Which of the following orbitals is meaningless?

Options

A. 6f
B. 2d
C. 7s
D. 3d

Answer

To determine which of the given orbitals is meaningless, we need to analyze the quantum numbers associated with each orbital. Each orbital is defined by four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (s).

### Step-by-step Solution:

1. **Understanding Quantum Numbers**:
- The principal quantum number (n) indicates the energy level and can take positive integer values (1, 2, 3, ...).
- The azimuthal quantum number (l) can take values from 0 to (n-1). It defines the shape of the orbital.
- The magnetic quantum number (m) can take values from -l to +l, including zero. It defines the orientation of the orbital.
- The spin quantum number (s) can be either +1/2 or -1/2, indicating the spin of the electron.

2. **Evaluating the Given Orbitals**:
- **6f Orbital**:
- For the 6f orbital:
- n = 6
- l = 3 (since f corresponds to l = 3)
- m can take values from -3 to +3 (total of 7 values: -3, -2, -1, 0, +1, +2, +3)
- s can be +1/2 or -1/2.
- All quantum numbers are valid.

- **2d Orbital**:
- For the 2d orbital:
- n = 2
- l = 2 (but l can only be 0 or 1 for n = 2)
- This is where the problem arises, as l cannot equal n.
- Therefore, the 2d orbital is meaningless.

3. **Conclusion**:
- The meaningless orbital among the options provided is the **2d orbital** because it violates the rule that l must be less than n.

### Final Answer:
The meaningless orbital is **2d**.