In a free radical, the carbon atom carrying unpaired electron is

Options

A. sp hybridised
B. `sp^2` hybridised
C. `sp^3` hybridised
D. `dsp^2` hybridised

Explanation

To determine the hybridization of the carbon atom carrying an unpaired electron in a free radical, we can follow these steps:

### Step 1: Understand the Structure of a Free Radical
A free radical is a species that contains an unpaired electron. In organic chemistry, free radicals often involve carbon atoms that have three bonds and one unpaired electron.

### Step 2: Identify the Hybridization of Carbon
The hybridization of a carbon atom can be determined based on the number of bonds it forms:
- **sp hybridization**: 2 bond pairs (linear geometry)
- **sp2 hybridization**: 3 bond pairs (trigonal planar geometry)
- **sp3 hybridization**: 4 bond pairs (tetrahedral geometry)
- **dsp2 hybridization**: 4 bond pairs with a d orbital involved (not common for carbon)

### Step 3: Analyze the Free Radical
In a free radical, the carbon atom typically forms three bonds (either with hydrogen atoms or other carbon atoms). This means that the carbon atom is involved in three bond pairs.

### Step 4: Determine the Hybridization
Since the carbon atom in the free radical forms three bonds, it will undergo **sp2 hybridization**. The remaining p orbital, which is unhybridized, will contain the unpaired electron.

### Step 5: Conclusion
Thus, the carbon atom carrying the unpaired electron in a free radical is **sp2 hybridized**.

### Final Answer
The correct answer is **sp2 hybridized**.

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