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 (l) is given as 4, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The subsidiary quantum number (l) defines the shape of the orbital and can take values from 0 to (n-1), where n is the principal quantum number. Each value of l corresponds to a specific type of orbital (s, p, d, f, g, etc.).

2. **Identifying the Value of l**:
- In this case, the subsidiary quantum number is given as l = 4. This corresponds to the f orbital type.

3. **Determining the Number of Orbitals**:
- The number of degenerate orbitals for a given value of l can be calculated using the formula:
\[ \text{Number of orbitals} = 2l + 1 \]
- Here, substituting l = 4 into the formula gives:
\[ \text{Number of orbitals} = 2(4) + 1 = 8 + 1 = 9 \]

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

### Final Answer:
The number of degenerate orbitals when the subsidiary quantum number is 4 is **9**.

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