Radiochemical Methods of Analysis: Theory and Practice

Theory and Practice

The rate of decay, or activity, for a radioactive isotope follows first-order kinetics

where A is the activity, N is the number of radioactive atoms present in the sample at time t, and λ is the radioisotope’s decay constant. Activity is given in units of dis- integrations per unit time, which is equivalent to the number of atoms undergoing radioactive decay per unit time.

As with any first-order process, equation 13.24 can be expressed in an inte- grated form.

Substituting equation 13.25 into equation 13.24 gives

By measuring the activity at time t, therefore, we can determine the initial activity, A₀, or the number of radioactive atoms originally present in the sample, N₀.

An important characteristic property of a radioactive isotope is its half-life, t_1/2, which is the amount of time required for half of the radioactive atoms to disinte- grate. For first-order kinetics the half-life is independent of concentration and is given as

Since the half-life is independent of the number of radioactive atoms, it remains constant throughout the decay process. Thus, 50% of the radioactive atoms disinte- grate in one half-life, 75% in two half-lives, and 87.5% in three half-lives.

Kinetic information about radioactive isotopes is usually given in terms of the half-life because it provides a more intuitive sense of the isotope’s stability. Know- ing, for example, that the decay constant for ⁹⁰₃₀Sr is 0.0247 yr–1 does not give an im- mediate sense of how fast it disintegrates. On the other hand, knowing that the half- life for ⁹⁰₃₀Sr is 28.1 years makes it clear that the concentration of  ⁹⁰₃₀Sr in a sample remains essentially constant over a short period of time.