Modes of Radioactive Decay

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General Concepts

It is common terminology to call an unstable radioactive nucleus the parent and the more stable product nucleus the daughter . In many cases, the daughter also is radioactive and undergoes further radioactive decay. Radioactive decay is spontaneous in that the exact moment at which a given nucleus will decay cannot be predicted, nor is it affected to any significant extent by events occurring outside the nucleus.

Radioactive decay results in the conversion of mass into energy. If all the products of a particular decay event were gathered together and weighed, they would be found to weigh less than the original radioactive atom. Usually, the energy arises from the conversion of nuclear mass, but in some decay modes, electron mass is converted into energy as well. The total mass-energy conversion amount is called the transition energy , sometimes designated Q . ^* Most of this energy is imparted as kinetic energy to emitted particles or converted to photons, with a small (usually insignificant) portion given as kinetic energy to the recoiling nucleus. Thus radioactive decay results not only in the transformation of one nuclear species into another but also in the transformation of mass into energy.

* Some texts and applications consider only nuclear mass, rather than the mass of the entire atom (i.e., atomic mass), in the definition of transition energy. As will be seen, the use of atomic mass is more appropriate for the analysis of radioactive decay because both nuclear and nonnuclear mass are converted into energy in some decay modes. As well, energy originating from either source can contribute to usable radiation or to radiation dose to the patient. For a detailed discussion of the two methods for defining transition energy, see Evans RD: The Atomic Nucleus . New York, 1972, McGraw-Hill, pp 117-133.

Each radioactive nuclide has a set of characteristic properties. These properties include the mode of radioactive decay and type of emissions, the transition energy, and the average lifetime of a nucleus of the radionuclide before it undergoes radioactive decay. Because these basic properties are characteristic of the nuclide, it is common to refer to a radioactive species, such as ¹³¹ I, as a radionuclide . The term radioisotope also is used but, strictly speaking, should be used only when specifically identifying a member of an isotopic family as radioactive; for example, ¹³¹ I is a radioisotope of iodine.

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Chemistry and Radioactivity

Radioactive decay is a process involving primarily the nucleus, whereas chemical reactions involve primarily the outermost orbital electrons of the atom. Thus the fact that an atom has a radioactive nucleus does not affect its chemical behavior and, conversely, the chemical state of an atom does not affect its radioactive characteristics. For example, an atom of the radionuclide ¹³¹ I exhibits the same chemical behavior as an atom of ¹²⁷ I, the naturally occurring stable nuclide, and ¹³¹ I has the same radioactive characteristics whether it exists as iodide ion ( I ⁻ ) or incorporated into a large protein molecule as a radioactive label. Independence of radioactive and chemical properties is of great significance in tracer studies with radioactivity—a radioactive tracer behaves in chemical and physiologic processes exactly the same as its stable, naturally occurring counterpart, and, further, the radioactive properties of the tracer do not change as it enters into chemical or physiologic processes.

There are two minor exceptions to these generalizations. The first is that chemical behavior can be affected by differences in atomic mass . Because there are always mass differences between the radioactive and the stable members of an isotopic family (e.g., ¹³¹ I is heavier than ¹²⁷ I), there may also be chemical differences. This is called the isotope effect . Note that this is a mass effect and has nothing to do with the fact that one of the isotopes is radioactive. The chemical differences are small unless the relative mass differences are large, for example, ³ H versus ¹ H. Although the isotope effect is important in some experiments, such as measurements of chemical bond strengths, it is, fortunately, of no practical consequence in nuclear medicine.

A second exception is that the average lifetimes of radionuclides that decay by processes involving orbital electrons (e.g., internal conversion, Section E , and electron capture, Section F ) can be changed very slightly by altering the chemical (orbital electron) state of the atom. The differences are so small that they cannot be detected except in elaborate nuclear physics experiments and again are of no practical consequence in nuclear medicine.

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Decay by β ⁻ Emission

Radioactive decay by β ⁻ emission is a process in which, essentially, a neutron in the nucleus is transformed into a proton and an electron. Schematically, the process is

The electron (e ⁻ ) and the neutrino (ν) are ejected from the nucleus and carry away the energy released in the process as kinetic energy. The electron is called a β ⁻ particle . The neutrino is a “particle” having no mass or electrical charge. * It undergoes virtually no interactions with matter and therefore is essentially undetectable. Its only practical consequence is that it carries away some of the energy released in the decay process.

* Actually, in β ⁻ emission an antineutrino, , is emitted, whereas in β ⁺ emission and EC, a neutrino, ν, is emitted. For simplicity, no distinction is made in this text. Also, evidence from high-energy physics experiments suggests that neutrinos may indeed have a very small mass, but an exact value has not yet been assigned.

Decay by β ⁻ emission may be represented in standard nuclear notation as

The parent radionuclide (X) and daughter product (Y) represent different chemical elements because atomic number increases by one. Thus β ⁻ decay results in a transmutation of elements. Mass number A does not change because the total number of nucleons in the nucleus does not change. This is therefore an isobaric decay mode, that is, the parent and daughter are isobars (see Chapter 2, Section D.3 ).

Radioactive decay processes often are represented by a decay scheme diagram . Figure 3-1 shows such a diagram for ¹⁴ C, a radionuclide that decays solely by β ⁻ emission. The line representing ¹⁴ C (the parent) is drawn above and to the left of the line representing ¹⁴ N (the daughter). Decay is “to the right” because atomic number increases by one (reading Z values from left to right). The vertical distance between the lines is proportional to the total amount of energy released, that is, the transition energy for the decay process ( Q = 0.156 MeV for ¹⁴ C).

The energy released in β ⁻ decay is shared between the β ⁻ particle and the neutrino. This sharing of energy is more or less random from one decay to the next. Figure 3-2 shows the distribution, or spectrum , of β ⁻ -particle energies resulting from the decay of ¹⁴ C. The maximum possible β ⁻ -particle energy (i.e., the transition energy for the decay process) is denoted by (0.156 MeV for ¹⁴ C). From the graph it is apparent that the β ⁻ particle usually receives something less than half of the available energy. Only rarely does the β ⁻ particle carry away all the energy ( ).

The average energy of the β ⁻ particle is denoted by . This varies from one radionuclide to the next but has a characteristic value for any given radionuclide. Typically, . For ¹⁴ C, .

Beta particles present special detection and measurement problems for nuclear medicine applications. These arise from the fact that they can penetrate only relatively small thicknesses of solid materials (see Chapter 6 , Section B.2). For example, the thickness is at most only a few millimeters in soft tissues. Therefore it is difficult to detect β ⁻ particles originating from inside the body with a detector that is located outside the body. For this reason, radionuclides emitting only β ⁻ particles rarely are used when measurement in vivo is required. Special types of detector systems also are needed to detect β ⁻ particles because they will not penetrate even relatively thin layers of metal or other outside protective materials that are required on some types of detectors. The implications of this are discussed in Chapter 7 .

The properties of various radionuclides of medical interest are presented in Appendix C . Radionuclides decaying solely by β ⁻ emission listed there include ³ H, ¹⁴ C, and ³² P.

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