A: Angular momentum of an electron in an atom is quantized
R : in an atom only orbitals are permitted in which angular momentum of the electron is a natural number multiple of `(h)/( 2 pi)`

Options

A. IF both assertion & reason are true and the reason is the correct explanation of the assertion then mark
B. IF both assertion & reason are true but the reason is not the correct explanation of the assertion , then mark
C. IF assertion is true statement but reason is false , then mark
D. If both assertion and reason are false statements then mark

Answer

To solve the question, we need to analyze the assertion and reason provided:

**Assertion (A):** Angular momentum of an electron in an atom is quantized.
**Reason (R):** In an atom, only orbitals are permitted in which angular momentum of the electron is a natural number multiple of \( \frac{h}{2\pi} \).

### Step-by-Step Solution:

1. **Understanding Angular Momentum in Quantum Mechanics:**
- According to classical mechanics, angular momentum (\(L\)) is defined as \(L = mvr\), where \(m\) is the mass of the electron, \(v\) is its velocity, and \(r\) is the radius of its orbit.
- However, in quantum mechanics, particularly in the Bohr model of the atom, angular momentum is quantized.

2. **Bohr's Postulate:**
- Bohr proposed that the angular momentum of an electron in a hydrogen atom is quantized and can only take on certain discrete values.
- The quantization condition is given by:
\[ L = mvr = n \frac{h}{2\pi} \]
where \(n\) is a natural number (1, 2, 3, ...), and \(h\) is Planck's constant.

3. **Conclusion from the Assertion:**
- Since the angular momentum can only take on values that are integral multiples of \( \frac{h}{2\pi} \), we conclude that the angular momentum of an electron in an atom is indeed quantized. Thus, the assertion (A) is true.

4. **Analyzing the Reason:**
- The reason states that "in an atom, only orbitals are permitted in which angular momentum of the electron is a natural number multiple of \( \frac{h}{2\pi} \)".
- This aligns perfectly with Bohr's postulate, as it specifies that only certain orbitals (those corresponding to specific values of \(n\)) are allowed, confirming that the angular momentum is quantized.

5. **Final Evaluation:**
- Both the assertion and reason are true, and the reason correctly explains the assertion.
- Therefore, we conclude that both statements are correct and the reason is a valid explanation of the assertion.

### Final Answer:
Both the assertion and reason are true, and the reason is the correct explanation of the assertion.