In the Bohr model an electron moves in a circular orbit around the proton . Considering the orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom; when the electron is in \(n^{th}\) excited state, is

\(n^{\prime}=(n+1)\)

As magnetic moment \(\mathrm{M}_{\mathrm{n}}=\mathrm{I}_{\mathrm{n}} \mathrm{A}=\mathrm{i}_{\mathrm{n}}\left(\pi \mathrm{r}_{\mathrm{n}}^{2}\right)\)

\(\mathrm{i}_{\mathrm{n}}=\mathrm{eV}_{\mathrm{n}}=\frac{\mathrm{mz}^{2} \mathrm{e}^{5}}{4 \varepsilon_{0}^{2} \mathrm{n}^{3} \mathrm{h}^{3}}\)

\(r_{n}=\frac{n^{2} h^{2}}{4 \pi^{2} k \pi n e^{2}}\left(k=\frac{1}{4 \pi \epsilon_{0}}\right)\)

Solving we get magnetic moment of the hydrogen atom for \(n^{\text {th }}\) excited state

\(\mathrm{M}_{\mathrm{n}^{*}}=\left(\frac{\mathrm{e}}{2 \mathrm{m}}\right) \frac{\mathrm{nh}}{2 \pi}\)