Predict the stability of a molecule if `N_(a) gtN_(b).`

Answer

To predict the stability of a molecule when \( N_a > N_b \) (where \( N_a \) is the number of anti-bonding electrons and \( N_b \) is the number of bonding electrons), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Bonding Electrons**: Electrons that occupy bonding molecular orbitals, which stabilize the molecule.
- **Anti-bonding Electrons**: Electrons that occupy anti-bonding molecular orbitals, which destabilize the molecule.

2. **Identify the Condition**:
- The condition given is \( N_a > N_b \). This means that the number of anti-bonding electrons is greater than the number of bonding electrons.

3. **Use the Bond Order Formula**:
- The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{1}{2} (N_b - N_a) \]
- Here, \( N_b \) is the number of bonding electrons and \( N_a \) is the number of anti-bonding electrons.

4. **Substitute the Values**:
- Since \( N_a > N_b \), it implies that \( N_b - N_a \) will be a negative value. Therefore, substituting into the bond order formula:
\[ \text{Bond Order} = \frac{1}{2} (N_b - N_a) < 0 \]

5. **Interpret the Bond Order**:
- A negative bond order indicates that the molecule is unstable. This is because the presence of more anti-bonding electrons than bonding electrons leads to a net destabilization of the molecular structure.

6. **Conclusion**:
- Since the bond order is negative, we conclude that the molecule is unstable.

### Final Answer:
If \( N_a > N_b \), the molecule is unstable due to a negative bond order.