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Step 1: Understanding HybridizationHybridization is the concept of mixing atomic orbitals to form new hybrid orbitals. The type of hybridization depends on the number of sigma bonds and lone pairs around the central atom. In this case, we will analyze the hybridization of each carbon atom in the given molecule.
Step 2: Analyzing Carbon 1 ($C_1$)Carbon 1 is bonded to two other carbon atoms and has one hydrogen atom attached. This means it forms three sigma bonds. The hybridization for three sigma bonds is $sp^2$. Therefore, the hybridization of Carbon 1 is $sp^2$.
Step 3: Analyzing Carbon 2 ($C_2$)Carbon 2 is bonded to one carbon atom and has one hydrogen atom attached. It has one double bond (with Carbon 1) and one single bond (with Carbon 3). This means it forms two sigma bonds and one pi bond. The hybridization for two sigma bonds is $sp$. Therefore, the hybridization of Carbon 2 is $sp$.
Step 4: Analyzing Carbon 3 ($C_3$)Carbon 3 is bonded to two other carbon atoms and has one hydrogen atom attached. This means it forms three sigma bonds. The hybridization for three sigma bonds is $sp^2$. Therefore, the hybridization of Carbon 3 is $sp^2$.
Step 5: Analyzing Carbon 4 ($C_4$)Carbon 4 is bonded to three hydrogen atoms. This means it forms four sigma bonds. The hybridization for four sigma bonds is $sp^3$. Therefore, the hybridization of Carbon 4 is $sp^3$.
Step 6: ConclusionBased on the analysis, the hybridization of the carbon atoms in the molecule is as follows:Carbon 1: $sp^2$, Carbon 2: $sp$, Carbon 3: $sp^2$, Carbon 4: $sp^3$. Thus, the correct answer is $sp^2$, $sp$, $sp^2$, $sp^3$.
