Q. At a given instant there are 25% undecayed radioactive nuclei. After $10\ s$ the number of undecayed nuclei reduces to 6.25%, the mean life of the nuclei is
A) $14.43\ s$
B) $7.21\ s$
C) $5\ s$
D) $10\ s$
Explanation
(b) In $10\ s$, number of nuclei has been reduced to one fourth (25% to 6.25%)
Therefore it’s half life is $T_{1/2} = 5\ s$
$\therefore$ Mean life $T = \frac{T_{1/2}}{0.693} = \frac{5}{0.693} = 7.21\ s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.