In which structure crystal field splitting energey `(CFSE)` for octahedral complex will be zero when `DeltaltP` .

Options

A. `d^(5)`
B. `d^(6)`
C. `d^(8)`
D. `d^(10)`

Explanation

To solve the question regarding the crystal field splitting energy (CFSE) for octahedral complexes when Δ < P, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Terms**:
- **Crystal Field Splitting Energy (CFSE)**: This is the energy difference between the split d-orbitals in a crystal field.
- **Δ (Delta)**: Represents the crystal field splitting energy.
- **P (Pairing Energy)**: The energy required to pair up electrons in the same orbital.

2. **Identifying the Condition**:
- The condition given is Δ < P, which indicates a weak field ligand scenario. In this case, the pairing of electrons is less favorable, leading to high spin complexes.

3. **Electron Configuration in Octahedral Complex**:
- In an octahedral field, the d-orbitals split into two sets:
- **T2g (lower energy)**: Contains three orbitals.
- **Eg (higher energy)**: Contains two orbitals.

4. **Filling the d-Orbitals**:
- For a high spin complex (where Δ < P), electrons will occupy the T2g and Eg orbitals without pairing until all orbitals are singly occupied.
- For example, in a d5 configuration, the electrons will fill as follows:
- T2g: 3 electrons (one in each orbital)
- Eg: 2 electrons (one in each orbital)

5. **Calculating CFSE**:
- The CFSE can be calculated using the formula:
\[ \text{CFSE} = (n_{T2g} \times -0.4 \Delta) + (n_{Eg} \times 0.6 \Delta) \]
- For a d5 configuration:
- \( n_{T2g} = 3 \) and \( n_{Eg} = 2 \)
- CFSE = \( (3 \times -0.4 \Delta) + (2 \times 0.6 \Delta) \)
- CFSE = \( -1.2 \Delta + 1.2 \Delta = 0 \)

6. **Conclusion**:
- The CFSE for a d5 configuration in an octahedral complex is zero when Δ < P. Similarly, for a d10 configuration, all orbitals are fully filled, leading to a similar CFSE of zero.
- Therefore, the structures where CFSE is zero under the condition Δ < P are d5 and d10 configurations.

### Final Answer:
The CFSE for octahedral complexes will be zero for d5 and d10 configurations when Δ < P.

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