Question

If the angular momentum of an electron is $\overrightarrow{J}$ then the magnitude of the magnetic moment will be

• A. $\frac{eJ}{m}$
• B. $\frac{2m}{eJ}$
• C. $eJ2m$
• D. $\frac{eJ}{2m}$

Answer 1

The correct option is D $\frac{eJ}{2m}$

$Given:$ Angular momentum of an electron = $\overrightarrow{J}$

$Solution:$ The magnetic momment of an electgron revolving in a circular orbit of radius $r$ is

$M$= $1.2evr$

And its angular momentum

$J$ = $Iw$ =$m{r}^2$$\times$ $\frac{v}{r}$ = $mvr$

$\therefore$ $\frac{M}{J}$= $\frac{1}{2}$ $\frac{evr}{mvr}$ =$\frac{1}{2}$ $\frac{e}{m}$

$\therefore$ $M$ = $\frac{eJ}{2m}$

$So,the$ $correct$ $option:D$