All radioactive nuclei decay with an exponential rate. The formula for the number of nuclei remaining is N(t) = N0 e-t/tau where N0 is the number at t = 0 and tau is the 'lifetime' of the nucleus. If you set N(t1/2) / N0 = 1/2 and solve for t1/2 you find t1/2 = ln(2) ~ 0.693 tau.
We can give a simple example. Tritium, the radioactive form of hydrogen, has a half-life of 12.3 years. If you have a tritium supply, in 12.3 years half of it will be gone. After another 12.3 years half of the remainder will be gone, so you'll only be left with a quarter of the starting amount. etc. Mike W.