Physics - Modern Physics Question with Solution | TestHub

From Bohr's quantization condition, $mvr=n\frac{h}{2\pi }$. Also, the centripetal force is provided by the electrostatic force: $\frac{m{v}^2}{r}=\frac{1}{4\pi {ϵ}_0}\frac{e^2}{r^2}$.

Solving these equations for $v$ and $r$, we find $v\propto \frac{1}{n}$ and $r\propto n^2$. The reason provides the fundamental quantization of angular momentum that leads to this inverse proportionality of speed with $n$.