How is the half-life of a radioactive isotope defined?

The half-life of a radioactive isotope is defined as the time required for the initial number of radioactive atoms in a sample to decrease by half. This concept is fundamental in nuclear physics and radiochemistry, as it provides a measure of the rate at which a radioactive substance decays. The half-life can vary significantly between different isotopes, ranging from fractions of a second to thousands or millions of years.

Understanding the half-life is crucial for applications in medicine, archaeology (carbon dating), and nuclear power, as it helps predict the behavior of radioactive materials over time. The other options do not accurately describe the half-life; full decay (complete disintegration of the isotope) takes longer than just the half-life, radioactive emissions do not specifically define the half-life, and the interval between isotope formations is unrelated to the decay process itself.