Radioactivity and half-life

An unstable atomic nucleus can spontaneously break apart, emitting radiation in the process — spontaneously meaning there's no trigger, no warning, and famously no way to predict when any single specific nucleus will decay.

What can be predicted, precisely, is the behaviour of a large group of identical nuclei: half-life is the time it takes for half of a sample to decay, on average. It's tempting to think two half-lives means everything is gone, but each half-life only removes half of whatever remains — after two half-lives, a quarter of the original sample is left, not zero, and the decay tails off without ever quite reaching absolute zero.

Half-life is a fixed property of the isotope itself, not of how much of it you happen to have. A gram of a radioactive isotope and a milligram of the exact same isotope decay at the same fractional rate, halving over identical time intervals, even though the actual number of atoms decaying per second is very different between the two samples.