The decay of radioactive materials is a random process. The probability that a nucleus decays in a unit of time (e.g. 1 s) is called decay constant.
Usually the decay constant is denoted by:
Its unit (in SI system): 1/s.

In the simulation on the right-hand side, 200 nuclei are decaying with the given probability.

The radioactive nuclei are represented by blue circles, the decay products are the red circles. For one particular nucleus we cannot predict when it will decay, but for a large number of nuclei we can make more or less precise predictions. The more nuclei we have, the better is the expected value approached by the number of the actual remaining nuclei. The expected number N(t) of the remaining nuclei can be calculated in function of time by the following mathematical expression: Here t is the time, N0 is the number of the radioactive nuclei at the beginning (t=0), and T is the half-life.

If you would like to see the simulation in full screen, please click here.