At some instant, a radioactive sample S1 having an activity 5 μ Ci has twice the number of nuclei as another sample S2 which has an activity of 10 μ Ci. The half lives of S1 and S2 are: (a) 20 years and 5 years, respectively (b) 20 years and 10years, respectively (c) 5 years and 20 years, respectively (d) 10 years and 20 years, respectively

Answer: (a). A = λ N: 5 = λ₁ (2N) and 10 = λ₂ N (in μ Ci). λ₂ = 4λ₁, so T₁ = 4T₂. Only 20 years and 5 years fits. So the answer is (a).

At some instant, a radioactive sample S1 having an activity 5 μ Ci… | JEE Main 2018 (16 Apr, Shift 1)

Q86JEE Main 2018 · 16 APR · SHIFT 1Medium

Law of Radioactive Decay

At some instant, a radioactive sample S1 having an activity 5 $\mu$ Ci has twice the number of nuclei as another sample S2 which has an activity of 10 $\mu$ Ci. The half lives of S1 and S2 are:

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Answer: (a)

$A = \lambda N$ : $5 = \lambda_1 (2N)$ and $10 = \lambda_2 N$ (in $\mu$ Ci).
$\lambda_2 = 4\lambda_1$ , so $T_1 = 4T_2$ .
Only 20 years and 5 years fits.
So the answer is (a).

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