Question

Activity of radioactive element decreased to one-third of original activity $R_{o}$ in $9\, yr$. After further $9\, yr$, its activity will be

• A. $R_{o}$
• B. $\frac{2}{3}R_{o}$
• C. $\frac{R_{o}}{9}$
• D. $\frac{R_{o}}{6}$

Answer 1

Answer: (C)

$\frac{R_{o}}{9}$

Answer 2

Activity $R+R_{0} e^{-\lambda t} \frac{R_{0}}{3}=R_{0} e^{-9 \lambda}$
$\Rightarrow e^{-9 \lambda}=\frac{1}{3}$ ... (i)
After further $9\, y r R=Re^{-\lambda t}=\frac{R_{0}}{3} e^{-9 \lambda}$ ... (ii)
From Eqs. (i) and (ii),
$R=\frac{R_{0}}{9}$