Question

A sample of radioactive material $A$, that has an activity of $10 \; mCi (1 \; Ci = 3.7 \times 10^{10}$ 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 :

• A. 20 days and 5 days
• B. 20 days and 10 days
• C. 5 days and 10 days
• D. 10 days and 40 days

Answer 1

Answer: (A)

20 days and 5 days

Answer 2

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