Which of the following orbital designations is not correct corresponding to quantum numbers ?

Options

A. `n = 5, l = 2 to 5d`
B. `n = 2, l = 0 to 2s`
C. `n = 4, l = 3 to 4f`
D. `n = 7, l = 2 to 7p`

Explanation

To determine which of the given orbital designations is not correct according to quantum numbers, we need to understand the relationship between the principal quantum number (n) and the azimuthal quantum number (l).

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- The principal quantum number (n) can take positive integer values (1, 2, 3, ...).
- The azimuthal quantum number (l) can take values from 0 to (n-1). This means for a given n, l can be 0, 1, 2, ..., (n-1).
- Each value of l corresponds to a specific type of orbital:
- l = 0 corresponds to s orbitals
- l = 1 corresponds to p orbitals
- l = 2 corresponds to d orbitals
- l = 3 corresponds to f orbitals
- l = 4 corresponds to g orbitals, and so on.

2. **Analyzing Each Option**:
- **Option 1**: n = 5, l = 2
- Here, l can take values 0, 1, 2, 3, or 4 (since n-1 = 4).
- l = 2 corresponds to a d orbital. Thus, this designation is correct (5d).

- **Option 2**: n = 2, l = 0
- For n = 2, l can be 0 or 1 (0 ≤ l < n).
- l = 0 corresponds to an s orbital. Thus, this designation is correct (2s).

- **Option 3**: n = 4, l = 3
- For n = 4, l can be 0, 1, 2, or 3 (0 ≤ l < n).
- l = 3 corresponds to an f orbital. Thus, this designation is correct (4f).

- **Option 4**: n = 7, l = 2
- For n = 7, l can take values 0, 1, 2, 3, 4, 5, or 6 (0 ≤ l < n).
- l = 2 corresponds to a d orbital. However, if the designation is 7p, this is incorrect because l = 2 should correspond to 7d.

3. **Conclusion**:
- The incorrect designation is **7p** when it should be **7d** for l = 2. Therefore, the answer is that the orbital designation **7p** is not correct.