As in the case of an atom, different types of atoms are called elements; in the case of a nucleus, different types of nuclei are termed nuclides. An element is characterized by its atomic number (Z) alone, whereas a nuclide is characterized by its mass number (A) and by its atomic number (Z). The mass number (A) of a nuclide is the sum of the number of its protons (Z) and neutrons (N); that is, A = Z + N.

As an example, , a nuclide of iodine contains 53 protons and 78 neutrons, which add up to 131, the mass number of this nuclide. A general notation for a nuclide is , where A and Z, respectively, are the mass number and the atomic number of the nuclide and X is the element to which this nuclide belongs.

Nuclides are classified according to their mass number, neutron number, and atomic (proton) number. Nuclides having the same atomic mass are called isobars (e.g., and ; both of these nuclides have the same mass number, 131). Nuclides having the same number of protons are called isotopes (e.g., and ). Because they contain the same number of protons and therefore have the same atomic number, isotopes always belong to the same element. Nuclides having the same number of neutrons are called isotones (e.g., and ; both of these nuclides contain six neutrons). As an aid to memory, a pair of corresponding letters in each definition is italicized.

How are neutrons and protons (a common name for the two combined is nucleon) arranged inside the nucleus? We have only a partial answer to this question so far. Our understanding of the structure of a nucleus when compared with the structure of an atom (i.e., arrangement of electrons in various shells and their interactions) is quite limited. It is postulated—with a wealth of supportive experimental data—that nucleons are arranged in spherical shells inside the nucleus in a manner similar to that of electrons in an atom. However, not much is known of the manner in which nucleons are stacked in these shells or about the transitions of nucleons between different shells. What is known and is important for the present discussion is that nucleons, like electrons in an atom, can also be excited to higher unoccupied shells by absorption of energy from outside the nucleus. The lowest possible arrangement of nucleons in the nucleus is known as the ground state of a nuclide. The higher
shells are commonly referred to as energy levels or excited states. Again, similar to electrons in an atom, nucleons in a nucleus are also bound with different binding energies. The binding energy (BE) of a nucleon (amount of energy needed to pull it out of the nucleus) varies from nuclide to nuclide. However, the average BE of nucleons for most nuclides is in the range of 5 to 8 MeV. This is about 1,000 times higher (MeV rather than keV) than the average binding energies of electrons in atoms. Therefore, it is hard to remove a proton or neutron from a nucleus. It requires transfer of a large amount of energy from outside that is, in general, only possible in nuclear reactors, accelerators, or cyclotrons.

The excited states of a nuclide, in general, are of a short duration (<10^-11 seconds) and decay to the ground state or lower energy states by emission of high-energy radiation in a manner similar to that of the excited states of an atom, which decay to the ground state of an atom by emitting light or x-rays.

Excited states have the same mass number, same atomic number, and the same number of neutrons as the ground state and therefore are called isomers (i.e., an isomer is an excited state of a nuclide). Note that the letter “e” has been italicized twice in the above definition, again as an aid to memory. The isomer of a nuclide is generally distinguished from its ground state by placing an asterisk after the symbol of the nuclide (e.g., * is an excited state of ). In a few cases, however, the lifetime of the excited state of a nuclide can be very long (seconds, minutes, or even years). When this occurs, the excited state is called a metastable state. Well-known examples of nuclides having metastable states are ^99mTc and ^113mIn. The letter “m” after the mass number in these two nuclides stands for metastable state and distinguishes them from their respective ground states of ⁹⁹Tc and ¹¹³In.

Even in their ground state, many nuclides are unstable. These unstable nuclides are called radionuclides. Radionuclides try to become stable by emitting electromagnetic radiation or charged particles. Electromagnetic radiation or charged particle emission is called radioactive decay. What makes a nuclide stable or radioactive? Two kinds of forces, strong and electromagnetic, determine the stability of a nuclide. The strong forces act between a pair of nucleons (e.g., proton-proton, proton-neutron, or neutron-neutron). They are attractive and act only when the distance between the two nucleons is very small. Electromagnetic forces act between protons only (because there is no charge on neutrons) and are repulsive (similar charges repel each other). The balance between these two forces—one attractive, the other repulsive—determines the stability of a nuclide. Whenever the balance between these two forces is disturbed, the nuclide becomes unstable and therefore radioactive. There are approximately 259 stable nuclides found in nature.

If one plots the number of neutrons (N) contained as a function of the number of protons (Z) in a nuclide for all stable nuclides, a curve as shown in Figure 2.1 results. This curve initially starts as
a straight line and then slowly bends toward the neutron number (N) for higher atomic numbers. From this curve, it can be seen that for a lighter nuclide (A < 50), the number of protons in stable nuclides is equal to the number of neutrons; for example, , a stable oxygen nuclide, contains eight neutrons and eight protons. For heavier nuclides (A > 100), however, the number of neutrons needed for the stability of a nuclide is much more than the number of protons; for example, , a stable iodine nuclide, contains 53 protons and 74 neutrons. The region on either side of the curve in Figure 2.1 is called the domain of radionuclides. If a radionuclide lies in the upper region, it contains an excess number of neutrons that cause the “unstability” of the radionuclide. On the other hand, if the radionuclide lies in the lower region, it is the excess of protons that makes the nuclide unstable.

A radionuclide tries to attain stability through radioactive decay. The stability may be achieved either by direct (single-step) decay to a stable nuclide or by decaying to several radionuclides in multiple steps and, finally, to a stable nuclide. For example, directly decays to a stable nuclide . On the other hand, Rafirst decays to , which decays to and finally to , a stable nuclide. The complete series for this is given below (the arrows denote the sequence of decay):

This latter process is often referred to as a radioactive series or chain. Well-known examples of a radioactive series in nuclear medicine are the decay of ⁹⁹Mo and ¹¹³Sn, which go through the following sequences:

The three processes through which a radionuclide tries to attain stability are called (1) alpha, (2) beta (isobaric transition), and (3) gamma (isomeric transition) decay. These names were given because at the time of the discovery of these processes their exact nature was not known. Three important conservation laws are pertinent here because they always hold true in radioactive processes or nuclear transformations. These are the law of conservation of energy, the law of conservation of mass number, and the law of conservation of electric charge.

The law of conservation of energy states that the total energy (mass energy + kinetic energy + energy in any other form, e.g., a photon) remains unchanged during a radioactive process or nuclear transformation. The law of conservation of mass number states that the sum of mass numbers remains unchanged in radioactive or nuclear processes. The mass number of a neutron or proton is assumed to be one and that of an electron zero. Similarly, the law of conservation of electric charge states that the total charge during a radioactive process or nuclear transformation remains unchanged.

Alpha (α) Decay. In alpha decay, a radionuclide emits a heavy, charged particle called α particle. An α particle is four times heavier than a proton or neutron and carries an electric charge that is twice that of a proton. In fact, α particle is a stable nuclide with atomic mass number A = 4 and atomic number Z = 2. This happens to be the nucleus of a helium atom.

From the conservation laws of the mass number and electric charge, it follows that during alpha decay, the mass number and the atomic number of the resulting nuclide (also known as the daughter nuclide) will be reduced by 4 and 2, respectively. Alpha decay can be expressed by the following equation:

Note that the mass number and the electric charge (in this case the sum of atomic numbers) on both sides of the equation are the same. An example of alpha decay is the decay of radium 226 to radon 222:

is a radionuclide that decays through alpha decay. Determine the nature of its daughter
nuclide. Because decays through the alpha decay process, the mass number of the daughter nuclide will be 4 less than that of the parent, that is, 222 – 4 = 218. Similarly, the atomic number will be reduced by 2, that is, 86 – 2 = 84. Therefore, the daughter nuclide has a mass number 218 and its atomic number is 84. According to the periodic table, the atomic number 84 belongs to the element Po. Therefore, the daughter nuclide is .

Radon 222 is a radioactive gas that escapes into the environment from the rocks or soil containing radium 226. A small amount of radium and, therefore radon, is present everywhere. Such amounts increase the background radiation and constitute a major part of background radiation exposure to humans. In rare cases, a combination of relatively large concentrations of radium in the soil and rocks and poor circulation in a house can sometimes produce hazardous concentrations of radon in the house. This should be dealt effectively for the safety of the occupants.

Two salient facts concerning alpha decay to remember are that it occurs mostly with radionuclides whose atomic mass number A is greater than 150 and the kinetic energy of the emitted α particle is fixed and discrete for a given decay. In the above example of alpha decay, the kinetic energy of α particle emitted is 4.780 MeV.

Beta (β) Decay, or More Appropriately, Isobaric Transition. During this transformation, a neutron or a proton inside the nucleus of a radionuclide is converted to a proton or a neutron, respectively. When a proton is converted into a neutron, the positive charge inside the nucleus is decreased by one, thus reducing the repulsive forces between protons. On the other hand, when a neutron is converted into a proton, the positive charge inside the nucleus is increased by one, and therefore, the repulsive forces between protons are increased. The result of the decrease or increase in the repulsive force within the nucleus is to balance the two forces (electromagnetic and strong) in an attempt to stabilize the nuclide (see Radionuclides and Stability of Nuclides, p. 10).

The conversion of a neutron into a proton or of a proton into a neutron is controlled by weak (as opposed to strong, electromagnetic, and gravitational) forces (see Chapter 1). The exact nature of weak forces is not known and is not pertinent to our discussion of beta decay. In this phenomenon, one of the following three processes occur: β^– (electron) emission, β⁺ (positron) emission, or electron capture (EC). Following any of these three processes, the mass number A remains unchanged, thus referred to as an isobaric transition.

β^– (Electron) Emission. In this process, a neutron inside the radionuclide is converted into a proton, and the excess energy is released as a pair of particles, an electron and an antineutrino . As such, there are no electrons or antineutrinos inside the nucleus. These are created from excess energy at the instant of radioactive decay. An antineutrino is a particle that has no rest mass and no electric charge (Z = 0). It rarely interacts with matter and therefore is of no biological significance. Its existence was postulated, so that the law of energy conservation would not be violated. However, its existence has now been confirmed experimentally. β^– decay can be expressed as

Note that both the mass number and the electric charge are conserved. Some well-known examples of β^– decay are , , and , which can be expressed as follows:

As can be seen, during β^– decay, the mass number (A) remains unchanged and the atomic number (Z) is increased by one. The kinetic energy of the emitted electron is not fixed because the total available energy in the decay (difference between the mass energy of the parent radionuclide and the daughter nuclide) has to be shared between the electron and the antineutrino.

In the above example, the difference between the mass energies of and , and , and and during decay is shared by the electron and the antineutrino. The sharing of the available energy is random; therefore, the electrons are emitted with varying amounts of kinetic energy (known as the β^– spectrum) ranging from zero to a maximum of E_β max. E_β max is the total available
energy in the case of a particular β^– decay. In the above examples, E_β max for ³H decay is 0.018 MeV; for ¹⁴C decay, it is 0.156 MeV; for ³²P decay, it is 1.71 MeV. The probability of an electron emission with a given kinetic energy E_β, P(E_β) varies greatly with the kinetic energy E_β. The variation of P(E_β) with E_β (i.e., β^– spectrum) is shown in Figure 2.2 for a typical β^– decay.