In a carbocation, the central carbon atom involved is

Options

A. sp-hybridized
B. `sp^(2)`-hybridized
C. `sp^(3)` -hybridized
D. `dsp^(2)`-hybridized

Answer

To solve the question about the hybridization of the central carbon atom in a carbocation, we need to analyze the structure of a typical carbocation.

### Step-by-Step Solution:

1. **Understanding Carbocation Structure**:
A carbocation is a positively charged ion where a carbon atom has only three bonds and no complete octet. For example, in the methyl carbocation (CH3+), the central carbon atom is bonded to three hydrogen atoms and has a positive charge.

2. **Counting Sigma Bonds**:
The hybridization of a carbon atom can be determined by counting the number of sigma bonds it forms. In the case of the methyl carbocation (CH3+), the central carbon atom forms three sigma bonds (one with each hydrogen atom).

3. **Determining Lone Pairs**:
In a carbocation, the central carbon atom does not have any lone pairs of electrons. Therefore, the number of lone pairs on the central carbon atom is zero.

4. **Calculating Hybridization Index**:
The hybridization index can be calculated using the formula:
\[ \text{Hybridization Index} = \text{Number of Sigma Bonds} + \text{Number of Lone Pairs} \]
For the methyl carbocation:
- Number of Sigma Bonds = 3
- Number of Lone Pairs = 0
Thus, the hybridization index = 3 + 0 = 3.

5. **Identifying Hybridization Type**:
Based on the hybridization index:
- An index of 2 corresponds to sp hybridization.
- An index of 3 corresponds to sp² hybridization.
- An index of 4 corresponds to sp³ hybridization.
Since the index is 3, the central carbon atom in a carbocation is sp² hybridized.

### Conclusion:
The central carbon atom in a carbocation is **sp² hybridized**.

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