How is the half-life of a radioactive substance determined?

The half-life of a radioactive substance is defined as the time required for half of the radioactive sample to decay into its daughter isotopes or stable products. This measurement is crucial because it provides a predictable and consistent way to understand the behavior of radioactive materials over time. When half of the original amount of a radioactive substance has decayed, the remaining quantity can be mathematically modeled to determine future decay rates, which is especially important in fields such as nuclear physics, radiometric dating, and medical applications.

Timing how long it takes for all the sample to decay would not yield useful information for the half-life, as it ignores the specific half-life behavior of the substance. Measuring the rate of decay to a stable isotope does not directly assess the half-life, as it focuses on the end result rather than the specific time taken for half the sample to decay. Observing changes in physical properties over time may provide some indirect information about decay but does not directly relate to the precise definition or calculation of half-life. Thus, focusing on the time it takes for half of a radioactive sample to decay is the most accurate method for determining its half-life.