Transient equilibrium
Transient equilibrium is illustrated in Figure 3.2. In this example, the half‐life of the parent nuclide is approximately 10 times that of the daughter. Following an elution that removes all of the available daughter, the amount of the daughter nuclide rapidly increases until the daughter activity slightly exceeds that of the parent at about four to five half‐lives. Thereafter the daughter activity declines at the same rate as the parent.
The preceding example of transient equilibrium is based on a decay scheme in which 100% of the parent nuclide decays to the daughter nuclide. However, in the commonly used 99Mo–99mTc generator, only 86% of the parent molybendum‐99 decays to the daughter technetium‐99m; the remainder decays directly to Technetium‐99 (Figure 3.3). As a result, the activity of 99mTc is always less than the activity of 99Mo (see Figure 3.3).
Secular equilibrium
For generators where the half‐life of the parent is greater than 100 times that of the daughter nuclide, since we are interested in time‐scales on the order of the daughter half‐life, we just consider the parent nuclide to be stable.
Secular equilibrium, like transient equilibrium, is achieved rapidly following an elution that removes all of the available daughter nuclide. Thereafter the activity of the daughter nuclide is approximately equal to that of the parent. However, the decay curve of the parent appears to be flat since its half‐life is so much longer than that of the daughter nuclide. An example of secular equilibrium can be seen with the 82Sr–82Rb generator (see Figure 3.4).
Cyclotrons
Cyclotrons are circular devices (Figure 3.5) in which charged particles such as protons and alpha particles are accelerated in a spiral path within a vacuum. The power supply provides a rapidly alternating voltage across the dees (the two halves of the circle). This produces a rapidly alternating electric field between the dees that accelerates the particles, which quickly acquire high kinetic energies. They spiral outward under the influence of the magnetic field until they have sufficient velocity and are deflected into a target.
Figure 3.2 Transient equilibrium.
Figure 3.3 Transient equilibrium in a 99Mo–99mTc generator.
A deflector is used to direct the particles out through a window of the cyclotron into a target. Some of the particles and kinetic energy from these particles are incorporated into the nuclei of the atoms of the target. These energized (excited) nuclei are unstable.
Figure 3.4 Secular equilibrium.
Figure 3.5 Cyclotron.
Indium‐111 (111In) is produced in a cyclotron. The accelerated (bombarding) particles are protons. The target atoms are cadmium‐112 (112Cd). When a proton enters the nucleus of a 112Cd atom, the 112Cd is transformed into 111In by discharging two neutrons. This reaction can be written as:
or
Other examples of cyclotron reactions include 121Sb(α,2n)123I, 68Zn(d,n)67Ga, and 10B(d,n)11C, where the symbols α and d denote alpha particles and deuterons (proton plus neutron) respectively.
Reactors
Radionuclides for nuclear medicine are also produced in nuclear reactors. Some examples include 131I, 133Xe, and 99Mo.
Reactor basics
A general schematic of a reactor is seen in Figure 3.6. A reactor is composed of fuel rods that contain large atoms (typically Uranium‐235, Uranium‐238, or Plutonium‐239) that are inherently unstable. These atoms undergo fission, (see Figure 1.14). Two or three neutrons and approximately 200 MeV of heat energy are emitted during this process. These neutrons leave the nucleus with moderately high kinetic energy and are referred to as fast neutrons. The neutrons are slowed with a moderator such as graphite, water, or heavy water. These “very slow” or thermal neutrons, and to a lesser extent the fast neutrons, in turn impact other fissionable atoms causing their fission, and so forth (Figure 3.7). If this chain reaction were to grow unchecked, the mass would explode. To maintain control, cadmium control rods are inserted to absorb the neutrons in the reactor. They can be further inserted or withdrawn to control the speed of the reaction. Medical nuclides are made in reactors by the processes of fission or neutron capture.
Kinetic energy
Kinetic means “motion.” The form of energy attributable to the motion of an object is its kinetic energy. Kinetic energy is related to both the mass (m) and velocity (v) of the object, specifically ½ mv2. A moving car has kinetic energy, a parked car does not. A speeding car contains a great deal of kinetic energy that can be dissipated rapidly as heat, noise, and the destruction of metal in a collision.
Figure 3.6 Schematic of a nuclear reactor.
