A more commonly used parameter is the half-life . Given a sample of a particular radionuclide, the half-life is the time taken for half the radionuclide's atoms to decay. For the case of one-decay nuclear reactions:
the half-life is related to the decay constant as follows: set  and  =  to obtain
This relationship between the half-life and the decay constant shows that highly radioactive substances are quickly spent, while those that radiate weakly endure longer. Half-lives of known radionuclides vary by almost 54 orders of magnitude, from more than  years ( sec) for the very nearly stable nuclide Te, to  seconds for the highly unstable nuclide H.
The factor of  in the above relations results from the fact that the concept of "half-life" is merely a way of selecting a different base other than the natural base  for the lifetime expression. The time constant  is the -life, the time until only 1/e remains, about 36.8%, rather than the 50% in the half-life of a radionuclide. Thus,  is longer than . The following equation can be shown to be valid:
Since radioactive decay is exponential with a constant probability, each process could as easily be described with a different constant time period that (for example) gave its "(1/3)-life" (how long until only 1/3 is left) or "(1/10)-life" (a time period until only 10% is left), and so on. Thus, the choice of  and  for marker-times, are only for convenience, and from convention. They reflect a fundamental principle only in so much as they show that the same proportion of a given radioactive substance will decay, during any time-period that one chooses.
Mathematically, the  life for the above situation would be found in the same way as aboveby setting ,  and substituting into the decay solution to obtain