If the susbsidiary quantum number of a subenergy level is 4, then no. of degenerate orbitals are

Options

A. 3
B. 5
C. 9
D. 11

Answer

To determine the number of degenerate orbitals when the subsidiary quantum number (azimuthal quantum number) is given as 4, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quantum Numbers**:
- The subsidiary quantum number (L) is also known as the azimuthal quantum number. It determines the shape of the orbital and is associated with the angular momentum of the electron in the atom.

2. **Identify the Given Value**:
- In this problem, the subsidiary quantum number (L) is given as 4.

3. **Use the Formula for Degenerate Orbitals**:
- The formula to calculate the number of degenerate orbitals is:
\[ \text{Number of degenerate orbitals} = 2l + 1 \]
- Here, \( l \) is the subsidiary quantum number.

4. **Substitute the Value of L into the Formula**:
- Substitute \( l = 4 \) into the formula:
\[ \text{Number of degenerate orbitals} = 2(4) + 1 \]

5. **Perform the Calculation**:
- Calculate \( 2(4) + 1 \):
\[ 2(4) = 8 \]
\[ 8 + 1 = 9 \]

6. **Conclusion**:
- Therefore, the number of degenerate orbitals when the subsidiary quantum number is 4 is **9**.

### Final Answer:
The number of degenerate orbitals is **9**.

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