In the context of half-life, what happens to the activity of a radioactive source over successive half-lives?

In the context of half-life, the activity of a radioactive source decreases by half with each successive half-life. This concept is grounded in the definition of half-life, which is the time required for half of the radioactive nuclei in a sample to decay. Given that activity is proportional to the number of undecayed nuclei (i.e., the rate of decay), as the number of undecayed nuclei decreases over successive half-lives, the activity correspondingly decreases as well.

For instance, if you start with a certain level of activity at time zero, after one half-life, the activity will be reduced to half of its original value. Following the next half-life, the activity will again be halved, resulting in a quarter of the original activity. This pattern continues with each half-life, resulting in a consistent and predictable decrease, illustrating the fundamental principle that the decay process is exponential in nature.

Understanding this pattern is crucial for anyone studying radioactive decay, as it helps predict the behavior of radioactive materials over time, including their safety and handling considerations.