# Does radioactivity ever reach zero?

## The mathematics only works with large numbers of nuclei

Radioactive decay is a random process operating at the scale of individual nuclei.

If we have a large number of nuclei then we can fit the decay to a smooth curve called an ‘exponential’. A real exponential curve never quite reaches zero so if radioactivity were perfectly exponential then there would always be some present.

However when only small numbers of nuclei are left then the nice smooth exponential relationship breaks down. Eventually every nucleus will decay and the radioactivity will drop to precisely zero.

In this lesson we use the notion of how long an isotope is radioactive for as a shorthand for ‘long enough to be too low to worry about’.