Can a stable molecule have zero bond order ? Justify your answer.

Answer

To determine whether a stable molecule can have a bond order of zero, we need to understand the concept of bond order and its implications for molecular stability.

### Step-by-Step Solution:

1. **Understanding Bond Order**:
Bond order is defined as the difference between the number of bonding electrons and the number of anti-bonding electrons, divided by two. The formula is:
\[ \text{Bond Order} = \frac{(N_b - N_a)}{2} \]
where \(N_b\) is the number of bonding electrons and \(N_a\) is the number of anti-bonding electrons.

2. **Example of He2**:
Let's consider the molecule \(He_2\) (helium dimer) as an example. The molecular orbital configuration for \(He_2\) is:
\[ \sigma_{1s}^2 \sigma_{1s}^*^2 \]
Here, \( \sigma_{1s} \) represents the bonding molecular orbital and \( \sigma_{1s}^* \) represents the anti-bonding molecular orbital.

3. **Counting Electrons**:
In \(He_2\), there are 2 electrons in the bonding orbital and 2 electrons in the anti-bonding orbital:
- Bonding electrons, \(N_b = 2\)
- Anti-bonding electrons, \(N_a = 2\)

4. **Calculating Bond Order**:
Using the bond order formula:
\[ \text{Bond Order} = \frac{(2 - 2)}{2} = \frac{0}{2} = 0 \]
Therefore, the bond order of \(He_2\) is 0.

5. **Implications of Zero Bond Order**:
A bond order of zero indicates that there are equal numbers of bonding and anti-bonding electrons. This means that the attractive forces (due to bonding electrons) are completely canceled out by the repulsive forces (due to anti-bonding electrons). As a result, the molecule does not have a net bond and, hence, cannot exist as a stable entity.

6. **Conclusion**:
Since \(He_2\) has a bond order of 0 and does not exist as a stable molecule, we conclude that a stable molecule cannot have a bond order of zero.

### Final Answer:
No, a stable molecule cannot have zero bond order. A bond order of zero indicates that the molecule does not exist, as the attractive and repulsive forces cancel each other out.