The hybridisation of `C` atoms in `(C - C)` single-bond of `H - C -= C - CH = CH_(2)` is :

Options

A. `H_(2) C = CH - C -= CH`
B. `HC -= C - CH_(2) - C -= CH`
C. `H_(2) C = C = C = CH_(2)`
D. `sp- sp^(2)`

Explanation

To determine the hybridization of the carbon atoms in the compound \( H - C \equiv C - C = CH_2 \), we will analyze the bonding and geometry around each carbon atom.

### Step-by-Step Solution:

1. **Identify the Structure**:
The given compound can be represented as:
\[ H - C \equiv C - C = CH_2 \]
Here, we have:
- A terminal carbon (C1) bonded to hydrogen (H) and connected to a carbon with a triple bond (C2).
- The second carbon (C2) is part of a triple bond with the first carbon (C1) and is also connected to another carbon (C3) with a single bond.
- The third carbon (C3) is involved in a double bond with the fourth carbon (C4, which is \( CH_2 \)).

2. **Determine Hybridization of Each Carbon**:
- **C1 (Terminal Carbon)**:
- C1 is bonded to one hydrogen atom and to C2 (which has a triple bond).
- Since it forms one sigma bond with C2 and one bond with H, it has a total of 2 regions of electron density.
- Therefore, C1 is **sp hybridized**.

- **C2 (Triple Bond Carbon)**:
- C2 is involved in a triple bond with C1 and a single bond with C3.
- It has a total of 2 regions of electron density (one sigma bond with C3 and one sigma bond from the triple bond with C1).
- Therefore, C2 is also **sp hybridized**.

- **C3 (Double Bond Carbon)**:
- C3 is bonded to C2 (with a single bond) and C4 (with a double bond).
- It has a total of 3 regions of electron density (one sigma bond with C2 and one sigma bond plus one pi bond with C4).
- Therefore, C3 is **sp² hybridized**.

- **C4 (Terminal Carbon)**:
- C4 is bonded to C3 with a double bond and two hydrogen atoms.
- It has a total of 3 regions of electron density (one sigma bond with C3 and two sigma bonds with H).
- Therefore, C4 is also **sp² hybridized**.

3. **Conclusion**:
The hybridization of the carbon atoms in the carbon-carbon single bond of \( H - C \equiv C - C = CH_2 \) is **sp hybridized for C1 and C2**, and **sp² hybridized for C3 and C4**.

### Final Answer:
The hybridization of the carbon atoms in the carbon-carbon single bond is **sp hybridized** for C1 and C2, and **sp² hybridized** for C3 and C4.