In allene `(C_(3)H_(4)),` the type (s) of the carbon atom (s) is (are) :

Options

A. `sp and sp^(3)`
B. `sp and sp^(2)`
C. only `sp^(2)`
D. `sp^(2) and sp^(3).`

Explanation

To determine the types of carbon atoms in allene (C₃H₄), we need to analyze its structure and the hybridization of the carbon atoms involved.

### Step-by-Step Solution:

1. **Identify the Structure of Allene (C₃H₄)**:
- Allene has the molecular formula C₃H₄.
- The structure can be represented as:
```
H H
\ /
C
/ \
C C
\ /
H
```
- In this structure, the central carbon is double bonded to two other carbons.

2. **Determine the Hybridization of Each Carbon Atom**:
- **Central Carbon (C)**:
- The central carbon is bonded to two other carbon atoms via double bonds and has no lone pairs.
- This carbon atom has a total of 2 bond pairs (double bonds) and no lone pairs.
- Therefore, the hybridization of the central carbon is **sp**.

- **Terminal Carbons (C)**:
- Each terminal carbon is bonded to two hydrogen atoms and one carbon atom via a double bond.
- Each terminal carbon has 3 bond pairs (2 single bonds with hydrogen and 1 double bond with the central carbon).
- Therefore, the hybridization of each terminal carbon is **sp²**.

3. **Summarize the Types of Carbon Atoms**:
- In allene, we have:
- 1 carbon atom with **sp** hybridization (the central carbon).
- 2 carbon atoms with **sp²** hybridization (the terminal carbons).
- Thus, the types of carbon atoms in allene are **sp and sp²**.

4. **Final Answer**:
- The types of carbon atoms in allene (C₃H₄) are **sp and sp²**.