Physics - Modern Physics Question with Solution | TestHub

Let${\lambda }_A=\lambda \therefore {\lambda }_B=2\lambda$

If$N_0$is total number of atoms in$A$and$B$at$t=0$, then initial rate of disintegration of$A=\lambda N_0$, and initial rate of disintegration of$B=2\lambda N_0$

As${\lambda }_B=2{\lambda }_A$

$\therefore T_B=\frac{1}{2}{T}_A$

$ie,$half-life of$B$is half the half-life of$A$.

After one half-life of$A$

${\left(-\frac{dN}{dt}\right)}_A=\frac{\lambda N_0}{2}$

Equivalently, after two half lives of$B$

${\left(-\frac{dN}{dt}\right)}_B=\frac{2\lambda N_0}{4}=\frac{\lambda N_0}{2}$

Clearly,${\left(-\frac{dN}{dt}\right)}_A=-{\left(\frac{dN}{dt}\right)}_B$

after$n=1 \mathrm{i.}\mathrm{e.},$one half-life of$A$