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