If `N_(B)` is the number of bonding electron and `N_(A)` is the number of antibonding electrons of a molecules. Then choose the incorrect statement(s) for the relationship , `N_(B)gtN_(A)`"

Options

A. Molecule may be stable or unstable
B. Molecule may have any integral, frational or zero value of bond order
C. Molecule is only paramagnetic species
D. Molecule does not exist

Explanation

To solve the question regarding the relationship between bonding electrons \(N_B\) and antibonding electrons \(N_A\) in a molecule, we need to analyze the statements provided and determine which are incorrect based on the principles of molecular orbital theory (MOT).

### Step-by-Step Solution:

1. **Understanding Bonding and Antibonding Electrons**:
- Bonding electrons (\(N_B\)) are those that occupy molecular orbitals that stabilize the molecule, while antibonding electrons (\(N_A\)) occupy molecular orbitals that destabilize it.
- According to molecular orbital theory, for a molecule to be stable, the number of bonding electrons must be greater than the number of antibonding electrons, i.e., \(N_B > N_A\).

2. **Analyzing Statements**:
- **Statement A**: "Molecule may be stable or may be unstable."
- This statement is true. The stability of a molecule indeed depends on the balance between bonding and antibonding electrons.

- **Statement B**: "Molecule may have integral, fractional, or zero bond order."
- This statement is misleading. While bond order can be zero (indicating instability), fractional bond orders are possible in certain cases. However, a bond order of zero implies that the molecule does not exist. Thus, this statement is partially incorrect.

- **Statement C**: "Molecule is only paramagnetic."
- This statement is false. A molecule can be paramagnetic (due to unpaired electrons) or diamagnetic (due to all electrons being paired). Therefore, this statement is incorrect.

- **Statement D**: "Molecule does not exist."
- This statement is also false. A molecule exists if it has a positive bond order. If the bond order is zero, then it does not exist, but it is not a general rule that molecules do not exist.

3. **Conclusion**:
- The incorrect statements based on the relationship \(N_B > N_A\) are **B, C, and D**.

### Summary of Incorrect Statements:
- **B**: Misleading regarding bond order.
- **C**: Incorrect assumption about magnetic nature.
- **D**: Incorrect generalization about molecular existence.