Which one of the following compounds has `sp^(2)` hybridisation ? .

Options

A. `CO_(2)`
B. `SO_(2)`
C. `N_(2)O`
D. `CO`

Explanation

To determine which compound has `sp²` hybridization, we can use the concept of steric number, which is calculated using the formula:

\[ \text{Steric Number} = \frac{1}{2} \left( \text{Number of Valence Electrons} + \text{Number of Monovalent Atoms} - \text{Cationic Charge} + \text{Anionic Charge} \right) \]

Let's analyze the given compounds one by one.

### Step 1: Analyze CO₂
- **Valence Electrons of Carbon**: 4
- **Monovalent Atoms**: 0
- **Cationic Charge**: 0
- **Anionic Charge**: 0

Using the formula:
\[ \text{Steric Number} = \frac{1}{2} (4 + 0 - 0 + 0) = \frac{4}{2} = 2 \]
This indicates `sp` hybridization.

### Step 2: Analyze SO₂
- **Valence Electrons of Sulfur**: 6
- **Monovalent Atoms**: 0
- **Cationic Charge**: 0
- **Anionic Charge**: 0

Using the formula:
\[ \text{Steric Number} = \frac{1}{2} (6 + 0 - 0 + 0) = \frac{6}{2} = 3 \]
This indicates `sp²` hybridization.

### Step 3: Analyze N₂O
- For the terminal nitrogen:
- **Bond Pairs**: 1 (triple bond contributes 1 sigma bond)
- **Lone Pairs**: 1

Using the formula:
\[ \text{Hybridization} = \text{Bond Pairs} + \text{Lone Pairs} = 1 + 1 = 2 \]
This indicates `sp` hybridization.

- For the central nitrogen:
- **Bond Pairs**: 2 (two sigma bonds)
- **Lone Pairs**: 0

Using the formula:
\[ \text{Hybridization} = 2 + 0 = 2 \]
This indicates `sp` hybridization.

- For oxygen:
- **Bond Pairs**: 1 (one sigma bond)
- **Lone Pairs**: 3

Using the formula:
\[ \text{Hybridization} = 1 + 3 = 4 \]
This indicates `sp³` hybridization.

### Step 4: Analyze CO
- **Valence Electrons of Carbon**: 4
- **Monovalent Atoms**: 0
- **Cationic Charge**: 0
- **Anionic Charge**: 0

Using the formula:
\[ \text{Steric Number} = \frac{1}{2} (4 + 0 - 0 + 0) = \frac{4}{2} = 2 \]
This indicates `sp` hybridization.

### Conclusion
From the analysis:
- CO₂: `sp` hybridization
- SO₂: `sp²` hybridization
- N₂O: `sp` and `sp³` hybridization
- CO: `sp` hybridization

Thus, the compound with `sp²` hybridization is **SO₂**.