Question

Activity of a radioactive element decreased to one third of original activity $I_0$ in $9years$. After further $9years$, its activity will be

• A. $I_0$
• B. $\frac{2}{3}{I}_0$
• C. $\frac{I_0}{9}$
• D. $\frac{I_0}{6}$

Answer 1

The correct option is C $\frac{I_0}{9}$

Activity $\frac{dN}{dt}=\lambda N_o{e}^{-\lambda t}$
$I\left(t\right)=I_o{e}^{-\lambda t}$

After $9$ years:
$\frac{1}{3}=e^{-9\lambda }$


After further $9$ years
$t=18years$
$I\left(18\right)=I_o{e}^{-18\lambda }$
$I\left(18\right)I_o=(e^{-9\lambda }{)}^2=(1/3{)}^2$
$I\left(18\right)=\frac{I_o}{9}$​​