Physics - Modern Physics Question with Solution | TestHub

Let$N_A$and$N_B$be the number of molecules of A and B after time t.

Also, after time t,$\frac{N_B}{N_A}=0.3\left(given\right)$Also, let$N_0$be the total number of nucleus initial

After time t,$N_A+N_B=N_0$

$N_A+0.3N_A=N_0$

$\therefore N_A=\frac{N_0}{1.3}$

Also, rate of disintegration of A

$N_A=N_0{e}^{-\lambda t}$

$\Rightarrow \frac{N_0}{1.3}=N_0{e}^{-\lambda t};\frac{1}{1.3}=e^{-\lambda t}or\log \left(1.3\right)=\lambda t$

$t=\frac{\log \left(1.3\right)}{\lambda }\therefore t=\frac{T\log \left(1.3\right)}{\log \left(2\right)}=\frac{T\log \left(1.3\right)}{\log 2}$