Answer: Daughter activity equals parent activity (after many daughter half-lives).
- A The decay constants of parent and daughter are exactly equal
- B Daughter activity equals parent activity (after many daughter half-lives)
- C The half-lives of the parent and daughter nuclei are exactly equal
- D The total measured activity of the sample falls to zero
Correct answer: B. Daughter activity equals parent activity (after many daughter half-lives)
Explanation: Secular equilibrium: when parent half-life much longer than daughter. Eventually daughter decays as fast as it is produced. A<sub>daughter</sub> = A<sub>parent</sub>.
Binding energy per nucleon rises sharply for light nuclei, peaks around iron-56 (the most stable nucleus), then slowly declines for heavier nuclei - which is exactly why fusing light nuclei or splitting heavy nuclei both release energy: each moves the products toward this stability peak.
Concept context
Radioactivity, nuclear reactions, fission, fusion, and binding energy.