The number of values of the orbital quantum number associated with the principal quantum number `n=3` is

Options

A. 1
B. 2
C. 9
D. 4

Answer

To find the number of values of the orbital quantum number associated with the principal quantum number \( n = 3 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The principal quantum number \( n \) indicates the main energy level of an electron in an atom. For \( n = 3 \), this corresponds to the third energy level.

2. **Orbital Quantum Number**:
- The orbital quantum number, denoted as \( l \), can take on integer values from \( 0 \) to \( n-1 \). This means for a given principal quantum number \( n \), the possible values of \( l \) are \( 0, 1, 2, \ldots, (n-1) \).

3. **Calculating Values of \( l \)**:
- For \( n = 3 \):
- The possible values of \( l \) are:
- \( l = 0 \) (s orbital)
- \( l = 1 \) (p orbital)
- \( l = 2 \) (d orbital)
- Therefore, the values of \( l \) are \( 0, 1, 2 \).

4. **Counting the Values of \( l \)**:
- The total number of values of \( l \) is \( n \) (which is 3) since \( l \) can take values from \( 0 \) to \( n-1 \).
- Thus, the number of values of the orbital quantum number associated with \( n = 3 \) is \( 3 \).

### Final Answer:
The number of values of the orbital quantum number associated with the principal quantum number \( n = 3 \) is **3**.

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