JEE Main 2013 — Atomic Physics Question with Solution

Magnetic moment of the hydrogen atom, when the electron is in ${\mathrm{n}}^{\text{th }}$ excited state, i.e., $n^{\prime }=(n+1)$ As magnetic moment ${\mathrm{M}}_{\mathrm{n}}={\mathrm{I}}_{\mathrm{n}}\mathrm{A}={\mathrm{i}}_{\mathrm{n}}\left(\pi {\mathrm{r}}_{\mathrm{n}}^2\right)$ $\begin{aligned} & i_n=e V_n=\frac{m z^2 e^5}{4 \varepsilon_0^2 n^3 h^3} \\ & r_n=\frac{n^2 h^2}{4 \pi^2 k z m e^2}\left(k=\frac{1}{4 \pi \epsilon_0}\right) \end{aligned}$ Solving we get magnetic moment of the hydrogen atom for ${\mathrm{n}}^{\text{th }}$ excited state $M_{n^{\prime }}=\left(\frac{e}{2m}\right)\frac{nh}{2\pi }$