Final answer:
OPTION 3.
The half-life of a radioactive substance is the time required for half of the radioactive nuclei in a sample to decay. It describes the rate at which a substance loses its radioactivity and varies widely among different isotopes.
Step-by-step explanation:
The half-life (often denoted t₁/₂) of a radioactive substance is the amount of time it takes for half of the initial amount of the radioactive nuclei to decay. This definition is related to the third option presented in the question: "the amount of time it takes for half of a radioactive substance to decay". Radioactive materials experience a decrease in their activity after each decay event, and this rate of decay is constant and unique to each radioactive isotope. Half-lives vary significantly across different elements and isotopes, from mere microseconds to billions of years. Radioactive decay follows a first-order process, which means that for any given sample of a radioactive isotope, the time required for half of the nuclei to decay remains constant throughout the decay process.