Magnetic moment of a moving electron,
which shown in the figure below,
Current, $i=\frac{e}{T}=\frac{e \omega}{2 \pi}$
$\left(\because \omega=\frac{2 \pi}{T}\right)$
As, magnetic moment,
$M= i A=\frac{e \omega}{2 \pi} \pi R^{2} $
$\Rightarrow M=\frac{e v}{2 R} R^{2}$
$( \because \omega = \frac{v}{R} )$
$\Rightarrow M=\frac{e v R}{2}=\frac{e L}{2 m}$
where, $L=m v r$ and $L=\frac{n h}{2 \pi}$
So, $M=\frac{e n h}{2 \pi m} $
$\Rightarrow M \propto n$
$\because e, h, m$ are constant of electron,
