Q. A sample of radioactive material A, that has an activity of $10 \; mCi(l \; Ci = 3.7 \times 10^{10}$ decays/s), has twice the number of nuclei as another sample of a different radioactive maternal B which has an activity of 20 mCi. The correct choices for hall-lives of A and B would then be respectively :

Solution:

Activity $A = \lambda N$
For A $\hspace10mm 10 = (2N_0) \lambda_A$
For B $\hspace10mm 20 = N_0 \lambda_B$
$\therefore \; \lambda_B = 4 \lambda_A \; \Rightarrow \; (T_{1/2})_A = 4 (T_{1/2})_B$

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