What is the definition of the half-life of a radioactive isotope?

The definition of the half-life of a radioactive isotope is the time it takes for one half of the sample to decay. This concept is fundamental in understanding radioactive decay, where an unstable atomic nucleus loses energy by radiation. During each half-life, half of the remaining radioactive atoms in a sample will decay into a more stable form or a different element, depending on the specific isotope in question.

For example, if you start with a certain amount of a radioactive isotope, after one half-life, only half of the original amount will remain; after two half-lives, only a quarter will remain, and so on. This characteristic behavior allows scientists to determine the age of materials (radiocarbon dating) and is crucial for applications in fields like medicine, archaeology, and nuclear physics.

The other options do not accurately describe half-life. The total decay of the entire sample does not occur within a half-life, and the concept of doubling relates to growth processes, not decay. Meanwhile, stability does not pertain directly to the half-life, as many isotopes do not become stable after one half-life. They may continue to decay over multiple half-lives before reaching a stable state.