which of the following statements about an electron with `m_1=+2` is incorrect?

Options

A. The electron could be in the third shell
B. The electron is in a non-spherical orbital
C. The electron may have `m_s=1/2`
D. The electron is not in a d-orbital

Answer

To determine which statement about an electron with \( m_L = +2 \) is incorrect, we will analyze the properties of the magnetic quantum number \( m_L \) and its relationship with the azimuthal quantum number \( l \).

### Step-by-Step Solution:

1. **Understanding the Magnetic Quantum Number (\( m_L \))**:
- The magnetic quantum number \( m_L \) describes the orientation of orbitals in a magnetic field. Its values range from \( -l \) to \( +l \), where \( l \) is the azimuthal quantum number.

2. **Identifying the Value of \( l \)**:
- Given \( m_L = +2 \), we can conclude that the azimuthal quantum number \( l \) must be at least 2 (since \( m_L \) can take values from \( -l \) to \( +l \)).
- Therefore, \( l = 2 \) is the minimum value that allows \( m_L = +2 \).

3. **Possible Values of \( m_L \)**:
- For \( l = 2 \), the possible values of \( m_L \) are \( -2, -1, 0, +1, +2 \). This confirms that \( m_L = +2 \) is valid for \( l = 2 \).

4. **Identifying the Orbital Type**:
- The azimuthal quantum number \( l = 2 \) corresponds to the d-orbitals. Thus, the electron with \( m_L = +2 \) is in a d-orbital.

5. **Evaluating the Statements**:
- **Statement 1**: "The electron could be in the third shell."
- This is true because the 3d orbital corresponds to \( n = 3 \) and \( l = 2 \).
- **Statement 2**: "The electron is in a non-spherical orbital."
- This is true because d-orbitals are indeed non-spherical in shape.
- **Statement 3**: "The electron may have \( m_s = +\frac{1}{2} \)."
- This is true because the spin quantum number \( m_s \) can be either \( +\frac{1}{2} \) or \( -\frac{1}{2} \).
- **Statement 4**: "The electron is not in a d-orbital."
- This is incorrect because we established that \( l = 2 \) indicates that the electron is indeed in a d-orbital.

6. **Conclusion**:
- The incorrect statement is **Statement 4**: "The electron is not in a d-orbital."

### Final Answer:
The incorrect statement is: **The electron is not in a d-orbital.**