Physics - Modern Physics Question with Solution | TestHub

As rate of disintegration is proportional to the number of atoms actually present, therefore,

${\text{N}}_0=\text{5000, N}=1250,\; t=\text{5 min}$

As$\text{ N}={\text{N}}_0{\text{e}}^{-\lambda \text{t}}$

$\therefore \text{ln}\frac{N}{N_0}=-\lambda t\text{ ; }\text{ln}\left(\frac{1250}{5000}\right)=-\lambda t\text{ ; }\text{ln}\left(\frac{1}{4}\right)=-\lambda \times 5;-2\text{ln}2=-\lambda \times 5\text{ ; }\lambda =0\text{.}4\text{ln}2$