Physics - Modern Physics Question with Solution | TestHub

The velocity of an electron in the $n^{\text{th}}$ orbit of a hydrogen atom is $v_n\propto \frac{1}{n}$.

The radius of the $n^{\text{th}}$ orbit is $r_n\propto n^2$.

The frequency of revolution is given by $f_n=\frac{v_n}{2\pi r_n}$.

Substituting the proportionalities, we get $f_n\propto \frac{1/n}{n^2}\Rightarrow f_n\propto \frac{1}{n^3}$.

Thus, the frequency of revolution is inversely proportional to $n^3$.

Answer: inversely proportional to ${\mathrm{n}}^3$