Physics - Modern Physics Question with Solution | TestHub

The radius of the $n^{\text{th}}$ orbit in Bohr's model is given by $r=\frac{{ϵ}_0{n}^2{h}^2}{\pi m{e}^2}$.

The velocity of the electron in the $n^{\text{th}}$ orbit is given by $v=\frac{e^2}{2{ϵ}_{0}nh}$.

The orbital period $T$ is the time taken to complete one revolution, which is $T=\frac{2\pi r}{v}$.

Substituting the values of $r$ and $v$:

$T=\frac{2\pi \left(\frac{{ϵ}_0{n}^2{h}^2}{\pi m{e}^2}\right)}{\frac{e^2}{2{ϵ}_{0}nh}}$

$T=\frac{2{ϵ}_0{n}^2{h}^2}{m{e}^2}\times \frac{2{ϵ}_{0}nh}{e^2}$

$T=\frac{4{ϵ}_0^2{n}^3{h}^3}{m{e}^4}$

Answer: $\frac{4{ϵ}_0^2{n}^3{h}^3}{m{e}^4}$