PX262 - A4 - bohr's model

bohr postulated that the electrons in atoms move in a fixed circular path around the nuclei and they do not radiate
such electrons will have orbital momenta given by: $L_{n} = v_{n} r_{n} M = \frac{n k}{2 π} = n ℏ$ where, $n \in Z$ , labelling the states

r_{n} = ϵ_{0} \frac{n^{2} h^{2}}{π M e^{2}}

\begin{matrix} a = ϵ_{o} \frac{h^{2}}{π M e^{2}} = 5.29 \times 10^{- 11} m \\ ∴ r_{n} = a n^{2} \end{matrix}