If the angular momentum of an electron is `vec(J)` then the magnitude of the magnetic moment will be

Options

A. `(eJ)/m`
B. `(eJ)/(2m)`
C. eJ 2m
D. `(2m)/(eJ)`

Explanation

To find the magnitude of the magnetic moment \( \vec{M} \) of an electron given its angular momentum \( \vec{J} \), we can follow these steps:

### Step 1: Understand the relationship between magnetic moment and angular momentum
The magnetic moment \( \vec{M} \) can be expressed in terms of the angular momentum \( \vec{J} \) of the electron. The relationship is given by:

\[ \vec{M} = \frac{e}{2m} \vec{J} \]

where:
- \( e \) is the charge of the electron,
- \( m \) is the mass of the electron,
- \( \vec{J} \) is the angular momentum.

### Step 2: Calculate the magnitude of the magnetic moment
To find the magnitude of the magnetic moment, we take the magnitude of both sides of the equation:

\[ M = \frac{e}{2m} |J| \]

### Step 3: Substitute the known values
Assuming we have the values for \( e \) (approximately \( 1.6 \times 10^{-19} \) C) and \( m \) (approximately \( 9.11 \times 10^{-31} \) kg), we can express the magnetic moment in terms of the angular momentum \( |J| \):

\[ M = \frac{e |J|}{2m} \]

### Step 4: Final expression
Thus, the final expression for the magnitude of the magnetic moment in terms of the angular momentum is:

\[ M = \frac{e |J|}{2m} \]

This gives us the required magnitude of the magnetic moment.