Q. The half-life of $Bi^{210}$ is 5 days. What time is taken by $(7/8)^{th}$ part of the sample to decay
A) 3.4 days
B) 10 days
C) 15 days
D) 64 days
Explanation
(c) By using $N = N_{0}\left( \frac{1}{2} \right)^{t/T};$ where $N = \left( 1 - \frac{7}{8} \right)N_{0} = \frac{1}{8}N_{0}$
So $\frac{1}{8}N_{0} = N_{0}\left( \frac{1}{2} \right)^{t/T} \Rightarrow \left( \frac{1}{2} \right)^{3} = \left( \frac{1}{2} \right)^{t/5} \Rightarrow t = 15\ days$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.