Question

The magnetic moment of an electron with orbital angular momentum $J$ will be :

• A. $\frac{e\overrightarrow{J}}{m}$
• B. $\frac{e\overrightarrow{J}}{2m}$
• C. $\frac{2m}{e\overrightarrow{J}}$
• D. $zero$

Answer 1

Answer: (B)

$\frac{e\overrightarrow{J}}{2m}$

Angular momentum $J=m\omega r^2$ where $\omega$ is the angular velocity$,r$ is the radius of the orbit
Magnetic moment $\mu =iA=\frac{e\omega }{2\pi }\pi r^2$
$\therefore \frac{\mu }{J}=\frac{\frac{e\omega }{2\pi }\pi r^2}{m\omega r^2}=\frac{e}{2m}$
$\Rightarrow \overrightarrow{\mu }=\frac{e}{2m}\overrightarrow{J}$