**Decay constants and half lives**

Most nuclear decays occur independently
(unlike those that occur in a chain reaction) where a given fraction of nuclei decay in a
given time, independent of the number of nuclei. In a time **D t** the number

The number that have not decayed at time * t*
is

where ** N_{0}**
is the number of undecayed nuclei at

A **half-life** is the time it
takes for half of the nuclei to disappear. At that point * N(t)* is
one half of

Taking the logarithm of both sides of the above
equation, gives the half life * t_{1/2}* in terms of the
exponential time

Working problems with exponential decays are good practice for many other fields. Exponential growth and decay are common concepts in biology, economics, and other sciences.