Which of the following represent(s) the correct set of four quantum numbers of a 5d electron ?

Options

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

Answer

To determine the correct set of four quantum numbers for a 5d electron, we need to understand the definitions and values of each quantum number:

1. **Principal Quantum Number (n)**: This quantum number indicates the energy level or shell in which the electron resides. For a 5d electron, the principal quantum number \( n \) is 5.

2. **Azimuthal Quantum Number (l)**: This quantum number describes the shape of the orbital. The values of \( l \) can range from 0 to \( n-1 \). For d orbitals, \( l \) is equal to 2. Therefore, for a 5d electron, \( l = 2 \).

3. **Magnetic Quantum Number (m_l)**: This quantum number describes the orientation of the orbital in space. The values of \( m_l \) range from \(-l\) to \(+l\), including 0. For \( l = 2 \), the possible values for \( m_l \) are -2, -1, 0, +1, and +2.

4. **Spin Quantum Number (m_s)**: This quantum number indicates the spin orientation of the electron. The possible values are \( +\frac{1}{2} \) (up spin) and \( -\frac{1}{2} \) (down spin).

Now, summarizing the quantum numbers for a 5d electron:
- \( n = 5 \)
- \( l = 2 \)
- \( m_l = -2, -1, 0, +1, +2 \) (any of these values can be chosen)
- \( m_s = +\frac{1}{2} \) or \( -\frac{1}{2} \) (any of these values can be chosen)

### Conclusion:
For a 5d electron, the correct set of quantum numbers should include \( n = 5 \), \( l = 2 \), and appropriate values for \( m_l \) and \( m_s \). Since all options provided in the question have \( n = 4 \), they are incorrect.