Which one of the following metal carbonyls involves the `d^2sp^3` hybridisation for the formation of metal-carbon `sigma` bonds and is paramagnetic ?

Options

A. `[Cr(CO)_6]`
B. `[V(CO)_6]`
C. `[Mo(CO)_6]`
D. `[W(CO)_6]`

Explanation

To solve the question of which metal carbonyl involves `d^2sp^3` hybridization for the formation of metal-carbon sigma bonds and is paramagnetic, we will analyze the given options step by step.

### Step 1: Identify the Metal and its Electronic Configuration
We will analyze the electronic configuration of the metals involved in the carbonyl complexes.

1. **Chromium (Cr)**: Atomic number = 24
- Electronic configuration: [Ar] 4s¹ 3d⁵

2. **Vanadium (V)**: Atomic number = 23
- Electronic configuration: [Ar] 4s² 3d³

3. **Molybdenum (Mo)**: Atomic number = 42
- Electronic configuration: [Kr] 5s¹ 4d⁵

4. **Tungsten (W)**: Atomic number = 74
- Electronic configuration: [Xe] 6s² 4f¹⁴ 5d⁴

### Step 2: Determine the Effect of CO as a Ligand
CO is a strong field ligand, which means it will cause pairing of electrons in the d-orbitals of the metal.

### Step 3: Analyze Each Metal Carbonyl
1. **Cr(CO)₆**:
- Configuration after pairing: 4s² 3d⁴ (all electrons paired)
- Hybridization: d²sp³
- Magnetic property: Diamagnetic (no unpaired electrons)

2. **V(CO)₆**:
- Configuration after pairing: 4s² 3d³ (one unpaired electron)
- Hybridization: d²sp³
- Magnetic property: Paramagnetic (one unpaired electron)

3. **Mo(CO)₆**:
- Configuration after pairing: 5s² 4d⁴ (all electrons paired)
- Hybridization: d²sp³
- Magnetic property: Diamagnetic (no unpaired electrons)

4. **W(CO)₆**:
- Configuration after pairing: 6s² 5d⁴ (all electrons paired)
- Hybridization: d²sp³
- Magnetic property: Diamagnetic (no unpaired electrons)

### Step 4: Conclusion
From the analysis, we find that the only metal carbonyl that exhibits `d²sp³` hybridization and is paramagnetic is **V(CO)₆**.

### Final Answer
**V(CO)₆** is the metal carbonyl that involves `d²sp³` hybridization for the formation of metal-carbon sigma bonds and is paramagnetic.

---