Physics - Modern Physics Question with Solution | TestHub

The angular momentum of an electron in the $n^{\text{th}}$ orbit of a hydrogen atom is given by Bohr's quantization condition:

$L=\frac{nh}{2\pi }$

Thus, $L\propto n$.

The velocity of an electron in the $n^{\text{th}}$ orbit of a hydrogen atom is given by:

$v=\frac{e^2}{2{ϵ}_{0}nh}$

Thus, $v\propto \frac{1}{n}$.

The ratio of angular momentum to velocity is:

$\frac{L}{v}\propto \frac{n}{1/n}=n^2$

Answer: ${\mathrm{n}}^2$