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 a principal quantum number \( n = 5 \) and azimuthal quantum number \( l = 3 \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
- The principal quantum number \( n \) is given as 5.
- The azimuthal quantum number \( l \) is given as 3.

2. **Determine the Type of Subshell**:
- The azimuthal quantum number \( l \) corresponds to different types of subshells:
- \( l = 0 \) corresponds to the s subshell.
- \( l = 1 \) corresponds to the p subshell.
- \( l = 2 \) corresponds to the d subshell.
- \( l = 3 \) corresponds to the f subshell.
- Since \( l = 3 \), we are dealing with the f subshell.

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

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

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