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 significance of each quantum number:

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

2. **Azimuthal Quantum Number (l)**: This describes the subshell or shape of the orbital. The value of \( l \) for d orbitals is 2.

3. **Magnetic Quantum Number (m)**: This specifies the orientation of the orbital in space. The possible values of \( m \) for \( l = 2 \) (d orbital) range from \( -l \) to \( +l \). Therefore, \( m \) can take values of -2, -1, 0, +1, and +2.

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

Now, let's summarize the quantum numbers for a 5d electron:

- \( n = 5 \) (principal quantum number)
- \( l = 2 \) (azimuthal quantum number for d)
- \( m = -2, -1, 0, +1, +2 \) (magnetic quantum number)
- \( s = +\frac{1}{2} \) or \( s = -\frac{1}{2} \) (spin quantum number)

Given this information, we can conclude that any correct set of quantum numbers for a 5d electron must include \( n = 5 \), \( l = 2 \), a valid \( m \) value from the set \{-2, -1, 0, +1, +2\}, and either \( s = +\frac{1}{2} \) or \( s = -\frac{1}{2} \).

### Conclusion:
If none of the options provided in the question meet these criteria, then all options would be incorrect.