Which of the following configuration of ions has zero CFSE in both strong and weak ligand fields ?

Options

A. `d^(10)`
B. `d^(8)`
C. `d^(6)`
D. `d^(4)`

Answer

To solve the question of which ion configuration has zero Crystal Field Stabilization Energy (CFSE) in both strong and weak ligand fields, we can follow these steps:

### Step 1: Understand CFSE
Crystal Field Stabilization Energy (CFSE) is the energy gained when electrons occupy the lower energy d orbitals (t2g) over the higher energy d orbitals (eg) in the presence of ligands. The CFSE can be calculated based on the number of electrons in these orbitals.

### Step 2: Identify the Electron Configurations
The question provides four configurations:
1. D10
2. D8
3. D6
4. D4

### Step 3: Analyze D10 Configuration
- In a D10 configuration, all five d orbitals are fully occupied (2 electrons in each orbital).
- When ligands approach, the d orbitals split into two sets: t2g (lower energy) and eg (higher energy).
- Since all orbitals are filled, there is no pairing of electrons, and thus, the CFSE is zero.

### Step 4: Analyze D8 Configuration
- In a D8 configuration, there are 8 electrons.
- The filling would typically lead to some electrons occupying the eg orbitals, which would result in a CFSE.
- The calculation for CFSE in D8 would show a non-zero value, indicating stabilization but not zero.

### Step 5: Analyze D6 Configuration
- In a D6 configuration, electrons can occupy both t2g and eg orbitals depending on whether the field is strong or weak.
- This configuration can lead to either high-spin or low-spin arrangements, resulting in non-zero CFSE.

### Step 6: Analyze D4 Configuration
- Similarly, in a D4 configuration, the electrons can also occupy both sets of orbitals, leading to non-zero CFSE.

### Step 7: Conclusion
From the analysis, only the D10 configuration has zero CFSE in both strong and weak ligand fields. The other configurations (D8, D6, and D4) result in non-zero CFSE due to the presence of unpaired electrons and the need for pairing in certain cases.

### Final Answer
The correct answer is **D10 configuration**.

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