Q. The half-life of $\ ^{215}$At is 100 $\mu s$. The time taken for the radioactivity of a sample of $\ ^{215}$At to decay to $\frac{1}{16}$ th of its initial value is
A) $400\ \mu s$
B) $6.3\ \mu s$
C) $40\ \mu s$
D) $300\ \mu s$
Explanation
(a) If $R$ is activity of radioactive substance after $n$ half lives,
then $R = R_{0}\left( \frac{1}{2} \right)^{n}$
$\frac{R_{0}}{16} = R_{0}\left( \frac{1}{2} \right)^{n}\therefore n = 4$
$t = n\ T = 4 \times 100 = 400\ \mu s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.