Which of the following paramagnetic complex with two unpaired electrons

Options

A. `[Fe(CN)_(6)]^(3-)`
B. `[Ni(H_(2)O)_(6)]^(2+)`
C. `[Ti(H_(2)O)_(6)]^(3+)`
D. None of these

Answer

To determine which of the given paramagnetic complexes has two unpaired electrons, we will analyze each complex step by step.

### Step 1: Identify the oxidation state and electron configuration of the central metal ion in each complex.

1. **Fe(CN)₆³⁻:**
- CN⁻ is a strong field ligand.
- The overall charge of the complex is -3, and CN⁻ contributes -6, so the oxidation state of Fe must be +3.
- Iron (Fe) has an atomic number of 26, so its electron configuration is [Ar] 3d⁶ 4s². In the +3 oxidation state, it loses two 4s electrons and one 3d electron, resulting in 3d⁵.
- Therefore, the electron configuration is 3d⁵.

2. **Ni(H₂O)₆²⁺:**
- H₂O is a neutral ligand.
- The overall charge of the complex is +2, so the oxidation state of Ni must be +2.
- Nickel (Ni) has an atomic number of 28, so its electron configuration is [Ar] 3d⁸ 4s². In the +2 oxidation state, it loses two 4s electrons, resulting in 3d⁸.
- Therefore, the electron configuration is 3d⁸.

3. **Ti(H₂O)₆³⁺:**
- H₂O is a neutral ligand.
- The overall charge of the complex is +3, so the oxidation state of Ti must be +3.
- Titanium (Ti) has an atomic number of 22, so its electron configuration is [Ar] 3d² 4s². In the +3 oxidation state, it loses two 4s electrons and one 3d electron, resulting in 3d¹.
- Therefore, the electron configuration is 3d¹.

### Step 2: Determine the number of unpaired electrons in each complex.

1. **Fe(CN)₆³⁻:**
- CN⁻ is a strong field ligand and causes pairing of electrons.
- For 3d⁵, all five electrons will pair up in the lower energy orbitals, resulting in **0 unpaired electrons**.

2. **Ni(H₂O)₆²⁺:**
- H₂O is a weak field ligand and does not cause pairing.
- For 3d⁸, the electron configuration will be:
- 3d: ↑↓ ↑↓ ↑↓ ↑ ↑ (2 paired, 2 unpaired)
- Thus, there are **2 unpaired electrons**.

3. **Ti(H₂O)₆³⁺:**
- H₂O is a weak field ligand and does not cause pairing.
- For 3d¹, there is only **1 unpaired electron**.

### Conclusion:
From the analysis, the complex **Ni(H₂O)₆²⁺** has **2 unpaired electrons** and is the required answer.