Which is a diamagnetic complex?

Options

A. `[Fe(H_(2)O)_(6)]^(3+)`
B. `[Fe(H_(2)O)]^(2+)`
C. `[Fe(CN)_(6)]^(3-)`
D. `[Fe(CN)_(6)]^(4-)`

Answer

To determine which complex is diamagnetic, we need to analyze the oxidation states, electron configurations, and the nature of the ligands involved in each complex. A diamagnetic complex has all its electrons paired, while a paramagnetic complex has unpaired electrons.

### Step-by-Step Solution:

1. **Identify the Complexes**: We are given four complexes with different ligands and need to determine which one is diamagnetic.

2. **Calculate the Oxidation State**:
- For each complex, we will set up the equation based on the charge of the complex and the nature of the ligands.
- For example, if we have a complex with 6 aqua ligands and a total charge of +3, the oxidation state of the central metal ion can be calculated as follows:
\[ x + 0 \cdot 6 = +3 \implies x = +3 \]
- This means the metal ion is in the +3 oxidation state.

3. **Determine Electron Configuration**:
- For Fe in the +3 state, the electron configuration would be:
- Argon core: \( [Ar] \)
- \( 4s^0 \) (since it loses the 4s electrons first)
- Remaining electrons in \( 3d \): \( 3d^5 \) (for +3 oxidation state).
- Thus, the configuration is \( [Ar] 3d^5 \).

4. **Analyze the Ligand Field Strength**:
- Aqua (H2O) is a weak field ligand, while cyano (CN-) is a strong field ligand.
- Weak field ligands do not cause pairing of electrons, while strong field ligands do.

5. **Check for Electron Pairing**:
- For the complexes with weak field ligands (like aqua), the \( 3d^5 \) configuration will remain unpaired, making the complex paramagnetic.
- For complexes with strong field ligands (like cyano), electrons will pair up. For example, in \( 3d^6 \) configuration, strong field ligands will cause pairing, resulting in \( 3d^6 \) having only one unpaired electron, which is still paramagnetic.

6. **Identify the Diamagnetic Complex**:
- Finally, if we analyze the last complex with a strong field ligand and find that all electrons are paired (for instance, \( 3d^6 \) with pairing), this complex will be diamagnetic.
- For example, if we have \( 3d^6 \) with strong field ligands, it could be represented as \( \uparrow\downarrow \, \uparrow\downarrow \, \uparrow\downarrow \, \uparrow \) (all paired), indicating that it is diamagnetic.

7. **Conclusion**:
- After analyzing all complexes, we find that the last complex (let's say option D) is diamagnetic because all electrons are paired.

### Final Answer:
The diamagnetic complex is **Option D**.