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Symbolically, isotopes are written with the chemical symbol and the atomic mass number as a superscript to the left of the symbol: 63Cu and 65Cu in the case of copper 63 and copper 65, respectively. For an isotope to remain stable, the neutron/proton ratio must lie within a relatively narrow range. If the ratio is outside this range, the nucleus is unstable and achieves stability through a spontaneous nuclear transformation that corrects the neutron/proton ratio. Such an unstable isotope is called a radioisotope. Radioisotopes emit various combinations of particles and gamma rays that are specific to each isotope; this process is called radioactive transformation or radioactive decay. In most cases, the transformed nucleus is a different element, one whose neutron/proton ratio is closer to stability than the unstable parent's nucleus.
All radioisotopes are uniquely identified by a set of three different characteristics:
Type of radiation that is emitted
Energy of the emitted radiation
Rate at which the radioisotope decays. This rate is described either by the half‐life, or by the fraction that decays per unit time (the decay rate constant).
3.3 Rate of Decay
The half‐life is defined as the period of time during which one‐half of the radioisotope decays. After a second half‐life period, one‐half of the remaining isotope decays, leaving one‐fourth of the original activity, and after the next half‐life, only one‐eighth of the original activity is left. More than 99% of the original activity is gone after seven half‐lives. Half‐lives of radioisotopes range from microseconds to billions of years.
The decay rate constant is defined as the instantaneous fractional decrease of the radioisotope. In the case of 226Ra, whose half‐life is 1600 years, the decay rate constant is 0.00043 per year. This means that it is decreasing at a rate of 0.043% per year. Radioisotopes with a short half‐life decay at a much faster rate. For example, 131I, with a half‐life of eight days, decays at a rate of 8.7% per day. Generally, the relationship between an initial amount of activity, A0, and the amount of activity left after a time t, and whose decay rate constant is λ per unit time, is given by
(1)
The half‐life, T1/2, is related to the decay rate constant by
The half‐time, T1/2, and the decay constant, λ, must be in the same time units when calculating with these decay equations.
3.4 Quantity of Radioactivity
Since radioactive isotopes are used because of their radioactivity, the unit for expressing the quantity of radioactive material is based on the disintegration rate. Thus, for example 3.7 × 1010 atoms in 1 g of 226Ra decay in 1 s, while 1.7 × 1014 atoms in 1 g of 210Po decay in 1 s. One gram of 210Po is much more radioactive than 1 g of 226Ra. Clearly, mass is not the most appropriate unit for specifying the quantity of a radioisotope. The traditional unit for the quantity of a radioisotope is Curie, symbolized by Ci. The Ci is defined as that quantity of a radioactive material in which 3.7 × 1010 atoms are transformed in 1 s. The commonly used subunits are the millicurie, mCi (10−3 Ci), microcurie, μCi (10−6 Ci), nanocurie, nCi (10−9 Ci), and picocurie, pCi (10−12 Ci).
In the SI system, the unit for the quantity of radioactivity is the becquerel (Bq). One becquerel is defined as that quantity of radioactive material in which one atom disintegrates in 1 s. Since the Bq is such a small quantity of radioactive material, the kilobecquerel (kBq) (103 Bq), megabecquerel (MBq) (106 Bq), and the terabecquerel (1012 Bq) are frequently used. 1 MBq = 27 μCi.
3.5 Specific Activity
The concentration of radioactivity is called the specific activity. Specific activity may be designated in traditional units of curies per unit mass or unit volume. In the SI system, the analogous quantities are given in megabecquerel per kilogram or in megabecquerel per cubic meter.
The specific activity, in Ci/g of a carrier free radioisotope, is given by
(2)
where TRa and Ti are the half‐lives, in the same time units, of 226Ra (T = 1600 years) and of the radioisotope, and Ai is the atomic mass number of the radioisotope. In the case of 131I, for example whose half‐life is eight days, the specific activity is
4 PARTICLE RADIATION
Radiation can be considered to be energy carried by one of several different kinds of subatomic particles. When these particles interact with living tissue they transfer their energy to the tissue. The energy that is absorbed by the tissue is dissipated in the disruption of atoms and molecules, thus leading to the biological effects associated with ionizing radiation. The particles of radiation are discussed below.
4.1 Alpha Particles
An alpha particle is a highly energetic nucleus of an ordinary helium atom, which consists of an assembly of two positively charged protons and two electrically neutral neutrons, and is designated by the symbol
Two important properties of alpha radiation are the high rate of energy transfer to the medium through which the alpha particles travel and, consequently, a very small penetration range into an absorbing medium. Although most alpha particles from radioisotopes have kinetic energies in the range of 3–7 MeV, they can penetrate only a few centimeters of air before exhausting all their kinetic energy. Tissue and other solid materials are almost opaque to alpha particles. A 5.3‐MeV alpha particle from 210Po, for example whose range in air is about 4 cm, can penetrate only about 0.005 cm of soft tissue. This thickness is less than that of the dead outer layer of skin. For this reason, alpha radiation originating from alpha‐emitting radioisotopes outside the body is not considered hazardous. However, alpha radiation from an internally deposited radioisotope transfers its kinetic energy directly to viable tissue. The high concentration of absorbed energy, together with the microscopic distribution of the absorbed energy, makes internally absorbed alpha radiation more toxic per unit amount of absorbed energy than energy absorbed from the other radiations.
4.2 Beta Particles
Beta particles are ordinary electrons that are ejected with a high kinetic energy from the nucleus of certain radioisotopes, resulting from the change of a neutron into a proton and the ejected beta particle. Emission of a beta particle results in the transformation of the beta emitter into another element whose atomic number is one greater than that of the parent, and whose atomic mass number remains unchanged. In the case of strontium‐90 (90Sr), for example a pure beta emitter, the daughter element is yttrium‐90 (90Y), the next higher element after Sr in the periodic table. In this case, the reaction does not stop with the production of 90Y.