Which of the following system has maximum number of unpaired electrons ?

Options

A. `d^(4)`(octahedral , low spin )
B. `d^(6)`(tetrahedral , high spin )
C. `d^(6)`(octahedral , low spin )
D. `d^(9)`(octahedral)

Answer

To determine which of the given systems has the maximum number of unpaired electrons, we will analyze each option step by step.

### Step 1: Analyze D4 Octahedral Low Spin
- **Configuration**: D4
- **Type**: Octahedral, Low Spin
- **Electron Filling**: In an octahedral field, the d-orbitals split into two sets: T2g (lower energy) and Eg (higher energy).
- **Filling Order**:
- Fill the T2g orbitals first: 3 electrons fill T2g (1, 2, 3).
- Then, pairing occurs in T2g: 2 electrons pair up (4, 5).
- **Unpaired Electrons**: 2 (from T2g).

### Step 2: Analyze D6 Tetrahedral High Spin
- **Configuration**: D6
- **Type**: Tetrahedral, High Spin
- **Electron Filling**: In a tetrahedral field, the d-orbitals split into two sets: E (lower energy) and T2 (higher energy).
- **Filling Order**:
- Fill the E orbitals first: 4 electrons fill E (1, 2, 3, 4).
- Then fill T2 orbitals: 5th and 6th electrons fill T2 (5, 6).
- **Unpaired Electrons**: 4 (1 in each of the 4 orbitals).

### Step 3: Analyze D6 Octahedral Low Spin
- **Configuration**: D6
- **Type**: Octahedral, Low Spin
- **Electron Filling**: In an octahedral field, the d-orbitals split into T2g and Eg.
- **Filling Order**:
- Fill T2g first: 6 electrons fill T2g (1, 2, 3, 4, 5, 6).
- Since it is low spin, pairing occurs immediately.
- **Unpaired Electrons**: 0 (all electrons are paired).

### Step 4: Analyze D9 Octahedral
- **Configuration**: D9
- **Type**: Octahedral
- **Electron Filling**: In an octahedral field, the d-orbitals split into T2g and Eg.
- **Filling Order**:
- Fill T2g first: 6 electrons fill T2g (1, 2, 3, 4, 5, 6).
- Fill Eg: 7th, 8th, and 9th electrons fill Eg (7, 8, 9).
- **Unpaired Electrons**: 1 (the last electron in Eg).

### Conclusion
After analyzing all options:
- D4 Octahedral Low Spin: 2 unpaired electrons
- D6 Tetrahedral High Spin: 4 unpaired electrons
- D6 Octahedral Low Spin: 0 unpaired electrons
- D9 Octahedral: 1 unpaired electron

**Maximum number of unpaired electrons is in the D6 Tetrahedral High Spin system, which has 4 unpaired electrons.**

### Final Answer
**The system with the maximum number of unpaired electrons is D6 Tetrahedral High Spin with 4 unpaired electrons.**