Half life

A constant chance

Nuclear sources of ionising radiation emit the radiation with a constant chance. But once it has been emitted, that’s it, so there are fewer nuclei left that can emit. This might remind you of the constant chance of a photon being absorbed by slices of an absorber: but now add slices of time.

A constant fraction

In each interval, a constant fraction decay. There is no way of altering this fraction, therefore for nuclear sources to become safer you just have to wait.