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At some instant, a radioactive sample S1 having an activity 5 μCi has twice the number of nuclei as another sample S2 which has an activity 10 μCi. The half lives of S1 and S2 are - [JEE-Main On line-2018]
- 10 years and 20 years, respectively
- 5 years and 20 years, respectively
- 20 years and 10 years, respectively
- 20 years and 5 years, respectively
Correct answer: 20 years and 5 years, respectively
Solution
From A = lambda*N: lambda1 = A1/N1 = 5/(2N2) and lambda2 = A2/N2 = 10/N2, so lambda1/lambda2 = 1/4. Since T = ln2/lambda, T1/T2 = lambda2/lambda1 = 4, giving T1 = 20 years and T2 = 5 years.
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