If ' $T$ ' is the half life of a radioactive substancethen its instantaneous rate of change of activity is proportional to

Question

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Activity, } R=\frac{-d N}{d t}=\lambda N \ & \frac{d R}{d t}=\frac{d}{d t}(\lambda N)=\lambda \frac{d N}{d t}=\lambda(-\lambda N)=-\lambda^2 N \ & \lambda=\frac{\log _{\mathrm{e}} 2}{T_{1 / 2}} \ 	herefore \quad & \lambda^2 N=\frac{\left(\log _{\mathrm{e}}ight)^2 N}{\mathrm{~T}_{1 / 2}^2} \ 	herefore \quad & \frac{\mathrm{dR}}{\mathrm{dt}} \propto \frac{1}{\mathrm{~T}_{1 / 2}^2}\end{aligned}$

If ' $T$ ' is the half life of a radioactive substancethen its instantaneous rate of change of activity is…

Solution