According to the Valence bond theory, which statement is incorrect regarding bonding between two carbon atoms ?

Options

A. A sigma `(sigma)` bond is weaker than a `pi-` bond
B. A sigam bond is stronger than a `pi-` bond
C. A double bond is stronger than a single bond
D. A double bond is shorter than a single bond

Answer

To determine which statement is incorrect regarding bonding between two carbon atoms according to the Valence Bond Theory, we need to analyze the bonding characteristics of carbon atoms, particularly in the context of a double bond, such as in ethylene (C2H4).

### Step-by-Step Solution:

1. **Understanding Carbon Hybridization**:
- Carbon has an atomic number of 6, with an electronic configuration of 1s² 2s² 2p².
- In a double bond scenario (like in C2H4), each carbon atom undergoes sp² hybridization. This means one s orbital and two p orbitals mix to form three sp² hybrid orbitals, leaving one p orbital unhybridized.

2. **Formation of Sigma and Pi Bonds**:
- The sp² hybrid orbitals of each carbon atom overlap laterally to form a sigma (σ) bond.
- The unhybridized p orbitals from each carbon atom overlap axially to form a pi (π) bond.
- Therefore, in a double bond, there is one σ bond and one π bond.

3. **Bond Strength and Length**:
- According to Valence Bond Theory, σ bonds are generally stronger than π bonds due to the greater extent of overlap in σ bonds.
- Consequently, a double bond (which consists of one σ bond and one π bond) is stronger than a single bond (which consists of only one σ bond).
- Additionally, because double bonds involve more bonding interactions (one σ and one π), they are shorter than single bonds.

4. **Evaluating Statements**:
- **Statement 1**: "Sigma bond is weaker than that of the pi bond" - This is incorrect because σ bonds are stronger than π bonds.
- **Statement 2**: "Sigma bond is shorter than that of the pi bond" - This is also incorrect because bond length is related to bond strength; σ bonds are shorter than π bonds due to their stronger nature.
- **Statement 3**: "Double bond is stronger than a single bond" - This is correct.
- **Statement 4**: "Double bond is shorter than that of the single bond" - This is also correct.

### Conclusion:
The incorrect statement regarding bonding between two carbon atoms according to the Valence Bond Theory is that "sigma bond is weaker than that of the pi bond."