All courses › Physics 1 › Half-life

Half-life

The half-life is the time it takes before half of the radioactive nuclei in a sample have decayed. After one half-life half remain, after two a quarter remain, and so on. Each nucleus decays at random, but for many nuclei the fraction that remains is predictable. The half-life is a property of the nuclide, not of how large the sample is. It does not change if you heat the substance.

Try it yourself

Half-life

N = N_0\left(\frac{1}{2}\right)^{t/T_{1/2}}

nuclei left after time t

Symbols

$N_0$	nuclei at the start
$T_{1/2}$	half-life	s, min or years
$t$	time	same unit

Example

A substance has a half-life of 5 years, and there are 8000 nuclei at the start.

After 15 years, which is $15/5 = 3$ half-lives: $N = 8000 / 2^3 = 1000$ .

Divide the number of nuclei by two once per half-life. Do not divide by the number of years.

Practise atoms, radiation and the universe for free →

← Electrical energy · Energy of a photon →

Part of Physics 1: Atoms, radiation and the universe.