Q. A radioactive sample S1 having an activity of $5\mu Ci$ 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
Explanation
(a) Given that $\lambda_{1}N_{1} = 5\mu Ci;\ \lambda_{2}N_{2} = 10\mu Ci;\ \lambda_{2}N_{2} = 2\lambda_{1}N_{1}$
Also $N_{1} = 2N_{2};$ Then $\lambda_{2}N_{2} = 2\lambda_{1}\left( 2N_{2} \right) \Rightarrow \lambda_{2} = 4\lambda_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.