How many 'sp' hybrid orbital are there in allene `C_(3)H_(4)` ?

Explanation

To determine how many 'sp' hybrid orbitals are present in allene (C₃H₄), we can analyze the structure and hybridization of the carbon atoms in the molecule. Here’s a step-by-step breakdown:

### Step-by-Step Solution:

1. **Identify the Structure of Allene**:
Allene has the molecular formula C₃H₄. Its structure consists of three carbon atoms arranged in a linear fashion with a double bond between the first and second carbon atoms.

2. **Determine the Hybridization of Each Carbon Atom**:
- The first carbon (C1) is bonded to another carbon (C2) and a hydrogen atom (H). It forms one double bond and one single bond. This means it has:
- 2 sigma bonds (1 with C2 and 1 with H)
- 2 pi bonds (from the double bond with C2)
- Thus, the hybridization of C1 is **sp²**.

- The second carbon (C2) is bonded to C1 and C3, and it also forms a double bond with C1 and a single bond with C3. This means it has:
- 2 sigma bonds (1 with C1 and 1 with C3)
- 2 pi bonds (from the double bond with C1 and another double bond with C3)
- Thus, the hybridization of C2 is also **sp²**.

- The third carbon (C3) is bonded to C2 and two hydrogen atoms. It forms:
- 1 sigma bond with C2
- 2 sigma bonds with H atoms
- Thus, the hybridization of C3 is **sp³**.

3. **Count the 'sp' Hybrid Orbitals**:
- The only carbon atom that exhibits 'sp' hybridization is the central carbon (C2) which is involved in two pi bonds (with C1 and C3).
- Therefore, there is **1 sp hybrid orbital** in the allene molecule.

### Final Answer:
There is **1 sp hybrid orbital** in allene (C₃H₄).