What is the half-life in radioactive decay?

• A. The time required for half of the parent isotopes to decay into daughter isotopes.
• B. The time it takes for the rock to cool halfway.
• C. The time needed for all daughter isotopes to become parent isotopes.
• D. The time it takes for the sample to reach equilibrium with surroundings.

Answer: (A)

Half-life is the time required for half of the original parent nuclei to decay into daughter nuclei. It’s a fixed property of a given radioactive isotope and doesn’t depend on how much material you have, its temperature, or its surrounding conditions. If you start with N0 parent atoms, after one half-life you have N0/2 left; after two half-lives you have N0/4, and so on. The decay follows an exponential pattern, often written as N(t) = N0 (1/2)^(t/t1/2) or N(t) = N0 e^{-kt} with k = ln 2 / t1/2. This concept is central to radiometric dating because measuring the current amounts of parent and daughter allows you to estimate how long the decay has been occurring, given a known half-life. The other ideas don’t fit: cooling timing is not related to radioactive decay; not all daughter isotopes turn back into the parent; and reaching equilibrium with surroundings isn’t about the timescale of decay.