Define radioactive half-life.

Define radioactive half-life.

• A. The time for all nuclei to decay
• B. The time for half the radioactive nuclei to decay
• C. The time for a nucleus to decay completely
• D. The time for production of radioactive material

Answer: (B)

Half-life is the time it takes for half of the unstable nuclei in a sample to decay. For a given isotope, this interval is constant and doesn’t depend on how much material you have or on environmental conditions. After one half-life, about half remains undecayed; after two half-lives, about a quarter remains, and so on, following N = N0(1/2)^(t/T1/2). This definition is why the correct choice is best: it directly describes the time needed for half of the radioactive nuclei to decay, which is the essence of what half-life measures. The idea that all nuclei would decay in a finite time isn’t correct because decay is probabilistic and some nuclei can persist for very long times; it isn’t the time for a nucleus to decay completely, and it isn’t about the production of radioactive material.

Half-life is the time it takes for half of the unstable nuclei in a sample to decay. For a given isotope, this interval is constant and doesn’t depend on how much material you have or on environmental conditions. After one half-life, about half remains undecayed; after two half-lives, about a quarter remains, and so on, following N = N0(1/2)^(t/T1/2).

This definition is why the correct choice is best: it directly describes the time needed for half of the radioactive nuclei to decay, which is the essence of what half-life measures. The idea that all nuclei would decay in a finite time isn’t correct because decay is probabilistic and some nuclei can persist for very long times; it isn’t the time for a nucleus to decay completely, and it isn’t about the production of radioactive material.