Which one of the following set of quantum numbers is not possible for 4p electron?

Options

A. `n = 4 , l = 1 , m - 1 , m_(s) = + (1)/(2)`
B. `n = 4, l = 1, m=0,m_(s) = +(1)/(2)`
C. `n = 4,l = 1,m=2,m_(s) + (1)/(2)`
D. `n=4,l=1,m=-1,m_(2) = - (1)/(2)`

Explanation

To determine which set of quantum numbers is not possible for a 4p electron, we need to understand the quantum numbers associated with the electron configuration.

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- For a 4p electron, the principal quantum number \( n \) is 4.

2. **Determine the Azimuthal Quantum Number (l)**:
- The azimuthal quantum number \( l \) for a p orbital is always 1 (since \( l = 0 \) for s, \( l = 1 \) for p, \( l = 2 \) for d, etc.).

3. **Calculate the Magnetic Quantum Number (m)**:
- The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \). Therefore, for \( l = 1 \):
- \( m \) can be \( -1, 0, +1 \).

4. **Set of Quantum Numbers**:
- The complete set of quantum numbers for a 4p electron can be represented as:
- \( n = 4 \)
- \( l = 1 \)
- \( m = -1, 0, +1 \)
- The spin quantum number \( s \) can be either \( +\frac{1}{2} \) or \( -\frac{1}{2} \).

5. **Identify the Incorrect Set**:
- Now, we need to evaluate the provided options to find a set of quantum numbers that does not fit the criteria for a 4p electron.
- Any set that has \( l \) not equal to 1 or \( m \) outside the range of -1 to +1 will be invalid.

6. **Conclusion**:
- If we find a set where \( l \) is not 1 or \( m \) is -2 or +2, that set is not possible for a 4p electron.
- For example, if we have \( (n=4, l=1, m=-2) \), this set is invalid because \( m \) cannot be -2 when \( l = 1 \).

### Final Answer:
The set of quantum numbers that is not possible for a 4p electron is the one where \( m \) is outside the range of -1 to +1, such as \( (n=4, l=1, m=-2) \).

---