Assertion (A) The magnetic moment `(mu)` of an electron revolving around the nucleus decreases with increasing principle quantum number (n).
Reason (R ) Magnetic moment of the revolving electron , `muprop` n.

Options

A. If both Assertion and Reason are true and Reason is correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If both Assertion and Reason are false.

Answer

To solve the problem, we need to analyze the assertion and reason provided in the question regarding the magnetic moment of an electron revolving around the nucleus.

### Step-by-Step Solution:

1. **Understanding Magnetic Moment**:
The magnetic moment (μ) of an electron in a circular orbit can be expressed as:
\[ \mu = I \cdot A \]
where \(I\) is the current and \(A\) is the area of the orbit.

2. **Current Calculation**:
The current \(I\) due to the revolving electron can be calculated as:
\[ I = \frac{e}{T} \]
where \(e\) is the charge of the electron and \(T\) is the time period of one complete revolution. The time period \(T\) can be expressed as:
\[ T = \frac{2\pi r}{v} \]
where \(r\) is the radius of the orbit and \(v\) is the velocity of the electron.

3. **Area Calculation**:
The area \(A\) of the circular orbit is given by:
\[ A = \pi r^2 \]

4. **Substituting Current and Area into Magnetic Moment**:
Now substituting \(I\) and \(A\) into the magnetic moment formula:
\[ \mu = I \cdot A = \left(\frac{e}{T}\right) \cdot \pi r^2 \]
Substituting \(T\):
\[ \mu = \left(\frac{e}{\frac{2\pi r}{v}}\right) \cdot \pi r^2 = \frac{e v r}{2} \]

5. **Using Bohr's Postulate**:
According to Bohr's postulate, the angular momentum \(L\) of the electron is quantized:
\[ L = mvr = n \frac{h}{2\pi} \]
where \(n\) is the principal quantum number and \(h\) is Planck's constant.

6. **Expressing Velocity in Terms of Quantum Number**:
From the angular momentum equation, we can express \(vr\) as:
\[ vr = \frac{n h}{2\pi m} \]

7. **Substituting Back to Magnetic Moment**:
Now substituting \(vr\) back into the expression for magnetic moment:
\[ \mu = \frac{e}{2} \cdot \frac{n h}{2\pi m} = \frac{e n h}{4\pi m} \]
This shows that the magnetic moment \(\mu\) is directly proportional to the principal quantum number \(n\):
\[ \mu \propto n \]

8. **Conclusion**:
- The assertion states that the magnetic moment decreases with increasing principal quantum number \(n\), which is **incorrect**.
- The reason states that the magnetic moment is proportional to \(n\), which is **correct**.

### Final Answer:
- Assertion (A) is **false**.
- Reason (R) is **true**.