Q. The activity of a radioactive element decreases to one-third of the original activity $A_{0}$ in a period of 9 yr. After a further lapes of 9 yr, its activity will be
A) $A_{0}$
B) $\frac{2}{3}A_{0}$
C) $\frac{A_{0}}{9}$
D) $\frac{A_{0}}{6}$
Explanation
(c) $\ \ \ \ \ \ \ \ \ \ \ \ \frac{A_{0}}{3} = A_{0}\left( \frac{1}{2} \right)^{9/T_{1/2}}$
$\ \ \ \ \ \ \ \ \ \ \ A’\ = \ \frac{A_{0}}{3}\left( \frac{1}{2} \right)^{9/T_{1/2}}$
$\therefore\ \ \frac{A'}{A_{0}/3} = \frac{1}{3}$
or $\ \ A’\ = \ \frac{A_{0}}{9}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.