Physics - Modern Physics Question with Solution | TestHub

Let${\mathrm{\lambda }}_{\mathrm{A}}=\mathrm{\lambda }$and${\mathrm{\lambda }}_{\mathrm{B}}=2\mathrm{\lambda }$

Initially rate of disintegration of$\mathrm{A}$is$\mathrm{\lambda }{\mathrm{N}}_0$and that of$\mathrm{B}$is$2\mathrm{\lambda }{\mathrm{N}}_0$.

After one half-life of$\mathrm{A}$, rate of disintegration of$\mathrm{A}$will becomes$\frac{\mathrm{\lambda }{\mathrm{N}}_0}{2}$

and that of$\mathrm{B}$would also be$\frac{\lambda N_0}{2}$(half-life) of$\mathrm{B}=\frac{1}{2}$(half-life of$\mathrm{A}$)

So, after one half-life of$\mathrm{A}$or two half-lives of$\mathrm{B}$.

${\left(-\frac{\mathrm{d}\mathrm{N}}{\mathrm{d}\mathrm{t}}\right)}_{\mathrm{A}}$

$={\left(-\frac{\mathrm{d}\mathrm{N}}{\mathrm{d}\mathrm{t}}\right)}_{\mathrm{B}}$

$\therefore \mathrm{n}=1$