In allene ({C_3}{H_4}), the type(s) of hybridization of the carbon atom is (are):A. s{p^2} and spB. s{p^2} and s{p^3}C. spand s{p^3}D. only s{p^2}

To determine the hybridization of the carbon atoms in allene (\( \text{C}_3\text{H}_4 \)), let’s examine the structure of allene.

### Structure of Allene

Allene has a linear structure around the central carbon atom with the formula:

\[ \text{H}_2\text{C}=\text{C}=\text{CH}_2 \]

In this structure:
- The central carbon is double-bonded to each of the two outer carbon atoms.
- The two outer carbon atoms are each bonded to two hydrogen atoms.

### Hybridization Analysis

1. **Central Carbon Atom:**
- The central carbon in allene forms two double bonds with the two outer carbons. Each double bond consists of one sigma bond and one pi bond.
- Therefore, the central carbon forms a total of two sigma bonds and two pi bonds, which requires \( \text{sp} \) hybridization (since \( \text{sp} \) hybridization results in two sp hybrid orbitals and two unhybridized p orbitals, which are used for pi bonding).

2. **Outer Carbon Atoms:**
- Each outer carbon atom forms two sigma bonds (one with the central carbon and one with a hydrogen) and has one pi bond with the central carbon.
- This requires \( \text{sp}^2 \) hybridization for each of these outer carbon atoms (since \( \text{sp}^2 \) hybridization results in three sp² hybrid orbitals and one unhybridized p orbital for the pi bond).

### Summary

- The central carbon in allene is \( \text{sp} \) hybridized.
- The outer carbons in allene are \( \text{sp}^2 \) hybridized.

Thus, the correct answer is:

**A. \( \text{sp}^2 \) and \( \text{sp} \)**