# A sample of radioactive material A, that has an activity of 10 mCi, has twice the number of nuclei as another sample

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A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 × 1010 decays/s), has twice the number of nuclei as another sample of a different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively :

(1) 20 days and 5 days

(2) 20 days and 10 days

(3) 5 days and 10 days

(4) 10 days and 40 days

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Ans: (1) 20 days and 5 days

Sol: Activity A = $\lambda$N

For A     10 = (2N0)$\lambda$A

For B     20 = N0$\lambda$B

$\therefore \lambda_B=4\lambda_A\implies(T_{1/2})_A =4(T_{1/2})_B$