Question

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 $S2$ can be

• A. 20 years and 5 years, respectively
• B. 20 years and 10 years, respectively
• C. 10 years each
• D. 5 years each

Answer 1

The correct option is A 20 years and 5 years, respectively

Radioactive decay equation $\frac{dN}{dt}=R=\frac{\ln \left(2\right)}{T}N$

Given : $N_{S1}=2N_{S2}$ $R_{S1}=5\mu Ci$ $R_{S2}=10\mu Ci$

$\therefore$ $\frac{R_{S1}}{R_{S2}}=\frac{N_{S1}{T}_{S2}}{N_{S2}{T}_{S1}}$

OR $\frac{5}{10}=\frac{2\times T_{S2}}{T_{S1}}$ $⟹T_{S1}=4T_{S2}$

$⟹$ $T_{S1}=20$ years and $T_{S2}=5$ years is the possible answer.