If the principal quantum has a value of `3` what are the permited values of the quantum number l ?

Explanation

To determine the permitted values of the azimuthal quantum number \( l \) when the principal quantum number \( n \) is given as 3, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Principal Quantum Number \( n \)**:
- The principal quantum number \( n \) indicates the energy level or shell of an electron in an atom. In this case, \( n = 3 \).

2. **Identify the Relationship Between \( n \) and \( l \)**:
- The azimuthal quantum number \( l \) (also known as the angular momentum quantum number) defines the shape of the orbital and can take on integer values. The values of \( l \) are determined by the principal quantum number \( n \).

3. **Determine the Range of \( l \)**:
- The permitted values of \( l \) range from \( 0 \) to \( n - 1 \). This means:
\[ l = 0, 1, 2, \ldots, (n - 1) \]

4. **Calculate the Permitted Values for \( n = 3 \)**:
- Substituting \( n = 3 \):
\[ l = 0, 1, 2 \]

5. **Conclusion**:
- Therefore, the permitted values of the azimuthal quantum number \( l \) when \( n = 3 \) are \( 0, 1, \) and \( 2 \).

### Final Answer:
The permitted values of the azimuthal quantum number \( l \) for \( n = 3 \) are \( 0, 1, \) and \( 2 \).

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