Q. The half-life of Radioactive substance is 20 min. The approximate time interval($t_{2} - t_{1}$) between the time $t_{2}$ when $\frac{2}{3}$ of it has decayed and time $t_{1}$ when $\frac{1}{3}$ of it had decayed is
A) 14 min
B) 20 min
C) 28 min
D) 7 min
Explanation
(b) $\ \ \ \ \ \ \ \ \ \ \ \ N_{1} = N_{0}\ - \ \frac{1}{3}N_{0}\ = \frac{2}{3}N_{0}$
$\ \ \ \ \ \ \ \ \ \ \ {\ N}_{2} = N_{0}\ - \ \frac{2}{3}N_{0}\ = \frac{1}{3}N_{0}$
$\therefore\ \ \ \ \ \ \ \ \frac{N_{1}}{N_{2}}\ = \ \left( \frac{1}{2} \right)^{n}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ n = 1$
$\therefore\ \ \ \ t_{2} - \ t_{1}\ \ = \ one\ half\ –life\ = \ 20\ \min$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.