half-life

The half-life of a radioactive material is the time it takes for half of its nuclei to decay away. Everyday image: imagine a pile of popcorn kernels in which half pop every minute, no matter how many you start with; after one minute half remain, after two minutes a quarter, after three an eighth, and so on. The question it answers: since we can never predict when one particular nucleus decays, how can we still put a reliable clock on a whole sample?

Precisely, after each half-life the amount of the original substance left is halved. Starting with N_0 nuclei, after a time t the number remaining is N = N_0 times (1/2)^(t / T), where T is the half-life. This is exponential decay: not a fixed amount lost each period, but a fixed fraction, so the material never quite reaches zero, it just keeps halving. Half-lives span an astonishing range, from tiny fractions of a second to billions of years, and each isotope has its own fixed value that no chemistry or temperature can alter.

Why it matters: half-life is what makes radiometric dating possible, comparing how much of a parent isotope is left tells you how long ago a rock formed or a tree died. It also sets how long nuclear waste stays dangerous and how a medical tracer must be timed. Honest caveat: half-life is a statistical statement about huge numbers of nuclei; for any single atom, the half-life is only the time at which it has a 50 percent chance of having decayed, and it might in fact decay in the next second or last for ages.