Essentials of Nuclear Medicine Physics, Instrumentation, and Radiation Biology. Rachel A. Powsner

is not possible to predict when an individual nuclide atom will decay, just as in preparing popcorn one cannot determine when any particular kernel of corn will open. However, the average behavior of a large number of the popcorn kernels is predictable. From experience with microwave popcorn, one knows that half of the kernels will pop within 2 minutes and most of the bag will be done in 4 minutes. In a like manner, the average behavior of a radioactive sample containing billions of atoms is predictable. The time it takes for half of these atoms to decay is called (appropriately enough) the half‐life, or in scientific notation T_1/2 pronounced “T one‐half”). It is not surprising that the time it takes for half of the remaining atoms to decay is also T_1/2. This process continues until the number of nuclide atoms eventually comes so close to zero that we can consider the process complete. A plot of A(t), the activity remaining, is shown in Figure 1.23.

Figure 1.21 Decay schematics.

      This curve, and therefore the average behavior of the sample of radioactivity, can be described by the decay equation:

      where A(0) is the initial number of radioactive atoms.

      A commonly used alternative form of the decay equation employs the decay constant (λ), which is approximately 0.693 divided by the half‐life (T_1/2):

      The decay equation can be rewritten as

The amount of activity of any radionuclide may be expressed as the number of decays per unit time. Common units for measuring radioactivity are the curie (after Marie Curie) or the SI unit, the becquerel (after another nuclear pioneer, Henri Becquerel). One becquerel is defined as one radioactive decay per second. Nuclear medicine doses are generally a million times greater and are more easily expressed in megabecquerels (MBq). One curie (Ci) is defined as 3.7 × 10¹⁰ decays per second (this was picked because it is approximately equal to the radioactivity emitted by 1 g of radium in equilibrium with its daughter nuclides). A partial list of conversion values is provided in Table 1.2.

A related term that is frequently confused with decay is the count, which refers to the registration of a single decay by a detector such as a Geiger counter. Most of the detectors used in nuclear medicine detect only a fraction of the decays, principally because the radiation from many of the decays is directed away from the detector. Count rate refers to the number of decays actually counted in a given time, usually counts per minute. All things being equal, the count rate will be proportional to the decay rate, and it is a commonly used, if inexact, measure of radioactivity.

Figure 1.22 Decay schemes showing principal transitions for technetium‐99m, indium‐111, iodine‐131 and radium‐226. Energy levels are rounded to three significant figures.

Figure 1.23 Decay curve. Note the progressive replacement of radioactive atoms (parent) by relatively more stable atoms (daughter) as shown schematically in each box.

Table 1.2 Conversion values for units of radioactivity

One curie (Ci) =		1 × 103 mCi	1 × 106 μCi	37 × 109 Bq	37 × 103 MBq
One millicurie (mCi) =	1 × 10–3 Ci		1 × 103 μCi	37 × 106 Bq	37 MBq
One microcurie (μCi) =	1 × 10–6 Ci	1 × 10–3 mCi		37 × 103 Bq	37 × 10–3 MBq
One bequerel (Bq)* =	27 × 10–12 Ci	27 × 10–9 mCi	27 × 10–6 μCi		1 × 10–6 MBq
One megabequerel (MBq) =	27 × 10–6 Ci	27 × 10–3 mCi	27 μCi	1 × 106 Bq

      ^* One bequerel = 1 decay per second.

Questions

      1 The chemical interactions between various elements are mainly determined by:The number of protons.The number of neutrons.The number of electrons in the outermost shell.The number of protons minus the number of electrons.

      2 For each of the five terms below, choose the best definition:Isobars.Isoclines.Isomers.Isotones.Isotopes.Atoms of the same element (equal Z) with different numbers of neutrons (N).Atoms of the same element (equal Z) with different numbers of protons.Atoms of different elements (different Z) with equal numbers of neutrons (N).Atoms of different elements with equal atomic mass (A).

      3 Which of the following statements are correct?There is a stable isotope of technetium.Atoms with atomic numbers (Z) > 83 are inherently unstable.For lighter elements nuclear stability is achieved with equal numbers of protons and neutrons; for heavier elements the number of neutrons exceeds the number of protons.

      4 For internal conversion to occur, the excess energy of the excited nucleus must equal or exceed:511 keV.1.022 MeV.The internal conversion coefficient.The average energy of the Auger electrons.The binding energy of the emitted electron.

      5 For an atom undergoing beta decay, the average energy of the emitted beta particles is approximately:511 keV.0.551 times the loss of atomic mass.One half of the total energy released for the individual event.One third of the maximum energy of the emitted beta particles.Equal to the average energy of the accompanying antineutrinos.

      6 You