium-137 and iodine-131. These have half-lives of 30 years and 8 days respectively. Our bodies need iodine for the healthy functioning of the thyroid gland, which maintains a proper metabolism. Foods rich in iodine include seafood, vegetables and salt.

Our bodies cannot tell the difference between normal iodine and radioactive iodine. To prevent the people in Japan from absorbing radioactive iodine into their thyroid glands, they were issued with iodine tablets. Taking an iodine tablet each day ensured that the thyroid gland was saturated with iodine and so any radioactive iodine ingested by eating contaminated food would not be taken into the body and deposited in the thyroid.

Many victims of the Chernobyl nuclear disaster in 1986 died of thyroid cancer years after the accident. They ingested radioactive iodine and this accumulated in the thyroid gland, eventually leading to cancer.

Physics file

Interactive

Nuclear physics and radioactivity22

Short-lived radioisotopes have an initially high activity. Their nuclei decay at a fast rate and so the sample lasts only for a short time. High-activity samples are extremely dangerous and must be handled with great caution.

Decay seriesGenerally, when a radionuclide decays, its daughter nucleus is not completely stable, and is itself radioactive. This daughter will then decay to a grand-daughter nucleus, which may also be radioactive, and so on. Eventually a stable isotope is reached and the sequence ends. This is known as a decay series.

The Earth is 4.5 billion years old (4.5 gigayears)—enough to have only four naturally occurring decay series remain active. These are: • the uranium series in which uranium-238 eventually becomes lead-206• the actinium series in which uranium-235 eventually becomes lead-207• the thorium series in which thorium-232 eventually becomes lead-208• the neptunium series in which neptunium-237 eventually becomes

bismuth-209. (Since neptunium-237 has a relatively short half-life, it is no longer present in the crust of the Earth, but the rest of its decay series is still continuing.)Geologists analyse the proportions of the radioactive elements in

a sample of rock to gain a reasonable estimate of the rock’s age. This technique is known as rock dating.

Figure 1.26 The uranium decay series. The half-life and emissions are indicated on each of the decays as radioactive uranium-238 is transformed into stable lead-206.

206

208

210

212

214

216

218

220

222

224

226

228

230

232

234

236

238

82 84 86 88 90 92

Pb

Pb Bi Po

Pb Bi Po

Po

Rn

Ra

Th

Th Pa U

U

α 138 days

μα 160 s

β 19 min

α 3 min

α 3.8 days

α 1.6 × 103 years

α 8 × 104 years

5αyears

β 24 days

β 6.7 h9α 4.5 × 10 years

yβ 2.6 × 106 ears

Atomic number (Z )

Mas

s nu

mb

er (A

)

β 20 years

β 27 min

2.5 × 10

23Chapter 1 Nuclear physics and radioactivity

Worked example 1.4A A sample of the radioisotope thorium-234 contains 8.0 × 1012 nuclei. The half-life of 234Th is 24 days. How many thorium-234 atoms will remain in the sample after:a 24 days?b 48 days?c 96 days?

Solution a Initially, there were 8.0 × 1012 thorium-234 nuclei. 24 days is one half-life, so half of these

will decay leaving 4.0 × 1012 thorium-234 nuclei.b 48 days is two half-lives. This means that there will be:

1

2 × 1

2 × 8.0 × 1012 = 2.0 × 1012 thorium-234 nucleic 96 days corresponds to four half-lives. In this time the number of atoms of the original

radioisotope will have halved four times. This means that:

1

2 × 1

2 × 1

2 × 1

2 = 1

16

or one-sixteenth of the original 234Th nuclei remain; i.e. 5.0 × 1011 nuclei.

Worked example 1.4B In 2 hours, the activity of a sample of a radioactive element falls from 240 Bq to 30 Bq. What is the half-life of this element?

Solution During each half-life, the activity of the radioisotope will fall by half. The activity of this element has decreased from 240 → 120 → 60 → 30 counts per second, so it has decayed through three half-lives in this 2 hour (120 minute) period. Thus the half-life must be 120/3 = 40 minutes.

Carbon dating is a technique used by archaeologists to determine the ages of fossils and ancient objects that were made from plant matter. In this method, the proportion of two isotopes of carbon—carbon-12 and carbon-14—in the specimen are measured and compared.

Carbon-12 is a stable isotope whereas carbon-14 is radioactive. Carbon-14 only exists in trace amounts in nature. In fact, carbon-12 atoms are about 1 000 000 000 000 (1012) times more prevalent than carbon-14 atoms.

Carbon-14 has a half-life of 5730 years and decays by beta emission to nitrogen-14. Its decay equation is:

146 C → 14

7 N + −10 β

Both carbon-12 and carbon-14 can combine with other atoms in the environment, for example with oxygen to form carbon dioxide. While plants and animals are alive, they take in carbon-based molecules and so all living things will contain the same percentage of carbon-14. In the environment, the production of carbon-14 is matched by its decay and so the proportion of carbon-14 atoms to carbon-12 remains constant.

Radiocarbon datingPhysics in action

Figure 1.27 Carbon-dating techniques were used to show that the Shroud of Turin was most probably made around the 14th century.

Continued on next page

Nuclear physics and radioactivity24

After a living thing has died, the amount of carbon-14 will decrease as these atoms decay to form nitrogen-14, and are not replaced. The number of atoms of carbon-12 does not change as this is a stable atom. So, over time, the proportion of carbon-14 to carbon-12 atoms falls. By comparing the proportion of carbon-14 to carbon-12 in a dead sample with that found in living things, and knowing the half-life of carbon-14 (5730 years), the approximate age of the specimen can be determined.

Consider this example. The count rate from a 1 g sample of carbon that has been extracted from an ancient wooden spear is 10 Bq. A 1 g sample of carbon from a living piece of wood gives a count rate of 40 Bq. We then assume that this was also the initial count rate of the spear. For its count rate to have reduced from 40 to 10 Bq, the spear must be (40 → 20 → 10) two half-lives of carbon-14 old, i.e. about 11 500 years old.

In 1988, scientists used carbon-dating techniques to show that the Shroud of Turin was probably a medieval forgery. Carbon-dating tests on samples of the cloth the size of a stamp established that there was a high probability that it was made between 1260 and 1390 AD, not around the time of Christ.

Radiocarbon dating is an important aid to anthropologists who are interested in finding out about the migration patterns of early peoples—including the Australian Aborigines. This technique is very powerful since it can be applied to the

Radiocarbon dating (continued)

Figure 1.28 This baby mammoth fossil was found in northern Russia in 2007. Carbon dating has shown that mammoths became extinct 11 000 years ago.

remains of ancient campfires. It is accurate and reliable for samples up to about 60 000 years old. Carbon dating cannot be used to date dinosaur bones as they are more than 60 million years old, but it can be used to determine the age of more recently extinct mammoth fossils.

Carbon dating is useful when examining samples that were once alive—such as wood or bones. However, this technique cannot be used to date the age of specimens that were never alive, such as rocks. There are a large number of dating procedures that are now used for this purpose. The oldest dating technique analyses remnants of uranium and lead that are found in the rock that is being examined. Uranium has two naturally occurring isotopes: uranium-235 and uranium-238. As was discussed earlier in Decay series (p. 22), uranium-235 decays through a number of steps and finishes up as lead-207. Uranium-238 undergoes a different series of decays to finally become lead-206. Scientists can compare the proportions of each isotope present using a mass spectrometer and, knowing the half-lives involved, determine the age of the rock. If, for example, a rock sample was quite young (i.e. it had crystallised relatively recently), it would contain higher levels of uranium and lower levels of lead because there has not been time for many uranium atoms to complete the decay process.

The oldest rocks that have been found on Earth have been dated at almost 4 billion years. Most rocks are much younger than this as a result of remelting and reforming over the ages. When rocks brought back from the Moon were analysed, they were found to be 4.2 billion years old. Furthermore, when different meteorites were analysed, they were all found to be exactly the same age of 4.56 billion years. These observations can be explained by assuming that the meteorites are parts

of asteroids that have drifted into Earth’s orbit. The current theory suggests that the solar system was formed all at once and that the age of the asteroids gives a reliable estimate of the age of the solar system. In other words, the age of the Earth and the rest of the solar system is about 4.6 billion years.

In all, there are about forty different dating techniques and they have been found to give very consistent and reliable results.

How old is the Earth?Physics in action

Figure 1.29 All meteorites have been found to be exactly the same age—4.56 billion years. This result has enabled scientists to fix the age of the Earth and the solar system at about 4.6 billion years.

25Chapter 1 Nuclear physics and radioactivity

• The rate of decay of a radioisotope is measured by its half-life. The half-life, t1/2 , of a radioisotope is the time that it takes for half of the nuclei in a sample of the radioisotope to decay.

• The activity of a sample indicates the number of radio active decays that are occurring in the sample

each second. Activity is measured in becquerels (Bq) where 1 Bq = 1 disintegration per second.

• The activity of any radioactive sample will decrease with time. Over a half-life, the activity of a sample will halve.

Half-life and activity of radioisotopes1.4 summary

1 1 A radioactive isotope has a half-life of 1 hour. If a sample initially contains 100 mg of this isotope, which one of the following correctly gives the amount of the radioisotope remaining after 2 hours have elapsed?A none B 50 mg C 25 mg D 100 mg

2 2 A radioactive element has a half-life of 15 minutes. If you start with a 20 g sample of this element, how much of the original radioisotope will remain after:a 15 minutes? b 30 minutes?c 45 minutes? d 1.5 hours?

3 3 A Geiger counter measures the radioactive disinte-grations from a sample of a certain radioisotope. The count rate recorded is shown below.

Count rate (Bq) 400 280 200 140 100 70

Time (minutes) 0 10 20 30 40 50

a Plot a graph of count rate against time.b Use your graph to estimate the activity of the

sample after 15 minutes. c What is the half-life of this element? Use both your

graph and the table to determine your answer.d Determine the activity of the sample after 60

minutes have elapsed.

4 4 The activity of a radioisotope changes from 6000 Bq to 375 Bq over a period of 1 h. What is the half-life of this element?

5 5 Gold-198 is a radioisotope with a half-life of 2.7 days. Consider one particular nucleus in a small sample of this substance. After 2.7 days this nucleus has not decayed. What is the probability that it will decay in the next 2.7 day period?

6 6 A hospital in Alice Springs needs 12 μg of the radio-isotope technetium-99m, but the specimen must be ordered from a hospital in Sydney. If the half-life of 99mTc is 6 hours and the delivery time between hospitals is 24 hours, how much must be produced in Sydney to satisfy the Alice Springs order?

7 7 Radioactive materials are considered to be relatively safe when their activity has fallen to below 0.1% of their initial value. a How many half-lives does this take?b Plutonium-239 is a by-product of nuclear reactors.

It has a half-life of about 24 000 years. For what period of time does a quantity of 239Pu have to be stored until it is considered safe to handle?

8 8 Uranium-235 has a half-life of 700 000 years, while the half-life of uranium-238 is many times longer at 4.5 × 109 years.a If you had 1 kg of each of these radioisotopes,

which one would have the greater activity?b The uranium that is mined in Australia and

elsewhere is 99.3% 238U and only 0.7% 235U. Explain why 235U currently exists in trace amounts only.

9 9 A Geiger counter is used to measure the radioactive disintegra tions from a sample of a certain radioisotope. The graph of the count rate is shown below.

1000

800

600

400

2000

0 5 10 15Time (min)

Act

ivity

(Bq

)

20 25 30

a Determine the half-life of the isotope.b What would be the activity of the isotope after

40 minutes?

1010 A geologist analyses a sample of uranium ore that has been mined at Roxby Downs in South Australia. You may refer to Figure 1.26, the decay series graph for uranium, when answering this question. a Explain why the sample would be expected to

contain significant traces of lead.b Explain why the geologist would be

unlikely to find any 214Po in the sample.

Half-life and activity of radioisotopes1.4 questions

Worked Solutions

Nuclear physics and radioactivity26

Radiation dose and its effect on humans1.5

Ionising radiation The term radiation is widely used and widely misunderstood. There are many different forms of radiation and the degree of danger that they present depends on their ability to interact with atoms. Some radiation has enough energy to interact with atoms, removing their outer-shell electrons and creating ions. For this reason, this radiation is known as ionising radiation. As was discussed in Section 1.3, alpha particles, beta particles and gamma rays are all ionising.

The electromagnetic spectrum consists of a variety of electromagnetic radiations: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. Electromagnetic radiation with a frequency above 2 × 1016 Hz is ionising. Thus gamma rays, X-rays and ultraviolet B and C radiations are ionising and you would be well advised to avoid exposure to them. When they interact with the tissue in an organism, they create ions which can lead to the development of cancerous tumours.

Non-ionising radiation includes radio waves, microwaves, visible light and UV-A radiation. We are exposed to significant amounts of such radiation each day without serious consequences.

The level of exposure to ionising radiation from the environment is called the background level.

Table 1.3 Summary of the different ionising and non-ionising types of radiation

Ionising radiation (high energy)

alpha particles, beta particles, gamma rays, X-rays, UV-B and UV-C radiation

Non-ionising radiation (low energy)

radio waves, microwaves, infrared, visible light, UV-A radiation

The background level of ionising radiation to which we are continually exposed is not a significant health problem. However, exposure to above-average levels of ionising radiation is dangerous. It may lead to long-term problems such as cancer and genetic deformities in future generations. Extremely high levels of exposure can cause death, and in extreme cases this can happen within just a few hours.

It is important that people who work with radiation in fields such as medicine, mining, nuclear power plants and industry are able to monitor closely the amount of radiation to which they are exposed. Furthermore, radiologists, who administer courses of radiation treatment to cancer patients, also need to be able to measure the amount of radiation that they are applying.

Measuring radiation exposure Absorbed dose

When a person is exposed to high-energy radiation, the energy of the radiation acts to break apart molecules and ionise atoms in the person’s body cells. The severity of this exposure depends on the amount of

The wicks or mantles used in old-style camping lamps are slightly radioactive. They contain a radioisotope of thorium, an alpha-particle emitter. They have not been banned from sale because they contain only small amounts of the radioisotope and could be used safely by taking simple precautions such as washing hands and avoiding inhalation or ingestion. A scientist from the Australian National University has called for the banning of these mantles on the grounds that they tend to crumble and turn to dust as they age. If this dust were to be inhaled, alpha particles could settle in someone’s lung tissue, possibly causing cancers to form.

Several years ago, a schoolboy in the United States used thousands of lamp mantles to construct a crude nuclear reactor. It raised the background level of radiation in his street by a factor of 9000!

Physics file

Figure 1.30 Radiologists administer very precise doses of ionising radiation that are designed to destroy cancer cells. This treatment is successful because rapidly dividing cancer cells are more susceptible than normal body cells to damage from ionising radiation.

Interactive

27Chapter 1 Nuclear physics and radioactivity

radiation energy that has been absorbed by the individual’s body. This quantity is known as the absorbed dose. The absorbed dose is the radiation energy that has been absorbed per kilogram of the target material.

To illustrate this, if a 25 kg child absorbed 150 J of radiation energy, then the absorbed dose would be 6 Gy. This is a massive dose and would be enough to kill the child within a few weeks. However, an adult, being much larger, would be less severely affected by this radiation. If a 75 kg adult absorbed 150 J of radiation energy, the absorbed dose would be just 2 Gy. This dose would give the adult a severe case of radiation sickness but would probably not be fatal. You can think of dose in the same way as one administers medicine. The small mass of a child means that taking just half a tablet might be equivalent to an adult taking two tablets.

Dose equivalent

Different forms of radiation have different abilities to ionise, and so cause different amounts of damage as they pass through human tissue. Alpha particles are the most ionising form of radiation. Their low speed, high charge and large mass mean that they interact with and ionise virtually every atom that lies in their path. This means that an absorbed dose of alpha radiation is much more damaging to human tissue than an equal absorbed dose of beta or gamma radiation. In fact, it is about 20 times more damaging. This weighting of the biological impact of the radiation is called the quality factor. A list of quality factors is shown in Table 1.4. In contrast to alpha particles, gamma rays and X-rays have no charge and move at the speed of light, flying straight past most atoms and interacting only occasionally as they pass through a substance. This is reflected in their low quality factor.

A measure of radiation dose that takes into account the absorbed dose and the type of radiation will give a more accurate picture of the actual effect of the radiation on a person. This is the dose equivalent. Dose equivalent is measured in sieverts (Sv), although millisieverts (mSv) and microsieverts (μSv) are more commonly used.

For example, an absorbed dose of just 0.05 Gy of alpha radiation is biologically equally as damaging as an absorbed dose of 1.0 Gy of beta radiation. While the energy carried by the alpha particles is lower than that of beta particles, each alpha particle does far more damage. In each case, the dose equivalent is 1 Sv, and 1 Sv of any radiation causes the same amount of damage.

ABSORB…D DOS… = energy absorbed by tissue

mass of tissue ABSORB…D DOS… is measured in joules/kilogram (J kg−1) or grays (Gy), i.e. 1 Gy = 1 J kg−1.

i

DOS… …QUIVAL…NT = absorbed dose × quality factor Dose equivalent is measured in sieverts (Sv).

i Table 1.4 Quality factors

Radiation Quality factor

Alpha particles 20

Neutrons* (>10 keV) 10

Beta particles 1

Gamma rays 1

X-rays 1

* Radiation from neutrons is only found around nuclear re actors and neutron bomb explosions.

Figure 1.31 Humans are exposed to radiation from many different sources. Almost 90% of our annual exposure is from the surrounding environment.

13% cosmicrays

17% foodand drink

37% naturalradioactivityin air

10.4%medical

1.6% coalburning

0.5% nuclearweaponsfallout

0.5% airtravel, etc.

0.001%nuclearpower

20% groundand building

Nuclear physics and radioactivity28

It is important to appreciate that 1 Sv is a massive dose of radiation and, while not being fatal, would certainly lead to a severe case of radiation illness.

In Australia the average annual background radiation dose is about 2.0 mSv, or 2000 μSv. A microsievert is a millionth of a sievert. Use Table 1.6 to estimate your annual dose.

Table 1.6 Annual radiation doses in Australia

Radiation source

Average annual

dose (μSv)

Local variations

Cosmic radiation

300 Plus 200 μSv for each round-the-world flight.Plus 20 μSv for each 10° of latitude.Plus 150 μSv if you live 1000 m above sea level.

Rocks, air and water

1350 Plus 1350 μSv if you live underground.Plus 1350 μSv if your house is made of granite.Minus 140 μSv if you live in a weatherboard house.

Radioactive foods and drinks

350 Plus 1000 μSv if you have eaten food affected by the Fukushima fallout.

Manufactured radiation

60 Plus 60 μSv if you live near a coal-burning power station.Plus 30 μSv from nuclear testing in the Pacific.Plus 20 μSv if you watch 20 hours of TV on a CRT television set each week.

Medical exposures

– Plus 30 μSv for a chest X-ray.Plus 300 μSv for a pelvic X-ray.Plus 5000 μSv if you have had a a CT scan.Plus 40 000 000 μSv for a course of radiotherapy using cobalt-60.

Worked example 1.5A A 10 g cancer tumour absorbs 0.0020 J of energy from an applied radiation source. a What is the absorbed dose for this tumour?b Calculate the dose equivalent if the source is an alpha emitter.c Calculate the dose equivalent if the source is a gamma emitterd Which radiation source is more damaging to the cells in the tumour?

Solution a Absorbed dose =

energy absorbedmass of tissue

= 0.020 J

0.010 kg = 0.20 Gy

b Dose equivalent = absorbed dose × quality factor = 0.20 × 20 = 4.0 Sv for the alpha emitter

c Dose equivalent = absorbed dose × quality factor = 0.20 × 1 = 0.20 Sv for the gamma emitter

d The alpha particle source is more damaging. It causes more ionisation in the cells and so has a higher dose equivalent.

The level of background radiation varies around the world as Table 1.5 shows. Locations of greater latitude and greater altitude receive a larger dose of cosmic rays. Aberdeen has a high reading because it is built on large deposits of granite that release radon, a radioactive gas. The soil in Chennai is slightly radioactive and is responsible for the higher than average doses received there.

Table 1.5 Background radiation levels around the world

Location Annual background radiation dose (μSv)

Australia (average level)

2000

New York, USA 1000

Paris, France 1200

Aberdeen, Scotland

5000

Chennai, India 8000

Physics file

Cosmic rays—atomic particles and gamma rays that continually bombard the Earth—emanate from the Sun and from deep space. We are, to a large extent, protected from these by the shielding effect of the Earth’s atmosphere and magnetosphere. Most people receive a dose of around 300 μSv each year due to cosmic radiation. However, when we travel at high altitudes, the atmosphere’s shielding effect is diminished. Passengers taking a return flight to Perth from Melbourne would be exposed to a dose of about 30 μSv.

Physics file

29Chapter 1 Nuclear physics and radioactivity

…ffective dose

The different organs of the body have different sensitivities to radiation doses. For example, if a person’s lung was exposed to a dose of 10 mSv, it would be more than twice as likely that cancers would develop than if the same 10 mSv dose was delivered to the liver. The weightings assigned by the International Commission of Radiological Protection (ICRP) to the various organs are shown in Table 1.7.

Effective dose is used to compare the risk of a non-uniform exposure to ionising radiation with the risks caused by a uniform exposure of the whole body. It is found by calculating a weighted average of the dose equivalents to different body parts, with the weighting factors, W, designed to reflect the different radiosensitivities of the tissues.

Worked example 1.5B During therapy for cancer, a patient’s lungs receive 2500 μSv and her thyroid gland receives 1000 μSv. Use Table 1.7 to calculate the effective dose of radiation to which this woman has been exposed.

Solution Effective dose = Σ(dose equivalent × W) = (2500 × 0.12) + (1000 × 0.05) = 350 μSvThis means that the cancer risk as a result of her whole body receiving a uniform dose of 350 μSv is the same as when her lungs receive 2500 μSv and her thyroid receives 1000 μSv (and her other organs receive no exposure).

The effects of radiation If at all possible, exposure to ionising radiation should be avoided. When alpha, beta or gamma radiation passes through a body cell, it may turn one of the molecules in the cell into an ion pair; for example, if the radiation ionises a water molecule, then a hydrogen ion and a hydroxide ion will be formed. These ions are highly reactive and can attack the DNA that forms the chromosomes in the nucleus of the cell. This can cause the cell to either die or divide and reproduce at an abnormally rapid rate. When the latter occurs, a cancerous tumour may form.

The effects of a dose of ionising radiation can be divided into two groups: the short-term somatic effects and the long-term genetic effects.

Somatic effects

Somatic effects arise when ordinary body cells are damaged, and depend on the size of the dose. Very high doses lead to almost immediate symptoms, lower doses could lead to symptoms developing years later.

Genetic effects

When cells in the reproductive organs (ovaries or testes) are damaged, the body suffers genetic effects. Cells in the reproductive organs develop

…FF…CTIV… DOS… = Σ(dose equivalent × W)Effective dose is measured in sieverts (Sv).

i

Table 1.7 The ICRP weighting values, W

Body part Weighting, W

Ovaries/testes 0.20

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

Rest of body 0.07

Total 1.00

Figure 1.32 Ionising radiation has enough energy to break the bonds within a water molecule and create a pair of ions.

H

HO

−

+H

H

Oγ ray

Nuclear physics and radioactivity30

into ova and sperm, so if the DNA in the chromosomes of these cells is damaged, this genetic change could be passed on to a developing embryo. The DNA changes in these damaged cells are known as mutations.

There are many different ways in which genetic defects can show up in future generations, including poor limb development, harelips and other birth abnormalities. They may surface in the next generation or lie dormant for several generations. In other words, if you suffer damage to your reproductive cells, your children may be quite normal but your grandchildren may be genetically weakened.

For these reasons, when a patient is undergoing radiotherapy, it is most important that their reproductive organs are well shielded from the radiation. These organs are among the most radiosensitive organs (i.e. easily damaged by radiation) in the body.

A developing foetus is also very sensitive to radiation and so pregnant women should avoid having X-rays. For this reason foetal images are now gathered using ultrasound techniques.

Table 1.8 The somatic effects of radiation doses

Whole body dose (Sv) Symptom

<1Non-fatalOnly minor symptoms such as nauseaWhite blood cell level drops

2

Death unlikelyRadiation sickness, i.e. nausea, vomiting and diarrhoeaSkin rashesHair lossBone marrow damage

450% likelihood of death within 2 monthsSevere radiation sicknessHigh probability of leukaemia and tumours

8Almost certain death within 1 or 2 weeksAcute radiation sickness—convulsions, lethargy

Figure 1.33 For the first half of the last century, many people thought exposure to radioactive materials was beneficial for their health. People drank radioactive water as a tonic and soaked in pools at radioactive spas.

Cancers that form on the skin, testes or in the breasts can often be detected by a simple external examination. However, in order to diagnose the presence of cancerous growths at specific sites inside the body, a variety of radioisotopes tagged to particular drugs are used. The radioisotope is known as a radioactive tracer. These drugs, radiopharmaceuticals, can be administered by swallowing (ingestion), inhalation or injection.

The radioisotope used in the radiopharmaceutical depends on the site of the suspected tumour. The body naturally distributes different elements to different organs. For example, iodine is sent to the thyroid gland by the liver. So if a radiopharmaceutical containing radioactive iodine is taken, most of this iodine will end up in the thyroid.

When the tracer has reached the target organ, a radiation scan is taken with a gamma ray camera. An unusual pattern

on the scan indicates a possible cancerous tumour. The radioisotopes used for this type of diagnosis need to be gamma ray emitters so that the radiation has enough penetrating ability to pass out of the body to reach the detector—the gamma ray camera. The isotope should have a relatively short half-life so that the patient is not subjected to any unnecessary long-term exposure to radiation.

The most commonly used radioactive tracer is technetium-99m. It is produced on site at hospitals with small nuclear generators. Technetium-99m is a gamma emitter with a half-life of 6 hours and is used to monitor the state of many organs in the body.

Radioactive tracers are also used to monitor other bodily functions. Some examples are shown in Table 1.9.

Detecting cancer with radioactive tracersPhysics in action

31Chapter 1 Nuclear physics and radioactivity

Table 1.9 Some radioactive tracers and their target organs

Radioactive tracer Function monitored

Iodine-123 Function of thyroid gland

Xenon-133 Function of lungs

Phosphorus-32 Blood flow through body

Iron-59 Level of iron uptake by spleen

Technetium-99mBlood flow in brain, lungs and heartFunction of liverMetabolism of bones

Figure 1.34 A gamma ray camera is being used to perform a bone scan. This patient has been injected with the radioisotope technetium-99m. This isotope is a γ emitter with a half-life of 6 h. The camera detects the emitted gamma rays and produces an image that can be seen on the computer screen.

• Exposure to background radiation is a natural and un avoid able part of our existence. Unnecessary ex pos ure to high-energy (or ionising) radiation can be dangerous and should be avoided.

• Absorbed dose is a measure of the radiation energy that our bodies absorb per kilogram of irradiated tissue. Absorbed dose is measured in grays (Gy); 1 Gy = 1 J kg−1.

• The quality factor of radiation is a weighting that indicates its damaging effect on body tissue. Alpha particles have a quality factor of 20, while beta and gamma radiation typically have a quality factor of 1.

• Dose equivalent gives a measure of the degree of biological damage that a dose of radiation causes. Dose equivalent = absorbed dose × quality factor. The units for dose equivalent are sieverts (Sv).

A typical background dose in Australia is about 2 mSv per year.

• Effective dose takes into account the radiosensitivity of the organ that has been exposed to ionising radiation.

• Effective dose = Σ(dose equivalent × W) and is meas-ured in sieverts (Sv).

• When ionising radiation passes through human tissue, it may ionise atoms and molecules in the body cells, which can lead to the development of cancerous cells.

• Exposure to ionising radiation can lead to both somatic and genetic effects. Depending on the radiation dose, somatic effects can vary from feelings of nausea to severe illness and even death. If a person’s reproductive cells are damaged by radiation, genetic abnormalities may arise in future generations.

Radiation dose and its effect on humans1.5 summary

1 1 a Which of following types of radiation is electro-magnetic in nature? (One or more answers.)A radio wavesB visible lightC ultraviolet radiation D beta particlesE gamma rays

b Which of the following types of radiation is ionising? (One or more answers.)A radio wavesB visible lightC alpha particlesD X-raysE beta particles

Continued on next page

Radiation dose and its effect on humans1.5 questions

Nuclear physics and radioactivity32

2 2 Use Table 1.4 to answer this question. Calculate the dose equivalent from a radiation source if the absorbed dose is 0.50 μGy and the radiation is:a alpha radiation b beta radiationc gamma radiation.

3 3 An 80 kg tourist absorbs a gamma radiation dose of 200 μGy during a return flight to London. a Calculate the dose equivalent that has been

received.b Determine the amount of radiation energy that

has been absorbed.

4 a 4 a Which one of the following is the most damaging radiation dose?A 200 μGy of gamma radiation B 20 μGy of alpha radiation C 50 μGy of beta radiation

b Which one of these is the most damaging radiation dose? A 200 μSv of gamma radiationB 20 μSv of alpha radiationC 50 μSv of beta radiation

5 5 When in space, astronauts usually receive a radiation dose of about 1000 μSv per day. The maximum allow-able annual dose for people working with radiation is 50 mSv.a The normal annual background dose per year on

Earth is 2 mSv. How many days does it take for astronauts to exceed this dose?

b How long would astronauts have to be in space before they exceeded the maximum annual dose for radiation workers?

c The record for time spent in space is held by cosmonaut Sergei Krikalev, who was on the Mir and the International Space Stations for a total of 803 days (and 9 hours and 39 minutes). How much radiation (in mSv) was the cosmonaut exposed to in this time?

6 6 Discuss some strategies that you could employ to minimise your exposure to ionising radiation.

7 7 In the immediate aftermath of the Chernobyl accident in 1986, 29 people died and more than 200 received hospital treatment for acute radiation sickness. Discuss the radiation dose to which these people must have been exposed.

8 8 a To treat cancer of the uterus, a radioactive source is implanted directly into the affected region. If the uterus receives a dose of 0.40 Gy per hour from the source, how many hours should it be left there to deliver a dose of 36 Gy?

b Explain why caesium-137, a beta emitter with a half-life of 33 years, is well suited for this task.

9 9 Which one of the following is most appropriate for use as a radioactive tracer to detect the presence of a brain tumour?A radon-222: α emitter, half-life = 3.8 daysB sulfur-35: β emitter, half-life = 97 daysC cobalt-60: γ emitter, half-life = 5.3 yearsD technetium-99m: γ emitter, half-life = 6 hours

10 10 Calculate the effective radiation dose for a woman whose organs received the following exposures during a course of radiotherapy. Her ovaries and bladder each received a dose of 35 mSv and her colon received a dose of 50 mSv.

Radiation dose and its effect on humans (continued)

1 Determine the number of protons, neutrons and nucleons in these isotopes.a 35

17Cl b 226

88Ra

2 Consider this list of different types of radiation: alpha particles, X-rays, infrared radiation, beta particles, microwaves, gamma rays. Which of these:a is a form of electromagnetic radiation?b has a positive electrical charge?c consists of four nucleons?d is a fast-moving electron?e is able to ionise matter?f has the greatest penetrating ability?

3 Find the value of x and y in each of these radioactive decay equations.

a 20881

TI → yxPb + β b 180

80Hg → y

xPt + α

4 Identify the emitted particle in each of these radioactive decays.

a 4520

Ca → 4521

Sc + X b 15070

Yb → 14668

Er + Xc 140

60Nd → 140

59Pr + X

5 a An electron travelling at high speed in the Australian Synchrotron has 3.0 GeV (3.0 × 109 eV) of energy. Calculate its energy in joules.

Chapter reviewNuclear physics and radioactivity

v and her

Worked Solutions

33Chapter 1 Nuclear physics and radioactivity

b Fruits and vegetables irradiated with gamma radiation to extend their shelf life and reduce waste do not become radioactive during this process. One gamma ray used has 2.1 × 10–13 joules of energy. How much energy is this in MeV?

6 A scientist has a 120 g sample of the radioisotope polonium-218. The first three steps in the decay series of polonium-218 are an alpha emission followed by two beta particle emissions. These decays have half-lives of 3, 27 and 19 minutes respectively. Use the periodic table when answering this question.

a How much polonium-218 remains after 15 minutes?b Write the equation for the alpha particle decay.c List the isotopes formed as a result of these three decays.d Which of these isotopes is predominant in the sample after

15 minutes? Explain your reasoning.

7 An archaeologist analyses an ancient bone and finds that it contains 20 g of carbon. The carbon from the bone was examined with a Geiger counter and gave a count rate of 80 disintegrations per minute. Carbon from the bones of recently deceased animals has a count rate of 16 disintegrations per gram per minute.

a Write the decay equation for carbon-14, a beta particle emitter.b How many disintegrations would be detected each minute

from a 1 g sample of the carbon from the ancient bone?c If the half-life of carbon-14 is 5730 years, what is the

approximate age of the bone?

8 The decay curve for a sample of the radioisotope technetium-99m is shown below. It emits gamma rays with 140 keV of energy and has an initial activity of 4.0 × 106 Bq.

Act

ivity

(MB

q)

Time (h)12

4

2

1

0

3

24

x

x

x

xx

a Calculate the energy of the gamma rays in joules.b Use the graph to determine the half-life of technetium-99m.c What is the activity of this sample after one half-life?d If the sample is produced in a hospital at 4 pm, what will its

activity be when it is used at 10 am the next day?

9 The radioisotope sodium-24 decays by emitting a beta particle and a gamma ray.

a Write the decay equation for sodium-24 and identify the nuclide that is produced.

b Discuss and compare the penetrating abilities of beta and gamma radiation in air.

c Which of these radiations would be stopped if the sample was stored in a steel box?

d Energy is produced as a result of this decay. What form does this energy take and which particles are carrying it?

10 A woman exposed to a large whole-body radiation dose was later found to suffer from anaemia (low red blood cell count). Is this a genetic or a somatic effect?

11 In the actinium decay series, 23592

U decays to eventually produce stable 207

82Pb. How many alpha decays and beta decays are there

in this decay series?

12 Protactinium-234 is a radioactive element with a half-life of 70 s. If a sample of this radioisotope contains 6.0 × 1010 nuclei, how many nuclei of this element will remain after:

a 70 s? b 140 s? c 210 s? d 7 minutes?

13 A laboratory produces 60 g of a radioisotope that has a half-life of 1 h. How much of the radioisotope will remain after 2 h?

A none B 60 g C 30 g D 15 g

14 When a sample of beryllium-9 is irradiated with protons, an alpha particle is released and a stable isotope is formed. Determine the identity of this isotope.

15 A Geiger counter was used to compare the activity of two samples of the same radioisotope. Sample A had double the activity of sample B.

a How do the half-lives of these two samples compare?b After two half-lives have passed, how will the activity of

sample A compare with that of sample B?

16 The decay process of an atom of the radioisotope nitrogen-12 is:12

7N → 12

6C + β+ + ν

a What changes have taken place in the nucleus of this atom?b Energy is produced as a result of this decay. What form does

this energy take and which particles are carrying it?

17 A small nuclear power station produced about 1000 MW of power. Two months after the reactor had been shut down, it was still generating about 5 MW of power due to the energy released from radioactive decay. Assuming that each decay releases 1 MeV of energy, calculate the activity of the reactor in becquerels.

18 A worker in an X-ray clinic takes an average of 10 X-ray photo-graphs each day and receives an annual radiation dose equivalent of 7500 μSv.

a Estimate the dose that the worker receives from each X-ray photograph.

b How does this dose compare with the normal background radiation dose?

19 Patient A receives a radiation dose of 5000 μSv to the stomach and 4000 μSv to the colon. Patient B receives a uniform whole body radiation dose of 1000 μSv. Who is at greater risk of

developing cancer from these radiation doses—patient A or patient B? Explain.

Chapter QuizWorked Solutions

Nuclear physics and radioactivity34

AREA OF STUDY REVIEW Nuclear physics and radioactivity

1 As a result of the disaster at the Fukushima nuclear power plant in 2011, the radioactive isotopes caesium-137 and iodine-131 were released into the atmosphere. Use a periodic table to determine the number of protons, neutrons and nucleons contained in a nuclide of each radioisotope.

2 A small sample of radioactive material is located in a lead container. The radioactive material emits radiation into a region of uniform magnetic field. The radiation is deflected as shown in the diagram. Identify the radiation (together with a brief description) associated with each of the paths i, ii, and iii.

iii

iii

3 Consider the following two high-energy particles: an electron with 1.5 × 109 eV and a gamma ray with 7.6 × 10–14 joules.

a Calculate the energy of the electron in joules.b You should find that the electron has much more energy than

the gamma ray, but which travels faster—the electron or the gamma ray?

4 From which part of a radioisotope—the nucleus or the electron cloud—are the following particles emitted?

a alpha particles b beta particles c gamma rays

5 A radioisotope K-40 has a half-life of 1.3 × 109 years and decays to a stable isotope Ar-40, which is used for dating rocks. Copy and complete the following table.

Time (× 109 years)

No. of K nuclei

No. of Ar nuclei

Ratio K:Ar

0 1000 0

1.3

2.6

3.9

The following information applies to questions 6 and 7. Gold-197 is stable but gold-198 is radioactive.

6 Discuss any differences in the chemical properties of these atoms.

7 Describe the difference in the composition of these two atoms.

8 A 73Li nucleus is bombarded with a high-speed proton resulting

in the production of two identical particles. Write the nuclear equation that describes this reaction.

9 Calculate the energy of these particles in MeV:

a an alpha particle with energy 1.4 × 10–12 J b a beta particle with energy 6.7 × 10–14 Jc a gamma ray with energy 8.0 × 10–14 J

The following information applies to questions 10–13. A Geiger counter measures the radioactive disintegrations from a sample of a certain radioisotope. The count rate is recorded in the table.

Activity (Bq) 800 560 400 280 200 140

Time (min) 0 5.0 10 15 20 25

1010 Plot a graph of activity versus time.

1111 Use your graph to estimate the activity of the sample after 13 minutes.

1212 What is the half-life of this element?

1313 Determine the activity of the sample after 30 minutes.

1414 If a particular atom in the sample has not decayed during the first half-life, which one of the following statements best describes its fate?

A It will definitely decay during the second half-life.B It has a 50% chance of decaying during the second half-life. C The probability that it will decay cannot be determined. D If it does not decay during the first half-life, it will not decay

at all. 1515 Explain why gamma rays have very low ionising ability and

therefore high penetrating ability.

1616 Explain why alpha particles have very high ionising ability and poor penetrating ability.

1717 A small nuclear power station in North Dakota produced about 2.0 GW of power. Some time after had it been decommissioned, the reactor was still generating about 8.0 MW of power due to the energy released from radioactive decay. Assuming that each decay releases 500 keV of energy, calculate the activity of the reactor in becquerels.

The following information applies to questions 18–21.

Tritium (hydrogen-3) is radioactive and its decay equation is shown.31H → X +

–10Y

1818 How many protons and neutrons are in each tritium nucleus?

1919 Which element is the daughter nuclide X?

2020 Which of the following best describes the nature of Y in the decay equation?

A It is a positron. B It is an electron.C It is a proton. D It is a neutron.

2121 One of the nucleons in tritium has spontaneously transformed during this decay. Which one and what has it transformed into?

The following information applies to questions 22–24. Gold-185 is an artificial radioisotope of gold. It is an alpha emitter.

35Area of study review

2222 Write a decay equation for gold-185. Use a periodic table to help you.

2323 Describe the nucleons that are in each gold-185 nucleus.

2424 If you held a speck of pure gold-185 in your hand, would you suffer from the radiation exposure? Discuss.

2525 Radiotherapy treatment of brain tumours involves irradiating the target area with radiation from an external source. Why is cobalt-60—a gamma emitter with a half-life of 5.3 years—generally used as the radiation source for this treatment?

2626 An airline pilot of mass 90 kg absorbs a gamma radiation dose of 300 μGy during a return flight to New York. Calculate the dose equivalent that has been received.

The following information applies to questions 27–29. The graph below shows the data obtained in an experiment to determine the half-life of sodium-26.

Act

ivity

(Bq

)

4000

Time (s)50 100 150 200 250 300

3000

2000

1000

0

2727 Use the graph to work out the half-life of sodium-26.

2828 If the initial sample contained 150 g of sodium-26, how much of this radioisotope will remain after 5 minutes?

2929 Sodium-26 is a beta emitter. Write the nuclear equation for its decay.

The following information applies to questions 30 and 31. A man received a uniform full-body radiation dose equivalent of 1200 mSv.

3030 What would the somatic effects of this dose be?

3131 Which organs cells would be at most risk of developing cancer during this exposure?

3232 The reason that an alpha particle has a higher quality factor than an X-ray is:

A Alpha particles travel faster than X-rays.B Alpha particles have less ionising power than X-rays.C Alpha particles have more ionising power than X-rays.D Alpha particles can penetrate flesh further than X-rays.

3333 During a course of radiotherapy, a man’s bone marrow was exposed to a radiation dose of 6000 μSv and his testes to a dose of 4000 μSv. What is the effective dose for this man?

The following information applies to questions 34 and 35. Consider the following nuclear equation. It describes an interaction between a beryllium-7 nucleus and an electron.

74Be +

–10e → 7

3Li + γ

3434 Explain why it is not correct to write the electron in the equation as a beta particle.

3535 A nuclear physicist was bombarding a sample of beryllium-7 with a beam of electrons in an effort to smash the electrons into the nuclei. Why would it be difficult for a collision between the electrons and the nuclei to occur?

The following information applies to questions 36 and 37. A nuclear scientist has prepared equal quantities of two radioisotopes of bismuth, 211Bi and 215Bi. These isotopes have half-lives of 2 minutes and 8 minutes respectively. Assume when answering these questions that each sample has the same number of atoms.

36 36 Which one of the following statements best describes the activities of these samples?

A The samples start with an equal activity, then bismuth-211 has the greater activity.

B Bismuth-211 initially has four times the activity of bismuth-215.

C Bismuth-215 initially has four times the activity of bismuth-211.

D Bismuth-211 initially has twice the activity of bismuth-215. 37 37 How will the activity of these samples compare after 8 minutes?

38 38 In a major incident in a nuclear reactor, a 75 kg employee received a full-body absorbed radiation dose of 5.0 Gy. The radiation was gamma rays.

a Calculate the amount of energy that was absorbed during this exposure.

b Calculate the dose equivalent for this person.c Describe some of the somatic effects that this person would

experience.The following information applies to questions 39 and 40. A worker in an X-ray clinic takes an average of ten X-ray photographs each day (she works 250 days a year) and receives an annual radiation dose equivalent of 0.03 Sv.

39 39 Estimate the dose that the worker receives from each X-ray photograph.

40 40 How does this worker’s annual dose compare with the normal background radiation dose?

Exam AdviceWorked Solutions