Environmental Engineering FOURTH EDITION

314 ENVIRONMENTAL ENGINEERING

accompanied by emission of additional energy in the form of gamma radiation. As a
result of these emissions, the radioactive atom is transformed into either an isotope of
the same element (neutron or gamma only emission) or into an isotope of a different
element (alpha or beta emission). This transformation is known as radioactive decay,
and the emissions are known as ionizing radiation. The rate of radioactive decay, or
rate of decrease of the number of radioactive nuclei, can be expressed by a first-order
rate equation

(16.1)

where

N = the number of radioactive nuclei and

Kb = a factor called the disintegration constant; Kb has the units of time-l.

Integrating over time, we get the classical equation for radioactive decay:

N = Noe-Kb'. (16.2)

The data points in Fig. 16-1 correspond to this equation.

After a specific time period t = t1/2, the value of N is equal to one-half of No, and

after each succeeding period of time t1p the value of N is one-half of the preceding N.

ti12 *tin 3t112 4t112 5tin

Time (t) increasing

Key:

tin=one half-life

2ti12=two half-lives, etc.

Figure 16-1. General description of radioactive decay.