Among the following sets of quantum numbers, which one is incorrect for 4d=electron?

Options

A. 4,3,2,+1/2
B. 4,2,1,+1/2
C. 4,2,-2,+1/2
D. 4,2,1,-1/2

Answer

To determine which set of quantum numbers is incorrect for a 4d electron, we need to understand the quantum numbers associated with the 4d orbital.

### Step-by-Step Solution:

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

2. **Identify the azimuthal quantum number (l)**:
- The azimuthal quantum number \( l \) corresponds to the type of orbital:
- \( s \) orbitals have \( l = 0 \)
- \( p \) orbitals have \( l = 1 \)
- \( d \) orbitals have \( l = 2 \)
- \( f \) orbitals have \( l = 3 \)
- Since we are dealing with a d orbital, \( l \) for 4d is 2.

3. **Identify the magnetic quantum number (m_l)**:
- The magnetic quantum number \( m_l \) can take values from \( -l \) to \( +l \). For \( l = 2 \):
- Possible values of \( m_l \) are: -2, -1, 0, +1, +2.

4. **Identify the spin quantum number (m_s)**:
- The spin quantum number \( m_s \) can have values of \( +\frac{1}{2} \) or \( -\frac{1}{2} \).

5. **Evaluate the given sets of quantum numbers**:
- We need to check each set of quantum numbers to see if they conform to the rules established above.

- **Example sets**:
- Set 1: (4, 2, 4, 2) → \( n = 4, l = 2, m_l = 4, m_s = 2 \) (Incorrect, as \( m_l \) should be between -2 and +2)
- Set 2: (4, 2, 2, +1/2) → \( n = 4, l = 2, m_l = 2, m_s = +1/2 \) (Correct)
- Set 3: (4, 2, -1, -1/2) → \( n = 4, l = 2, m_l = -1, m_s = -1/2 \) (Correct)
- Set 4: (4, 2, 0, +1/2) → \( n = 4, l = 2, m_l = 0, m_s = +1/2 \) (Correct)

6. **Conclusion**:
- The incorrect set of quantum numbers for a 4d electron is (4, 2, 4, 2) because the value of \( m_l \) is outside the permissible range.

### Final Answer:
The incorrect set of quantum numbers for a 4d electron is (4, 2, 4, 2).