Which of the following orbital does not make sense?

Options

A. `3d`
B. `2f`
C. `5p`
D. `7s`

Explanation

To determine which of the given orbitals does not make sense, we need to analyze the quantum numbers associated with each orbital. The four quantum numbers are:

1. Principal quantum number (n)
2. Azimuthal quantum number (l)
3. Magnetic quantum number (m)
4. Spin quantum number (s)

However, for this question, we will focus primarily on n and l.

### Step-by-Step Solution:

1. **Identify the given orbitals**: The orbitals provided are 3d, 2f, 5p, and 7s.

2. **Determine the values of n and l for each orbital**:
- For **3d**:
- n = 3 (principal quantum number)
- l = 2 (for d orbitals)
- For **2f**:
- n = 2 (principal quantum number)
- l = 3 (for f orbitals)
- For **5p**:
- n = 5 (principal quantum number)
- l = 1 (for p orbitals)
- For **7s**:
- n = 7 (principal quantum number)
- l = 0 (for s orbitals)

3. **Check the validity of l values**: The azimuthal quantum number (l) must satisfy the condition:
- \( l \) can take values from 0 to \( n-1 \).
- Therefore, for each value of n:
- For n = 3, l can be 0, 1, or 2 (valid for 3d).
- For n = 2, l can be 0 or 1 (invalid for 2f, since l = 3 is not allowed).
- For n = 5, l can be 0, 1, 2, 3, or 4 (valid for 5p).
- For n = 7, l can be 0, 1, 2, 3, 4, 5, or 6 (valid for 7s).

4. **Conclusion**: Since 2f has an invalid value of l (3) for n = 2, it does not make sense. Therefore, the orbital that does not exist is **2f**.

### Final Answer:
The orbital that does not make sense is **2f**.

---