Physics - Modern Physics Question with Solution | TestHub

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 ${\mathrm{M}}_{\mathrm{n}}={\mathrm{I}}_{\mathrm{n}}\mathrm{A}={\mathrm{i}}_{\mathrm{n}}\left(\pi {\mathrm{r}}_{\mathrm{n}}^2\right)$ $\begin{array}{rl}& i_n=e{V}_n=\frac{m{z}^2{e}^5}{4{\epsilon }_0^2{n}^3{h}^3}\\ & r_n=\frac{n^2{h}^2}{4{\pi }^{2}kzm{e}^2}\left(k=\frac{1}{4\pi {ϵ}_0}\right)\end{array}$ Solving we get magnetic moment of the hydrogen atom for ${\mathrm{n}}^{\text{th }}$ excited state $M_{n^{\prime }}=\left(\frac{e}{2m}\right)\frac{nh}{2\pi }$