In `MO` energy diagram for heteronuclear diatomic molecule is similar However, the energies of the `AO` s of the atom having higher atomic number being lower, the diagram will be unsymmetrical, but that will not make a difference in the electron count The bond order is half the difference in the number of electrns of the bonding `(sigma and pi)` and anti-bonding `(sigma and pi)` `MO s` For a bond to have been formed the bond order the shorter is the bond distance and the greater is the bond dissociation energey But if the bond order is smae in the above two cases, then the bond distance will be greater and the bond dissocation energy smaller in the case which has more populated anti-bonding orbitals The presence of unpaired electron(s) in a molecualr orbital will make the system paramagnetic
Which of the following orders is correct in respect of bond dissociation energey ? .

Options

A. `N_(2)^(o+) gtN_(2)^(Θ)`
B. `O_(2)gtO_(2)^(Θ)`
C. `NO^(o+)gtNO`
D. All of these

Explanation

To solve the question regarding the bond dissociation energy of heteronuclear diatomic molecules based on their molecular orbital (MO) configurations, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Bond Order**:
- The bond order (B.O.) is calculated using the formula:
\[ \text{Bond Order} = \frac{N_B - N_A}{2} \]
where \(N_B\) is the number of electrons in bonding molecular orbitals and \(N_A\) is the number of electrons in anti-bonding molecular orbitals.

2. **Analyzing Given Molecules**:
- We need to analyze the bond order for the given molecules: \(N_2^+, N_2^-, O_2, O_2^-, NO^+, NO\).

3. **Calculating for \(N_2^+\)**:
- Configuration: \(\sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^1\)
- Total Electrons: 13
- Bonding Electrons (\(N_B\)): 10
- Anti-bonding Electrons (\(N_A\)): 2
- Bond Order: \(\frac{10 - 2}{2} = 4\)

4. **Calculating for \(N_2^-\)**:
- Configuration: \(\sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2 \pi_{2p_x}^*^1\)
- Total Electrons: 15
- Bonding Electrons (\(N_B\)): 10
- Anti-bonding Electrons (\(N_A\)): 5
- Bond Order: \(\frac{10 - 5}{2} = 2.5\)

5. **Comparing \(N_2^+\) and \(N_2^-\)**:
- \(N_2^+\) has a higher bond order (4) compared to \(N_2^-\) (2.5), indicating a stronger bond and higher bond dissociation energy.

6. **Calculating for \(O_2\)**:
- Configuration: \(\sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^1 \pi_{2p_y}^*^1\)
- Total Electrons: 16
- Bonding Electrons (\(N_B\)): 10
- Anti-bonding Electrons (\(N_A\)): 6
- Bond Order: \(\frac{10 - 6}{2} = 2\)

7. **Calculating for \(O_2^-\)**:
- Configuration: \(\sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^2 \pi_{2p_y}^*^1\)
- Total Electrons: 17
- Bonding Electrons (\(N_B\)): 10
- Anti-bonding Electrons (\(N_A\)): 7
- Bond Order: \(\frac{10 - 7}{2} = 1.5\)

8. **Comparing \(O_2\) and \(O_2^-\)**:
- \(O_2\) has a bond order of 2, while \(O_2^-\) has a bond order of 1.5. Thus, \(O_2\) has a higher bond dissociation energy.

9. **Calculating for \(NO^+\)**:
- Configuration: \(\sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2\)
- Total Electrons: 14
- Bonding Electrons (\(N_B\)): 10
- Anti-bonding Electrons (\(N_A\)): 4
- Bond Order: \(\frac{10 - 4}{2} = 3\)

10. **Calculating for \(NO\)**:
- Configuration: \(\sigma_{1s}^2 \sigma_{1s}^*^2 \sigma_{2s}^2 \sigma_{2s}^*^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^*^1\)
- Total Electrons: 15
- Bonding Electrons (\(N_B\)): 10
- Anti-bonding Electrons (\(N_A\)): 5
- Bond Order: \(\frac{10 - 5}{2} = 2.5\)

11. **Comparing \(NO^+\) and \(NO\)**:
- \(NO^+\) has a bond order of 3, while \(NO\) has a bond order of 2.5. Thus, \(NO^+\) has a higher bond dissociation energy.

12. **Conclusion**:
- The correct order of bond dissociation energy based on the calculated bond orders is:
\[ N_2^+ > N_2^- > O_2 > O_2^- > NO^+ > NO \]