Physics - Modern Physics Question with Solution | TestHub

The rate of disintegration is given by $R=R_0{e}^{-\lambda t}$.

Given $R_0=9000$ disintegrations per minute, $R=3000$ disintegrations per minute, and $t=2$ minutes.

Substituting the values:

$3000=9000e^{-2\lambda }$

$e^{-2\lambda }=\frac{3000}{9000}=\frac{1}{3}$

$e^{2\lambda }=3$

Taking natural logarithm on both sides:

$2\lambda ={\log }_{e}3$

$\lambda =0.5{\log }_{e}3$

Answer: $0.5{\log }_e{}^3$