What is a half-life in the context of radioactivity?

A half-life is defined as the time taken for half of the radioactive atoms in a sample to undergo decay. This concept is fundamental in understanding the behavior of radioactive materials and how they diminish over time.

Radioactive decay is a random process at the level of individual atoms; however, the half-life provides a statistical measure that allows scientists to predict how long it will take for a certain proportion of a radioactive sample to decay. For instance, if you start with 100 radioactive atoms, after one half-life, you would have approximately 50 atoms remaining. After two half-lives, about 25 would remain, and so forth, following an exponential decay pattern.

In contrast, the other options do not accurately represent the concept of half-life. For example, the time required for an atom to split is more related to nuclear fission processes rather than decay over time. The notion of the duration taken for all radioactive atoms to decay is misleading because, theoretically, some atoms may never decay, or it may take an impractically long time for this to happen. Lastly, while the stability of an atom can relate to the decay process, it is not quantitatively defined by the term "half-life." Thus, the chosen answer embodies the precise definition