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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
\epsfysize=4 cm

It is convenient to introduce the half-life, T1/2, 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

N = N_0
\displaystyle{ \left(\frac{1}{2}\right) }^{t/T_{1/2}}.

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.