Definition of Radioactive Half-Life Steps:

• Recall that half-life describes the statistical decay rate in a large sample of radioactive nuclei.
• Understand it as the fixed time interval for the number of undecayed nuclei to reduce by half, regardless of initial amount.
• Eliminate options implying complete decay or single-nucleus behavior, as decay is probabilistic and exponential.
• Select the option matching the standard definition from nuclear physics.

Why B is correct:

• Half-life is defined as the time required for half of the unstable nuclei in a sample to decay, per the exponential decay law $N = N_0 (1/2)^{t/T}$, where $T$ is the half-life.

Why the others are wrong:

• A: No finite time exists for all nuclei to decay, as the process approaches zero asymptotically.
• C: Time for a single nucleus to decay is random and unpredictable, not a defined half-life.
• D: While similar, it vaguely refers to "nucleus number" without specifying unstable/radioactive ones, risking confusion with total atoms.

Final answer: B