The molecule is not having 3c-2e bond is :

Options

A. `BeH_2` (dimer)
B. `BeH_2` (solid )
C. `C_2H_6`
D. `B_2H_6`

Answer

To solve the question regarding which molecule does not have a 3-centre-2-electron (3c-2e) bond, we will analyze the bonding in the given molecules.

### Step-by-Step Solution:

1. **Understanding 3c-2e Bonds**:
- A 3c-2e bond involves three atoms sharing two electrons. This is typically seen in compounds where there is a bridging atom that connects two other atoms, allowing for the sharing of electrons.

2. **Analyzing BEH2 Dimer**:
- The BEH2 dimer (Beryllium Hydride) forms a structure where beryllium is bonded to two hydrogen atoms.
- In this case, the bonding is primarily 2-centre-2-electron (2c-2e) bonds, as each hydrogen shares its single electron with beryllium, resulting in no 3c-2e bond.

3. **Analyzing BEH4**:
- The BEH4 molecule can form a structure where beryllium is surrounded by four hydrogen atoms.
- This configuration can lead to the formation of 3c-2e bonds due to the presence of bridging hydrogen atoms.

4. **Analyzing C2H6 (Ethane)**:
- Ethane (C2H6) consists of carbon atoms bonded to hydrogen atoms.
- Each carbon atom forms 2c-2e bonds with hydrogen atoms, and there are no 3c-2e bonds present in this structure.

5. **Analyzing B2H6 (Diborane)**:
- Diborane (B2H6) is known for having 3c-2e bonds due to the presence of bridging hydrogen atoms that connect the two boron atoms.
- This results in the formation of 3c-2e bonds.

6. **Conclusion**:
- Among the molecules analyzed, C2H6 (Ethane) is the molecule that does not have a 3-centre-2-electron bond. Therefore, the answer to the question is **C2H6**.

### Final Answer:
The molecule that does not have a 3-centre-2-electron bond is **C2H6 (Ethane)**.