The number of states in a shell with principal quantum number `n=3` is

Options

A. 3
B. 9
C. 15
D. 18

Answer

To find the number of states in a shell with a principal quantum number \( n = 3 \), we can use the formula that relates the principal quantum number to the number of states (or the number of electrons that can occupy that shell). The formula is:

\[ \text{Number of states} = 2n^2 \]

### Step-by-Step Solution:

1. **Identify the principal quantum number**:
- Given \( n = 3 \).

2. **Apply the formula**:
- Substitute \( n \) into the formula:
\[ \text{Number of states} = 2n^2 = 2(3^2) \]

3. **Calculate \( n^2 \)**:
- Calculate \( 3^2 \):
\[ 3^2 = 9 \]

4. **Multiply by 2**:
- Now multiply by 2:
\[ 2 \times 9 = 18 \]

5. **Conclusion**:
- Therefore, the number of states in a shell with principal quantum number \( n = 3 \) is \( 18 \).

### Final Answer:
The number of states in a shell with principal quantum number \( n = 3 \) is \( 18 \).

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