Question

Magnetic moment due to the motion of the election in $n^{th}$ energy state of hydrogen atom is proportional to_________

• A. $n^{-2}$
• B. $n$
• C. $n^2$
• D. $n^3$

Answer 1

Answer: (B)

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,
$M=iA=\frac{e\omega }{2\pi }\pi R^2$
$\Rightarrow M=\frac{ev}{2R}{R}^2$
$(\because \omega =\frac{v}{R})$
$\Rightarrow M=\frac{evR}{2}=\frac{eL}{2m}$
where, $L=mvr$ and $L=\frac{nh}{2\pi }$
So, $M=\frac{enh}{2\pi m}$
$\Rightarrow M\propto n$
$\because e,h,m$ are constant of electron,