Half life

The half-life of a radioactive substance is a measure of how quickly radioactive decay takes place. Suppose at some initial time we start with N₀ radioactive nuclei, and then measure the number N at a later time t. One finds N behaves as in the following graph.

 

Figure 13.1: Nuclear decay in time

It is convenient to introduce the half-life, T_1/2, of a substance, defined as the time after which exactly one half of a the originally active nuclei remain. In terms of this, the number of nuclei N remaining at time t, given N₀ at time t = 0, is given by

Thus, after a period of one half-life, ${\frac{1}{2}}$ of a substance remains, after another half life ${\frac{1}{2}}$ x ${\frac{1}{2}}$ = ${\frac{1}{4}}$ of a substance remains, and so on. Half-lives of substances range from tiny fractions of a second to millions of years.