What is a half-life in nuclear physics?

In nuclear physics, the concept of half-life refers to the time required for half of the radioactive nuclei in a given sample to undergo decay. This characteristic is crucial for understanding radioactive decay processes, as it provides a measure of the stability and longevity of a radioactive isotope. The half-life is a constant for each isotope and is independent of the quantity of material present; thus, no matter how much of the substance you start with, the time it takes for half of it to decay will always be the same.

The other definitions do not accurately capture the nature of half-life. For example, the time taken for all nuclei in a sample to decay would imply a definitive end point, which is not how half-lives operate; they continue indefinitely as long as there are parent nuclei present. A complete cycle of decay doesn't exist in this context, as decay isn't a cyclical process but rather a probabilistic one, where each nucleus has a certain likelihood of decaying at any moment. Lastly, the time interval between nuclear reactions does not specifically correspond to half-life and does not pertain to the decay of a single isotope, as reactions can be influenced by several factors other than straightforward radioactive decay.