Which of the following statements are correct for an electron that has `n = 4` and `m = - 2`

Options

A. (1) The electron may be present in a d-orbital
B. (2) The electron in the fourth principal electronic shell
C. (3) The electron may be in a p- orbital
D. (4) The electron must have the spin quantum number `= + 1//2`

Explanation

To determine which statements are correct for an electron with quantum numbers \( n = 4 \) and \( m = -2 \), we need to analyze each statement based on the principles of quantum mechanics.

### Step-by-Step Solution:

1. **Understanding the Quantum Numbers**:
- The principal quantum number \( n \) indicates the energy level or shell of the electron. Here, \( n = 4 \) means the electron is in the fourth energy shell.
- The magnetic quantum number \( m \) indicates the orientation of the orbital. The values of \( m \) can range from \(-l\) to \(+l\), where \( l \) is the azimuthal quantum number.

2. **Identifying the Orbital Type**:
- For \( n = 4 \), the possible values of \( l \) are \( 0, 1, 2, 3 \), which correspond to the s, p, d, and f orbitals respectively.
- The magnetic quantum number \( m = -2 \) suggests that \( l \) must be at least \( 2 \) (since \( m \) can take values from \(-l\) to \(+l\)).
- Therefore, \( l = 2 \) corresponds to d orbitals. The specific d orbital that corresponds to \( m = -2 \) is the \( d_{xy} \) orbital.

3. **Evaluating the Statements**:
- **Statement 1**: "The electron may be present in a d-orbital."
- This statement is **correct** because \( m = -2 \) corresponds to one of the d orbitals.

- **Statement 2**: "The electron is in the fourth principal electronic shell."
- This statement is also **correct** because \( n = 4 \) indicates that the electron is indeed in the fourth shell.

- **Statement 3**: "The electron may be in a p-orbital."
- This statement is **incorrect** because the magnetic quantum number \( m \) for p orbitals can only be \(-1, 0, +1\). Since \( m = -2 \), the electron cannot be in a p-orbital.

- **Statement 4**: "The electron must have the spin quantum number +1/2."
- This statement is **incorrect**. An electron can have a spin quantum number of either \( +1/2 \) (spin up) or \( -1/2 \) (spin down). Therefore, it is not necessary for the electron to have a spin of \( +1/2 \).

### Final Conclusion:
The correct statements are:
- Statement 1: Correct
- Statement 2: Correct
- Statement 3: Incorrect
- Statement 4: Incorrect

Thus, the correct options are **1 and 2**.