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

Options

A. (a) `sp and sp^(3)`
B. (b) `sp and sp^(2)`
C. (c) only `sp^(3)`
D. (d) `sp^(2) and sp^(3)`

Explanation

To determine the hybridization of the carbon atoms in allene (C₃H₄), we can follow these steps:

### Step 1: Draw the Lewis Structure of Allene
Allene has the following structure:
```
H H
\ /
C = C
/ \
H C
|
H
```
In this structure, we can see that there are three carbon atoms (C₁, C₂, and C₃) and four hydrogen atoms.

### Step 2: Analyze Each Carbon Atom
1. **Carbon 1 (C₁)**:
- It is bonded to two hydrogen atoms (single bonds) and one carbon atom (double bond).
- Total bond pairs = 3 (2 single bonds + 1 double bond).
- Hybridization = sp² (since it has 3 bond pairs).

2. **Carbon 2 (C₂)**:
- It is bonded to two carbon atoms (double bonds).
- Total bond pairs = 2 (both are double bonds).
- Hybridization = sp (since it has 2 bond pairs).

3. **Carbon 3 (C₃)**:
- It is bonded to one carbon atom (double bond) and two hydrogen atoms (single bonds).
- Total bond pairs = 3 (1 double bond + 2 single bonds).
- Hybridization = sp² (since it has 3 bond pairs).

### Step 3: Summarize the Hybridization
- **C₁**: sp²
- **C₂**: sp
- **C₃**: sp²

### Conclusion
The hybridization of the carbon atoms in allene (C₃H₄) is:
- C₁: sp²
- C₂: sp
- C₃: sp²

Thus, the types of hybridization present in allene are sp and sp².