`d^(6)` configuration will result in total spin of :

Options

A. `3/2`
B. `1/2`
C. `2`
D. `1`

Answer

To determine the total spin for a \(d^6\) electron configuration, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Electron Configuration**:
- The \(d\) subshell can hold a maximum of 10 electrons (5 orbitals, each can hold 2 electrons).
- For \(d^6\), there are 6 electrons in the \(d\) orbitals.

2. **Apply Hund's Rule**:
- According to Hund's rule, electrons will fill degenerate orbitals (orbitals of the same energy) singly before pairing up.
- Therefore, the first 5 electrons will each occupy one of the 5 \(d\) orbitals singly.

3. **Distribute the Electrons**:
- The first 5 electrons will occupy the 5 \(d\) orbitals with parallel spins (let's assume all are spin-up).
- The 6th electron will pair up with one of the already occupied orbitals.

4. **Count the Spins**:
- For the 5 electrons in the \(d\) orbitals, each contributes a spin of \(+\frac{1}{2}\).
- The 6th electron, which is paired, will contribute a spin of \(-\frac{1}{2}\).

5. **Calculate the Total Spin**:
- Total spin = (Number of spin-up electrons) \(\times \frac{1}{2} + (Number of spin-down electrons) \times (-\frac{1}{2})\)
- Here, we have 5 spin-up electrons and 1 spin-down electron.
- Total spin = \(5 \times \frac{1}{2} + 1 \times (-\frac{1}{2})\)
- Total spin = \(\frac{5}{2} - \frac{1}{2} = \frac{4}{2} = 2\)

6. **Final Result**:
- The total spin for the \(d^6\) configuration is **2**.