Which of the following is diamagnetic complex

Options

A. `[Co(Ox)_(3)]^(3-),[Fe(CN)_(6)]^(2-)`
B. `[Co(Ox)_(3)]^(3-),[FeF_(6)]^(3-)`
C. `[Fe(Ox)_(3)]^(3-),[FeF_(6)]^(3-)`
D. `[Fe(CN)_(6)]^(2-),[CoF_(6)]^(3-)`

Explanation

To determine which of the given complexes is diamagnetic, we need to analyze each complex based on the presence of unpaired electrons. A diamagnetic complex is one that has no unpaired electrons and is not attracted to a magnetic field.

### Step-by-Step Solution:

1. **Identify the Complexes**: The complexes given are:
- \( \text{COOX}_3^{3-} \) and \( \text{FeCN}_6^{2-} \)
- \( \text{COOX}_3^{3-} \) and \( \text{FeF}_6^{3-} \)
- \( \text{FeOX}_3^{3-} \) and \( \text{FeF}_6^{-} \)
- \( \text{FeCN}_6^{2-} \) and \( \text{COF}_6^{3-} \)

2. **Analyze the First Pair**:
- **For \( \text{COOX}_3^{3-} \)**:
- Oxidation state of Cobalt (Co):
\[ X + 3(-2) = -3 \implies X = +3 \]
- Electronic configuration of \( \text{Co}^{3+} \): \( \text{[Ar]} 3d^6 \)
- Filling the orbitals (strong field ligand):
- Electrons fill as: \( T_{2g}^6 \) (all paired).
- **Conclusion**: No unpaired electrons → Diamagnetic.

- **For \( \text{FeCN}_6^{2-} \)**:
- Oxidation state of Iron (Fe):
\[ X + 6(-1) = -2 \implies X = +4 \]
- Electronic configuration of \( \text{Fe}^{4+} \): \( \text{[Ar]} 3d^4 \)
- Filling the orbitals (strong field ligand):
- Electrons fill as: \( T_{2g}^4 \) (one unpaired electron).
- **Conclusion**: Unpaired electrons → Not diamagnetic.

3. **Analyze the Second Pair**:
- **For \( \text{FeF}_6^{3-} \)**:
- Oxidation state of Iron:
\[ X + 6(-1) = -3 \implies X = +3 \]
- Electronic configuration of \( \text{Fe}^{3+} \): \( \text{[Ar]} 3d^5 \)
- Filling the orbitals (weak field ligand):
- Electrons fill as: \( T_{2g}^3 \) and \( E_g^2 \) (all unpaired).
- **Conclusion**: Unpaired electrons → Not diamagnetic.

4. **Analyze the Third Pair**:
- **For \( \text{FeOX}_3^{3-} \)**:
- Oxidation state of Iron:
\[ X + 3(-2) = -3 \implies X = +3 \]
- Electronic configuration of \( \text{Fe}^{3+} \): \( \text{[Ar]} 3d^5 \)
- Filling the orbitals (strong field ligand):
- Electrons fill as: \( T_{2g}^5 \) (one unpaired electron).
- **Conclusion**: Unpaired electrons → Not diamagnetic.

5. **Analyze the Fourth Pair**:
- **For \( \text{COF}_6^{3-} \)**:
- Oxidation state of Cobalt:
\[ X + 6(-1) = -3 \implies X = +3 \]
- Electronic configuration of \( \text{Co}^{3+} \): \( \text{[Ar]} 3d^6 \)
- Filling the orbitals (weak field ligand):
- Electrons fill as: \( T_{2g}^6 \) (all paired).
- **Conclusion**: No unpaired electrons → Diamagnetic.

### Final Conclusion:
The only diamagnetic complex from the given options is \( \text{COOX}_3^{3-} \).