A. Equations for Nuclear Reactions
Radioactivity is the decay or disintegration of the nucleus of an atom. During
the process, either alpha or beta particles may be emitted. Energy, in the form
of gamma rays, may also be released by this process, and a different atom is
formed. This new atom may be of a different element, or a different isotope
of the same element. All of these characteristics and more can be shown by using
an equation to describe the radioactive process.
Like a chemical equation, a nuclear equation must be balanced. First, the total mass of the products must equal the total mass of the reactants. Second, the total charge of the reactants (the sum of their atomic numbers) must equal the total charge of the products.
Consider the equation for the decay of radium-226 to radon-222, with the simultaneous loss of an alpha particle and energy in the form of a gamma ray. Radium-226 is the reactant; radon, an alpha particle, and a gamma ray are the products. The equation is:
In the notation for particles, the superscript shows the mass of the particle, and the subscript shows the charge. The charge on each of these particles is its atomic number. The equation is balanced with respect to mass because the sum of the masses of the reactants (226) equals the sum of the masses of the products (222 + 4 + 0). The equation is balanced with respect to charge because the sum of the atomic numbers of the reactants (88) equals the sum of the atomic numbers of the products (86 + 2 + 0). The energy change accompanying the reaction is shown by the release of gamma rays.
A similar equation can be written for nuclear decay by beta emission. Iodine-131 is a beta emitter commonly used in nuclear medicine. The equation for its decay is:
Note that both the charge and the mass are balanced and that iodine-131 emits both a gamma ray and a beta particle. For this reason, iodine-131 is known as a beta-gamma emitter. Carbon-14, the isotope widely used in radiodating of archaeological artifacts containing carbon, is also a beta emitter:
How can nuclei give off beta particles (high-energy electrons) if the nucleus has no electrons? The process is not yet clearly understood, but it may occur through the disintegration of a neutron to form a proton and the emitted electron:
The electron is ejected and the proton remains in the nucleus. In beta emission, the atomic number of the product nucleus is one greater than that of the reactant nucleus because the nucleus now contains one more proton. The mass of the product nucleus is approximately the same as that of the reactant nucleus because an electron's mass is negligible with respect to that of a proton.
Emission of a gamma ray changes neither the mass nor the charge of the nucleus. It accompanies the rearrangement of a nucleus from a less stable, more energetic nuclear configuration to a more stable, less energetic form. The identity and mass of the nucleus stay the same. The changes caused by the emission of the three types of radiation are summarized in Table 4.5.
Given the atomic number and mass number of a radioactive isotope and the type of radiation emitted during its decay, we can easily predict the mass number, atomic number, and identity of the new element formed.
| Radiation emitted | Change in Atomic number |
Change in Mass number |
|---|---|---|
| alpha particle |
|
|
| beta particle |
|
|
| gamma ray |
|
|
Iodine-131 has a half-life of 8.1 days. If you start today with a 25-mg sample of iodine-131, after 8.1 days that sample will contain only 12.5 mg iodine-131. At the end of 16.2 (2 X 8.1) days, the sample will contain only 6.25 mg iodine-131. Of course, the matter in the sample does not disappear; it changes to another element, the product of the radioactive decay of iodine-131. Figure 4.3 shows the amounts of iodine-131 remaining after the passage of several half-lives, given an initial sample containing 25 mg of the isotope.
| Isotope | Emissions | Half-life |
|---|---|---|
|
|
 |
12.3 years |
|
|
|
5730 years |
|
|
|
4.5 days |
|
|
 |
5.26 years |
|
|
|
2.7 days |
|
|
|
8.1 days |
|
|
|
45.1 days |
|
|
|
67.0 hours |
|
|
|
14.3 days |
|
|
|
15.0 hours |
| FIGURE 4.3 Rate of decay of iodine-131 as a function of time. |
Knowing the identity of a radioisotope, its half-life, and the type of radiation it emits, you can determine the identity of the product and calculate the amount formed in a given period of time.
