Half-life measures decay rate statistically

Steps:

• Recall that radioactive decay is probabilistic, not deterministic for individual atoms.
• Define half-life as the time interval for half the original nuclei in a sample to decay.
• Eliminate options implying decay of single atoms or total sample, as decay is random.
• Confirm by noting half-life is constant for a given isotope, independent of sample size.

Why C is correct:

• It matches the standard definition: half-life $t_{1/2}$ is the time for the number of undecayed atoms $N$ to reduce to $N/2$, per the decay law $N = N_0 e^{-\lambda t}$.

Why the others are wrong:

• A: Incorrect, as no finite time decays all atoms completely due to exponential decay.
• B: Wrong, since individual atom decay time is unpredictable; half-life applies to populations.
• D: False, as half-life affects atom count, not nucleon number, which remains constant in alpha/beta decay.

Final answer: C