The half-life of a radioactive substance is essentially a measure of the time it takes for a sample to decay to half its original value, whether that be in terms of count rate or number of nuclei. The natural question to ask after this is: “Why measure the half-life, instead of something more instantaneous?”
To answer that, we must first acknowledge the random nature of radioactivity. By “random”, we mean unpredictable - simply put, you can never predict when a particular nucleus is going to decay at a given moment in time. For that reason, it becomes futile to even try to calculate something like instantaneous activity.
So then what’s a better approach? Well, we can take advantage of the fact that the decay process over a period of time has an exponential decaying trend. With that, finding half-life becomes really easy, and far more useful!
