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

**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, *A*_{0}, or the number of radioactive atoms
originally present in the sample,
*N*_{0}.

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 ^{90}_{30}Sr 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 ^{90}_{30}Sr
is 28.1 years makes it clear that the concentration of ^{90}_{30}Sr
in a sample remains essentially constant
over a short period of time.

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Modern Analytical Chemistry: Kinetic Methods of Analysis : Radiochemical Methods of Analysis: Theory and Practice |

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