In aldehydes, the carbonyl group is bonded to a carbon and hydrogen, while in ketones it is bonded to two carbon atoms. The carbonyl group is bonded to oxygen are known as carboxylic acid and their derivatives.

The hybridization of the \(C\) in the carbonyl group is:

\(sp^2\)

The correct answer is option 2. \(sp^2\).

Let us go into detail about the hybridization of the carbon atom in a carbonyl group (\(C=O\)).

In a carbonyl group, the carbon atom is double-bonded to an oxygen atom. The carbon atom in the carbonyl group undergoes \(sp^2\) hybridization, and here's how it happens:

1. \(s\) Orbital:

The carbon atom contributes one \(2s\) orbital to the hybridization.

2. \(p\) Orbitals:

The carbon atom contributes two \(2p\) orbitals to the hybridization.

3. Hybrid Orbitals:

The \(2s\) and two \(2p\) orbitals undergo hybridization to form three \(sp^2\) hybrid orbitals. These hybrid orbitals are oriented in a trigonal planar arrangement.

4. Sigma Bond (\(\sigma\)):

One of the \(sp^2\) hybrid orbitals forms a sigma bond (\(\sigma\)) with the oxygen atom by overlapping with the oxygen's \(2p\) orbital.

5. Pi Bonds (\(\pi\)):

The remaining two \(sp^2\) hybrid orbitals on carbon overlap with the \(2p\) orbitals of the oxygen atom to form two pi bonds (\(\pi\)). These pi bonds are located above and below the plane of the sigma bond.

The resulting structure is a trigonal planar arrangement around the carbon atom with a sigma bond and two pi bonds. This hybridization allows for the formation of a stable and planar carbonyl group commonly found in various organic compounds, such as aldehydes and ketones.