To determine which statements are correct for an electron with quantum numbers \( n = 4 \) and \( m = 2 \), we need to analyze the quantum numbers and their implications.
### Step-by-Step Solution:
1. **Understanding Quantum Numbers**:
- The principal quantum number \( n \) indicates the energy level of the electron. In this case, \( n = 4 \) means the electron is in the fourth energy level.
- The azimuthal quantum number \( l \) (often represented as \( L \)) determines the shape of the orbital and can take values from \( 0 \) to \( n-1 \). Therefore, for \( n = 4 \), \( l \) can be \( 0, 1, 2, \) or \( 3 \).
- The magnetic quantum number \( m \) (or \( m_l \)) can take values from \( -l \) to \( +l \). Given \( m = 2 \), this means \( l \) must be at least \( 2 \) (since \( m \) cannot exceed \( l \)).
2. **Determining Possible Values of \( l \)**:
- Since \( n = 4 \), the possible values of \( l \) are \( 0, 1, 2, 3 \).
- However, since \( m = 2 \), the only valid values for \( l \) are \( 2 \) and \( 3 \) (as \( m \) must be less than or equal to \( l \)).
3. **Determining Possible Values of Spin \( s \)**:
- The spin quantum number \( s \) can only be \( +\frac{1}{2} \) or \( -\frac{1}{2} \). Therefore, the electron can have either of these two values.
4. **Evaluating the Statements**:
- **Statement A**: "Value of \( l \) may be \( 2 \)" - This is correct since \( l \) can indeed be \( 2 \).
- **Statement B**: "Value of \( l \) may be \( 3 \)" - This is also correct since \( l \) can be \( 3 \).
- **Statement C**: "Value of \( s \) may be \( +\frac{1}{2} \)" - This is correct as \( s \) can be either \( +\frac{1}{2} \) or \( -\frac{1}{2} \).
- **Statement D**: "Value of \( l \) may be \( 0, 1, 2, 3 \)" - This is incorrect because \( l \) cannot be \( 0 \) or \( 1 \) in this case.
5. **Conclusion**:
- The correct statements are A, B, and C. Statement D is incorrect.
### Final Answer:
The correct statements for an electron with quantum numbers \( n = 4 \) and \( m = 2 \) are:
- A: Value of \( l \) may be \( 2 \) (Correct)
- B: Value of \( l \) may be \( 3 \) (Correct)
- C: Value of \( s \) may be \( +\frac{1}{2} \) (Correct)
- D: Value of \( l \) may be \( 0, 1, 2, 3 \) (Incorrect)
