Magnetic moment due to the motion of the electron in nth energy of hydrogen atom is proportional to

Options

A. n
B. `n^(0)`
C. `n^(5)`
D. `n^(3)`

Explanation

To determine the proportionality of the magnetic moment due to the motion of an electron in the nth energy level of a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Magnetic Moment**:
The magnetic moment (M) of an electron in orbit is related to its angular momentum (L). The formula for magnetic moment due to the motion of an electron is given by:
\[ M = \frac{e}{2m} L \]
where \( e \) is the charge of the electron and \( m \) is its mass.

2. **Angular Momentum**:
The angular momentum (L) of an electron in the nth orbit of a hydrogen atom is quantized and given by:
\[ L = n \frac{h}{2\pi} \]
where \( n \) is the principal quantum number and \( h \) is Planck's constant.

3. **Substituting Angular Momentum into Magnetic Moment**:
Substituting the expression for angular momentum into the magnetic moment formula, we get:
\[ M = \frac{e}{2m} \left(n \frac{h}{2\pi}\right) \]

4. **Identifying Proportionality**:
From the equation above, we can see that the magnetic moment M is directly proportional to the principal quantum number \( n \):
\[ M \propto n \]

5. **Conclusion**:
Therefore, the magnetic moment due to the motion of the electron in the nth energy level of the hydrogen atom is proportional to \( n \).

### Final Answer:
The magnetic moment \( M \) is proportional to \( n \).