For an octahedral complex, which of the following d electron configuration will give maximum crystal-field stabilisation energy?

Options

A. High spin `d^(6)`
B. Low - spin `d^(4)`
C. Low spin `d^(5)`
D. High - spin `d^(7)`

Explanation

To determine which d electron configuration gives the maximum crystal-field stabilization energy (CFSE) for an octahedral complex, we need to analyze the electronic configurations provided and calculate their respective CFSE values.

### Step-by-Step Solution:

1. **Understand the Crystal Field Theory (CFT)**:
- In an octahedral complex, the d orbitals split into two sets: the lower-energy t2g (three orbitals) and the higher-energy eg (two orbitals).
- The energy difference between these two sets is denoted as Δ (delta).

2. **Identify the Electron Configurations**:
- We will consider the following configurations:
- High spin d6
- Low spin d4
- Low spin d5
- High spin d5

3. **Calculate CFSE for Each Configuration**:
- **High Spin d6**:
- Configuration: t2g^4 eg^2
- CFSE = (Number of electrons in t2g × -0.4Δ) + (Number of electrons in eg × +0.6Δ)
- CFSE = (4 × -0.4Δ) + (2 × +0.6Δ) = -1.6Δ + 1.2Δ = -0.4Δ

- **Low Spin d4**:
- Configuration: t2g^4 eg^0
- CFSE = (4 × -0.4Δ) + (0 × +0.6Δ) = -1.6Δ

- **Low Spin d5**:
- Configuration: t2g^5 eg^0
- CFSE = (5 × -0.4Δ) + (0 × +0.6Δ) = -2.0Δ

- **High Spin d5**:
- Configuration: t2g^3 eg^2
- CFSE = (3 × -0.4Δ) + (2 × +0.6Δ) = -1.2Δ + 1.2Δ = 0Δ

4. **Compare the CFSE Values**:
- High Spin d6: -0.4Δ
- Low Spin d4: -1.6Δ
- Low Spin d5: -2.0Δ
- High Spin d5: 0Δ

5. **Determine Maximum CFSE**:
- The highest value (least negative) is 0Δ from the high spin d5 configuration. Therefore, the configuration with maximum crystal-field stabilization energy is the high spin d5.

### Final Answer:
The d electron configuration that gives the maximum crystal-field stabilization energy in an octahedral complex is **High Spin d5**.