Which of the following are diamagnetic?
(I) `K_(4)[Fe(CN)_(6)]`
(II) `K_(3)[Cr(CN)_(6)]`
(III) `K_(3)[Co(CN)_(6)]`
(IV) `K_(2)[Ni(CN)_(4)]`
Select the correct answer using the codes given below:

Options

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

Answer

To determine which of the given coordination compounds are diamagnetic, we will analyze each compound step by step, focusing on the oxidation state of the central metal ion, its electron configuration, and the effect of the ligands on electron pairing.

### Step 1: Analyze `K₄[Fe(CN)₆]`
1. **Determine the oxidation state of Fe**:
- The overall charge of the complex is -4.
- CN is a -1 ligand, and there are 6 CN ligands:
\[ x + 6(-1) = -4 \implies x - 6 = -4 \implies x = +2 \]
- Therefore, Fe is in the +2 oxidation state.

2. **Electron configuration of Fe²⁺**:
- The ground state configuration of Fe is [Ar] 4s² 3d⁶.
- For Fe²⁺, it loses two electrons from the 4s orbital:
\[ \text{Fe}^{2+}: [Ar] 3d^6 \]

3. **Effect of CN⁻ (strong field ligand)**:
- CN⁻ is a strong field ligand and causes pairing of electrons.
- The electron configuration in the 3d orbitals will be:
\[ \uparrow\downarrow \, \uparrow\downarrow \, \uparrow\downarrow \, \uparrow \, \uparrow \]
- All electrons are paired, indicating that this complex is **diamagnetic**.

### Step 2: Analyze `K₃[Cr(CN)₆]`
1. **Determine the oxidation state of Cr**:
- The overall charge of the complex is -3.
- Using the same logic as above:
\[ x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3 \]
- Therefore, Cr is in the +3 oxidation state.

2. **Electron configuration of Cr³⁺**:
- The ground state configuration of Cr is [Ar] 4s² 3d⁵.
- For Cr³⁺, it loses three electrons (two from 4s and one from 3d):
\[ \text{Cr}^{3+}: [Ar] 3d^3 \]

3. **Effect of CN⁻ (strong field ligand)**:
- Pairing occurs, but there are still unpaired electrons:
\[ \uparrow \, \uparrow \, \uparrow \]
- This complex has unpaired electrons, indicating that it is **paramagnetic**.

### Step 3: Analyze `K₃[Co(CN)₆]`
1. **Determine the oxidation state of Co**:
- The overall charge of the complex is -3.
- Using the same logic:
\[ x + 6(-1) = -3 \implies x - 6 = -3 \implies x = +3 \]
- Therefore, Co is in the +3 oxidation state.

2. **Electron configuration of Co³⁺**:
- The ground state configuration of Co is [Ar] 4s² 3d⁷.
- For Co³⁺, it loses three electrons (two from 4s and one from 3d):
\[ \text{Co}^{3+}: [Ar] 3d^6 \]

3. **Effect of CN⁻ (strong field ligand)**:
- Strong field ligand causes pairing:
\[ \uparrow\downarrow \, \uparrow\downarrow \, \uparrow\downarrow \, \uparrow \]
- All electrons are paired, indicating that this complex is **diamagnetic**.

### Step 4: Analyze `K₂[Ni(CN)₄]`
1. **Determine the oxidation state of Ni**:
- The overall charge of the complex is -2.
- Using the same logic:
\[ x + 4(-1) = -2 \implies x - 4 = -2 \implies x = +2 \]
- Therefore, Ni is in the +2 oxidation state.

2. **Electron configuration of Ni²⁺**:
- The ground state configuration of Ni is [Ar] 4s² 3d⁸.
- For Ni²⁺, it loses two electrons from the 4s orbital:
\[ \text{Ni}^{2+}: [Ar] 3d^8 \]

3. **Effect of CN⁻ (strong field ligand)**:
- Strong field ligand causes pairing:
\[ \uparrow\downarrow \, \uparrow\downarrow \, \uparrow\downarrow \, \uparrow \, \uparrow \]
- All electrons are paired, indicating that this complex is **diamagnetic**.

### Conclusion
Based on the analysis:
- **Diamagnetic complexes**: `K₄[Fe(CN)₆]`, `K₃[Co(CN)₆]`, `K₂[Ni(CN)₄]`
- **Paramagnetic complex**: `K₃[Cr(CN)₆]`

Thus, the correct answer is **(I), (III), and (IV)**, which corresponds to option **B**.