The product of angular speed and tangential speed of electron in nth orbit of hydrogen atom is

velocity of an electron in the nth orbit is inversely proportional to n and radius of the nth orbit is directly proportional to $n^2$

$$\begin{gathered} v\times \omega =v\times \frac{v}{r}=\frac{v^2}{r} \\ v\times \omega \propto \frac{1}{n^2}\frac{1}{n^2}\propto \frac{1}{n^4} \end{gathered}$$