In a nuclear reaction, the period of time required for one-half of the remaining atoms to disintegrate. Let be the decay constant so that
where N is the number of atoms left at time t and is the initial number of atoms. Setting N equal to half the original number of atoms,
Rearranging gives
therefore, the half-life is given by
More generally, in a process growing or shrinking exponentially, the half-life is time required for a factor of two change in population size.
Branching Ratio, Decay Constant, Nuclear Decay
