When an electron revolves around the nucleus, then the ratio of magnetic moment to angular momentum is

Options

A. `e/(2m)`
B. `(2e)/m`
C. `e/m`
D. `(e/m)^2`

Answer

To solve the problem of finding the ratio of magnetic moment to angular momentum for an electron revolving around a nucleus, we can follow these steps:

### Step-by-Step Solution:

1. **Define Angular Momentum (L)**:
The angular momentum (L) of an electron revolving around the nucleus can be expressed as:
\[ L = mvr \]
where \( m \) is the mass of the electron, \( v \) is its velocity, and \( r \) is the radius of the orbit.

2. **Calculate Time Period (T)**:
The time period (T) for one complete revolution of the electron is given by:
\[ T = \frac{2\pi r}{v} \]

3. **Determine Current (I)**:
The current \( I \) due to the revolving electron can be calculated as the charge \( e \) divided by the time period \( T \):
\[ I = \frac{e}{T} = \frac{e}{\frac{2\pi r}{v}} = \frac{ev}{2\pi r} \]

4. **Calculate Magnetic Moment (μ)**:
The magnetic moment \( \mu \) is given by the product of current and area:
\[ \mu = I \cdot A \]
where \( A \) is the area of the circular path:
\[ A = \pi r^2 \]
Substituting for \( I \):
\[ \mu = \left(\frac{ev}{2\pi r}\right) \cdot \pi r^2 = \frac{evr}{2} \]

5. **Find the Ratio of Magnetic Moment to Angular Momentum**:
Now, we can find the ratio of magnetic moment \( \mu \) to angular momentum \( L \):
\[ \frac{\mu}{L} = \frac{\frac{evr}{2}}{mvr} \]
Simplifying this expression:
\[ \frac{\mu}{L} = \frac{evr}{2mvr} = \frac{e}{2m} \]

6. **Final Result**:
Therefore, the ratio of magnetic moment to angular momentum is:
\[ \frac{\mu}{L} = \frac{e}{2m} \]

### Conclusion:
The final answer is:
\[ \frac{\mu}{L} = \frac{e}{2m} \]