Bohr's postulate to explain stable orbits in a hydrogen atom:The stationary orbits are those orbits for which the angular momentum of the electron is an integral multiple of $\frac{h}{2\pi}$, where $h$ is Planck's constant. Electron in an atom revolves because of the balance of Coulomb force of attraction between the protons and electrons and the centripetal force. In $n^{\text{th}}$ orbit, $\frac{m v^2_n}{r_n} = \frac{1}{4\pi\varepsilon_0} \frac{e^2}{r^2_n}$ $\therefore v_n = \frac{e}{\sqrt{4\pi\varepsilon_0 m r_n}} \dots (i)$ Again, $r_n = \frac{\varepsilon_0 h^2 n^2}{e^2 \pi m} \dots (ii)$ Putting in equation (i) $v_n = \frac{e}{\sqrt{4\pi\varepsilon_0 m \frac{\varepsilon_0 h^2 n^2}{e^2 \pi m}}}$ $= \frac{e^2}{2\varepsilon_0 h m}$ $\therefore v_n \propto \frac{1}{n}$