How many orbitals are possible for n = 3, l=2 ?

Options

A. 1
B. 3
C. 5
D. 7

Explanation

To determine how many orbitals are possible for n = 3 and l = 2, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantum Numbers**:
- The principal quantum number (n) is given as 3.
- The azimuthal quantum number (l) is given as 2.

2. **Understand the Relationship Between n and l**:
- The value of l can range from 0 to (n-1). Therefore, for n = 3, l can take the values 0, 1, or 2.
- The corresponding subshells for these values of l are:
- l = 0 corresponds to the s subshell (3s).
- l = 1 corresponds to the p subshell (3p).
- l = 2 corresponds to the d subshell (3d).

3. **Determine the Number of Orbitals**:
- The number of orbitals in a subshell can be calculated using the formula:
\[ \text{Number of orbitals} = 2l + 1 \]
- Substitute the value of l into the formula:
\[ \text{Number of orbitals} = 2(2) + 1 = 4 + 1 = 5 \]

4. **Conclusion**:
- Therefore, for n = 3 and l = 2, there are **5 orbitals** in the d subshell.

### Final Answer:
There are 5 orbitals possible for n = 3 and l = 2.