What is the definition of half-life in radioactive decay?

• A. The time required for a radionuclide’s activity to decrease to one-half of its initial value due to radioactive decay.
• B. The time required for the radionuclide to emit half of its energy.
• C. The time it takes for the radiation intensity to reach half of its initial level at the source.
• D. The time for half of the radioactive atoms to transform into a stable form.

Answer: (A)

Half-life is the time it takes for the activity of a radionuclide to fall to half of its initial value due to radioactive decay. Activity, the rate of decays per second, is proportional to how many undecayed nuclei are present, so as those nuclei decay, the activity decreases exponentially. After one half-life, the activity is halved; after two half-lives, it’s a quarter of the original, and so on. The relationship between half-life and the decay constant λ is T1/2 = ln(2)/λ, showing that each nuclide has its own characteristic time scale for decay.

This definition focuses on how quickly the source is emitting decays, not on how much energy is released per decay, which is constant per event and does not determine the half-life. It also avoids tying the concept to measured intensity at a distance, since intensity depends on geometry in addition to activity. Finally, it isn’t about half of the atoms becoming stable, because many decay chains involve daughter nuclides that may themselves be radioactive. The half-life is specifically the intrinsic time needed for the parent’s activity to reduce to half.