Answer: lambda = ln 2 / T1/2.
- A lambda = T1/2 / ln 2
- B lambda = ln 2 / T1/2
- C lambda = T1/2 × ln 2
- D lambda = 1 / T1/2
Correct answer: B. lambda = ln 2 / T1/2
Explanation: N = N₀ e-lambda t. At t = T1/2: 1/2 = e^(-lambda T1/2). lambda × T1/2 = ln 2. lambda = ln 2 / T1/2 = 0.693/T1/2.
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.