Question

In a hydrogen atom, an electron of charge e revolves in a orbit of radius $r$ with speed $v$. Then, magnetic moment associated with electron is

• A. $\frac{evr}{2}$
• B. $2\,evr$
• C. $evr$
• D. $\frac{evr}{3}$

Answer 1

Answer: (A)

$\frac{evr}{2}$

Answer 2

Magnetic moment of revolving electron,
$\mu_{e}=i \times A$
where, $i=$ current and $A=$ area,
$\therefore \mu_{e}=\frac{e}{T} \times \pi r^{2}$ (As current, $i=\frac{\text { charge }}{\text { time }}=\frac{e}{T}$
where, $T=$ time period of revolution and $r=$ radius of orbit.

$\mu_{e}= \frac{e}{2 \pi r} \times v \times \pi r^{2}$
($\because$ Time period $(T)=\frac{\text {distance}}{\text {speed}})$
where, $v=$ velocity of revolving electron
$\Rightarrow \mu_{e}=\frac{ e v r }{ 2}$
Hence, the magnetic moment of revolving electron is $\frac{e V r}{2}$.