Q. A radioactive sample $S_{1}$ having an activity of 5$\mu Ci$ has twice the number of nuclei as another sample $S_{2}$ which has an activity of 10$\ \mu Ci$. The half lives of $S_{1}$ and $S_{2}$ can be
A) 20 yr and 5 yr ,respectively
B) 20 yr and 10 yr ,respectively
C) 10 yr each
D) 5 yr each
Explanation
(a) Activity of $S_{1}\ = \frac{1}{2}\ (activity\ of\ S_{2})$
Or $\ \ \ \ \ \ \ \ \lambda_{1}N_{1} = \frac{1}{2}(\lambda_{2}N_{2}$)
Or $\frac{\lambda_{1}}{\lambda_{2}} = \frac{N_{2}}{{2N}_{1}}$
Or $\ \ \ \ \ \ \ \ \frac{T_{1}}{T_{2}} = \frac{{2N}_{1}}{N_{2}}$
Given $\ \ \ \ \ \ \ N_{1} = 2N_{2}$
$\therefore\ \ \ \ \ \ \ \ \ \frac{T_{1}}{T_{2}} = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.