Question

The rate of disintegration of a radioactive substance falls from $800$ decay/min to $100$ decay/min in 6 hours. Then the half life of the radioactive substance in hours is:

Answer 1

$A=A_0{e}^{-\lambda t}$
$\Rightarrow 100=800e^{-\lambda (6\times 60)}$
(Taking time in minutes)
$\Rightarrow e^{-360\lambda }=1/8$
$\Rightarrow -360\lambda =ln\frac{1}{8}=-ln8\Rightarrow \lambda =\frac{ln{2}^3}{360}=\frac{ln2}{120}$
$\therefore T_{1/2}=\frac{ln2}{\lambda }=\frac{ln2}{\left(ln2/120\right)}=120\text{min}$
$\text{or}{T}_{1/2}=2\text{hrs}$