# I Nuclear decay

1. Mar 18, 2017

### Trollfaz

Given that an unstable particle has a constant probability of decaying per unit time, why is it said that its chance of surviving falls exponentially?

2. Mar 18, 2017

### BvU

It's like froth on beer: the more there is, the more there decays.
Or (in the other direction) like money accumulating on a bank: the more there is, the more interest (in absolute sense) you get, which gains interest again, etc.

Probability $p$ is given, number of decays is proportional to number of particles $N$, so $${dN\over dt} = - p N$$.

At an "I" level you can solve this kind of differential equation

3. Mar 18, 2017

### Staff: Mentor

It has a constant probability to decay per unit time if it still lives. This survival probability goes down over time, therefore the probability to see a decay after time x goes down with increasing x. If you solve the differential equation, you see that it goes down exponentially.