A radioactive sample has a half-life of 8.0 days. What fraction of the original radioactive nuclei remains undecayed after 32 days?
Answer and explanation
Correct answer: A. 1/16 (6.25 percent)
- Step 1: Number of elapsed half-lives: n = t / t_1/2 = 32 / 8.0 = 4 half-lives. Step 2. Remaining fraction: N / N0 = (1/2)^n = (1/2)^4 = 1/16 = 0.0625 = 6.25%. Answer: 1/16 (6.25 percent). Why not the others: 1/8 is after 3 half-lives (24 days); 1/4 is after 2 half-lives (16 days).
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