1 Atoms, Nuclei and Radioactivity Elizabeth M. Parvin CHAPTER OUTLINE Introduction Transverse and Longitudinal Waves Atomic Structure Electromagnetic Radiation Particles Continuous Spectra and Characteristic Radiation The Atom and the Nucleus Radioactive Decay The Forces Stable and Unstable Isotopes Electron Energy Levels Half-life Band Theory of Solids Alpha Decay Impurity Bands Beta Decay Particles in Electric and Magnetic Fields Gamma Decay Electric Fields Electron Capture and Internal Conversion Magnetic Fields Radioactive Decay Series The Lorentz Equation Radionuclides of Medical Interest Waves INTRODUCTION fundamental particles; the protons and neutrons are composed of quarks. Charges are, as is customary in physics, given as multiples of À The aim of this first chapter is to lay some of the foundations of the the electronic charge, e, which is 1.602  10 19 C. The proton and pos- physics of radiotherapy. It starts, in the section titled Atomic Structure, itron have charges of +e and the electron has a charge of –e; all the other by looking at the main subatomic particles and the forces that hold particles listed are neutral. The fourth column gives the masses in kilo- them together in the atom. This leads on to an examination of the dif- grams, but in nuclear physics, it is common practice to express the mass ferent types of nuclei, with an emphasis on some of the important ones of a particle not in kilograms but in terms of its rest mass energy. This is used in medical physics. The behaviour of charged particles in electric based on Einstein’s famous equation, which gives the equivalence of and magnetic fields, central to much of the physics of radiotherapy, is mass and energy: covered in section titled Particles in Electric and Magnetic Fields. E ¼ mc2 Waves, including the electromagnetic spectrum, and the basics of 1.1 radioactive decay are introduced in the following sections. where m is the mass of the particle, c is the speed of light in a vacuum À For some readers, this chapter will be a reminder of previous knowl- (2.998  108 ms 1) and E is the energy. For an electron, the rest mass À À edge, for others it will be new territory. For the latter, the references energy associated with a mass of 9.109  10 31 kg is 8.187  10 14 should provide some more in-depth material that it has not been pos- joules (J). It is more convenient to express this very small magnitude sible to include here. For convenience, SI units are listed in the Physical of energy in units of the electron-volt (eV), where Units and Constants Section. 1eV¼ 1:602  10À19 J 1.2 ATOMIC STRUCTURE The electron volt is the amount of energy acquired by an electron when Particles it is accelerated through a voltage of 1 volt (see the section titled Electric Most readers will be familiar with the idea that molecules are composed Fields), hence the name electron volt. Using this conversion, we arrive at of atoms chemically bonded together. Perhaps the most familiar exam- the values given in column 5 of Table 1.1. Note that the proton and neu- ple is the water molecule, which consists of two hydrogen atoms tron (known collectively as nucleons) are very much more massive than — bonded to one oxygen atom to give the well-known molecular formula the electron and positron, and that the neutrino has almost zero mass the exact value is still the subject of experiment. H2O. In radiotherapy, we are often more interested in the particles that make up the atom—these are known as subatomic particles. The positron is the antiparticle of the electron, having the same β+ Table 1.1 lists the properties of the sub-atomic particles of most rel- mass but the opposite charge; it is emitted during decay (see the sec- evance to radiotherapy; the proton, neutron, electron, positron, neutrino tion titled Beta Decay) and is important in positron emission tomog- β and antineutrino. Strictly, only the electron, positron and neutrinos are raphy (PET) (see Chapter 6). Neutrinos play a role in decay (see 2 CHAPTER 1 Atoms, Nuclei and Radioactivity 3 the section titled Beta Decay). The photon is the particle associated with respectively and are known as isotopes of carbon. For many elements, electromagnetic radiation (see the section titled Waves). some of the isotopes are radioactive (see the section titled Radioactive Decay) and this fact can be very useful in clinical investigations because The Atom and the Nucleus the chemical behaviour of all the isotopes is the same. For example, 15 The atom is the smallest identifiable amount of an element. Each atom radioactive 8 O is taken up by the body in the same way as the stable 16 consists of a central nucleus, made up of protons and neutrons, which is (i.e. nonradioactive) isotope, 8 O, and can be used in PET; the radioac- ‘ ’ 131 surrounded by a cloud of electrons. The diameter of an atom and tive iodine isotope 58 I is taken up by the thyroid gland in the same way À10 À14 127 nucleus are typically 10 m and 10 m, respectively. To put these as the stable isotope 58 I, so can be used to treat thyroid cancer. dimensions into a more accessible perspective, if the atomic nucleus is represented by the point of a pencil (diameter approximately 0.5 mm) The Forces held in the centre of a medium-sized room (say 5 m  5 m), then the The next point to address is the question of what holds the atoms electron cloud surrounding the nucleus would extend to the walls of together. The protons in the nucleus are positively charged, and the the room. electrons surrounding the nucleus are negatively charged, so there is It is the number of protons in a nucleus that determines the type of an attractive force between them. This electrostatic or Coulomb force element. Because the protons in the nucleus are positively charged and depends on the product of the charges and is inversely proportional the electrons are negatively charged, a neutral atom must contain equal to the square of the distance between them. For one electron numbers of protons and electrons. It is the electrons, which surround (charge –e) and a nucleus (charge Z), the magnitude of the force the nucleus and are often described as orbiting it, that interact with (Fel) is given by the equation electrons from other atoms, thereby determining the chemical behav- Ze2 iour of the atom. Fel ¼ k 1.4 For example, a hydrogen atom has one proton in the nucleus, helium r 2 has two, carbon has six and so on. This number is known as the atomic where k is a constant and r is the distance between the electron and the number, Z, of the element. The elements listed in order of increasing nucleus. This inverse-square relationship is analogous to the gravita- atomic number form the periodic table of the elements [1]. tional force between two masses and we could use the rules of classical As shown in Table 1.1, the neutrons in the nucleus carry no charge physics to calculate the orbits of the electrons around the nucleus (anal- but do have a similar mass to the protons. The electrons have a very ogous to the orbits of the planets around the Sun). However, there is small mass, so the mass of an atom is almost entirely due to from one big difference between the planetary orbits and the orbits of the the mass of the protons and neutrons. The sum of the number of neu- electrons around the nucleus; in the planetary case, it is possible to have trons (N) and protons in a nucleus is known as the atomic mass num- any value of the radius (and therefore energy), whereas, in the atomic ¼ ber, A and A Z + N. Because both A and Z are needed to identify a case, quantum theory only allows certain permitted orbits. This gives nucleus, the notation used is of the form rise to electron energy levels (or shells), which are the subject of the A section titled Electron Energy Levels. Z X 1.3 For like charges, the Coulomb force is repulsive, so, because the pro- The symbol shown here as X is the chemical symbol for the element—H tons in the nucleus are all positively charged, it might be expected that for hydrogen, He for helium, C for carbon and so on—and A and Z the Coulomb force would cause the nucleus to fly apart. However, there are the mass and atomic numbers. Because Z determines the chemistry is another force that acts on both protons and neutrons: the strong force. and therefore the element, strictly speaking, it is not necessary to have This force acts on protons and neutrons and other heavy particles called 12 the value of Z shown. For example, 6 C represents a carbon nucleus with hadrons; it is independent of charge and is always attractive, but only at six protons and six neutrons, but it could be written simply as 12C, or even very short range. Fig. 1.1 shows the way in which the energy of a proton as carbon-12 because carbon always has six protons. However, to avoid varies depending on how far away from the nucleus it is. As a proton confusion, it is often easier to include both atomic and mass numbers. approaches the nucleus, it experiences a repulsive force but, if it has For any one element, the number of protons is always the same, but enough energy to overcome this ‘Coulomb barrier’ and gets within the number of neutrons, and hence A, can vary.