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

The activity of a radioactive source refers to the rate at which decay events occur, often measured in decays per second. Half-life is defined as the time required for half of the radioactive nuclei in a sample to decay. Therefore, over each successive half-life, the amount of the radioactive substance decreases to half of its previous value.

When considering activity, as the number of radioactive nuclei declines, the activity decreases correspondingly. After one half-life, the activity drops to half of its original value. This trend continues through each subsequent half-life; after two half-lives, the activity will have decreased to one-quarter of the original amount, and after three half-lives, it will reduce to one-eighth, and so on.

This characteristic of halving the activity with each half-life clearly demonstrates that the activity does not remain constant or increase. It also does not simply decrease to zero immediately, but rather approaches zero over time as the substance continues to decay. Thus, the correct understanding of the behavior of activity in the context of half-life is that it decreases by half with each passing half-life.