Question

The angular momentum of electron is $J$. Its magnetic moment will be

• A. $\frac{mJ}{2e}$
• B. $\frac{eJ}{2m}$
• C. $\frac{2m}{ej}$
• D. $\frac{emj}{2}$

Answer 1

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

Let, $\mu$ be the magnetic moment of an electron.

The angular momentum for an electron revolving in a orbit is

$J=mvr$

where, m is mass and v is velocity of electron and r is radius of orbit.

Now, the current is the charge per unit time crossing any point on the orbit.

$I=\frac{q}{t}$

$I=qf$ ...................(since, $f=\frac{1}{t}$)

The frequency is the velocity of electron along the circumference of orbit. hence

$I=q\frac{v}{2\pi r}$

The magnetic moment is:

$\mu =IA$

where, A is the area of the circular orbit.

$\mu =q\frac{v}{2\pi r}\left(\pi r^2\right)$

$\mu =q\frac{vr}{2}$

$\mu =q\frac{mvr}{2m}$

$\mu =\frac{qJ}{2m}$

$\mu =\frac{eJ}{2m}$ ....................(since, e is electronic charge)