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,
An important characteristic property of a radioactive isotope
is its half-life, t1/2,
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
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.