Half of the time required for the nucleus of a radioactive element to decay is called the half-life. As the radiation continues, the intensity drops exponentially, and the time it takes to reach half its original value is called the half-life of the isotope. The rule of nuclear decay is :N= NO *(1/2)^(T /T), where: NO refers to the number of nuclei at the initial time (T =0), T is the decay time, T is the half-life, and N is the number of nuclei left after decay. The half-lives of radioactive elements vary widely from much less than a second to tens of billions of years.