For principal quantum number n=5 the total number of orbital having l=3 is

Options

A. 7
B. 14
C. 9
D. 18

Answer

To solve the question regarding the total number of orbitals for the principal quantum number \( n = 5 \) and the azimuthal quantum number \( l = 3 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number \( n \)**:
- The principal quantum number \( n \) indicates the energy level of the electron in an atom. Here, \( n = 5 \).

2. **Identify the Azimuthal Quantum Number \( l \)**:
- The azimuthal quantum number \( l \) determines the shape of the orbital. The value of \( l \) can take on integer values from \( 0 \) to \( n-1 \).
- For \( l = 3 \), this corresponds to the f-orbital.

3. **Determine the Type of Orbital**:
- Since \( l = 3 \), we are dealing with the f-orbital. The f-orbitals are characterized by the azimuthal quantum number \( l = 3 \).

4. **Calculate the Number of Orbitals**:
- The number of orbitals in a subshell is given by the formula \( 2l + 1 \).
- For \( l = 3 \):
\[ \text{Number of orbitals} = 2(3) + 1 = 6 + 1 = 7 \]

5. **Conclusion**:
- Therefore, for \( n = 5 \) and \( l = 3 \), the total number of orbitals is **7**.

### Final Answer:
The total number of orbitals having \( l = 3 \) for \( n = 5 \) is **7**.

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