Which of the following complexes are paramagnetic in nature ?
`[Fe(CN)_(6)]^(3-), [Fe(CN)_6]^(4-) , [CoF_6]^(3-), Ni(CO)_(4)`.

Options

A. I and IV
B. I and II
C. I and III
D. III and IV

Answer

To determine which of the given complexes are paramagnetic in nature, we need to analyze the electronic configurations of the metal ions in each complex and the effect of the ligands on the electron filling in the d-orbitals.

### Step-by-Step Solution:

1. **Identify the oxidation states of the metal ions in each complex**:
- For `[Fe(CN)₆]^(3-)`: Iron is in the +3 oxidation state.
- For `[Fe(CN)₆]^(4-)`: Iron is in the +2 oxidation state.
- For `[CoF₆]^(3-)`: Cobalt is in the +3 oxidation state.
- For `Ni(CO)₄`: Nickel is in the 0 oxidation state.

2. **Determine the electronic configurations of the metal ions**:
- **Iron (Fe)**:
- Fe (atomic number 26): Ground state configuration is [Ar] 4s² 3d⁶.
- Fe³⁺: [Ar] 3d⁵ (removing 3 electrons from 4s and 3d).
- Fe²⁺: [Ar] 3d⁶ (removing 2 electrons from 4s and 3d).
- **Cobalt (Co)**:
- Co (atomic number 27): Ground state configuration is [Ar] 4s² 3d⁷.
- Co³⁺: [Ar] 3d⁶ (removing 3 electrons).
- **Nickel (Ni)**:
- Ni (atomic number 28): Ground state configuration is [Ar] 4s² 3d⁸.

3. **Consider the ligands and their field strength**:
- **Cyanide (CN⁻)**: A strong field ligand that causes pairing of electrons.
- **Fluoride (F⁻)**: A weak field ligand that does not cause significant pairing.
- **Carbon monoxide (CO)**: A strong field ligand that causes pairing of electrons.

4. **Fill the d-orbitals according to the ligand field theory**:
- For `[Fe(CN)₆]^(3-)` (Fe³⁺, 3d⁵):
- Strong field ligand (CN⁻) will cause pairing. Configuration: ↑↓ ↑↓ ↑↓ ↑ ↑ (5 unpaired electrons).
- **Result**: Paramagnetic (5 unpaired electrons).

- For `[Fe(CN)₆]^(4-)` (Fe²⁺, 3d⁶):
- Strong field ligand (CN⁻) will cause pairing. Configuration: ↑↓ ↑↓ ↑ ↑ (4 unpaired electrons).
- **Result**: Paramagnetic (4 unpaired electrons).

- For `[CoF₆]^(3-)` (Co³⁺, 3d⁶):
- Weak field ligand (F⁻) will not cause pairing. Configuration: ↑ ↑ ↑ ↑ ↑ (6 electrons filled, 4 paired).
- **Result**: Paramagnetic (4 unpaired electrons).

- For `Ni(CO)₄` (Ni, 0 oxidation state, 3d⁸):
- Strong field ligand (CO) will cause pairing. Configuration: ↑↓ ↑↓ ↑↓ ↑ (8 electrons filled, all paired).
- **Result**: Diamagnetic (no unpaired electrons).

5. **Conclusion**:
- The complexes that are paramagnetic are:
- `[Fe(CN)₆]^(3-)`
- `[Fe(CN)₆]^(4-)`
- `[CoF₆]^(3-)`
- The complex that is diamagnetic is:
- `Ni(CO)₄`

### Final Answer:
The paramagnetic complexes are: `[Fe(CN)₆]^(3-)`, `[Fe(CN)₆]^(4-)`, and `[CoF₆]^(3-)`.