Radioactive decay is a random process. You cannot predict when an individual nucleus will decay but with large numbers of nuclei you can use a statistical approach.

Activity

The activity of a sample is the average number of  disintegrations per second its unit is the becquerel (Bq).

One becquerel is one decay per second. DN = change in number of undecayed nuclei
Dt = change in time in seconds

Decay constant l

The decay constant l  is the probability that a nucleus will decay per second so its unit is s-1.

activity = decay constant   x    the number of undecayed nuclei  A = activity in becquerel (Bq)
N = the number of undecayed nuclei
l = decay constant (s-1) N0 = number of undecayed nuclei at t=0
t = time after t=0 in seconds
N = the number of undecayed nuclei at time t
l = decay constant (s-1)

Half life

The half life is the time for half the nuclei to decay.  Half lives can vary from seconds (e.g. radon-224 half life = 55 seconds) to millions of years (e.g. potassium-40 half life = 1.3 x 109 years). This has implications for radioactive waste from nuclear power stations which will need to be stored safely for a very long time.