`N_2` and `O_2` are converted to mono cations `N_2^+` and `O_2^+` respectively, which statement is wrong ?

Options

A. the n N- N bond weakens
B. the O - O bond order increases
C. the O - O bond length decreases
D. `N_(2)^(+)` becomes diamagnetic

Answer

To determine which statement is wrong regarding the conversion of \(N_2\) and \(O_2\) to their respective monocations \(N_2^+\) and \(O_2^+\), we can analyze the bond order and magnetic properties of these species step by step.

### Step 1: Determine the electron configuration and bond order of \(N_2\) and \(O_2\)

1. **For \(N_2\)**:
- Total electrons: 14 (7 from each nitrogen atom)
- Bond order formula:
\[ \text{Bond Order} = \frac{(N_b - N_a)}{2} \]
where \(N_b\) is the number of bonding electrons and \(N_a\) is the number of antibonding electrons.
- For \(N_2\), the configuration is \((\sigma_{1s})^2(\sigma_{1s}^*)^2(\sigma_{2s})^2(\sigma_{2s}^*)^2(\sigma_{2p_z})^2(\pi_{2p_x})^2(\pi_{2p_y})^2\).
- Bond order = 3 (since \(N_b = 10\) and \(N_a = 0\)).

2. **For \(O_2\)**:
- Total electrons: 16 (8 from each oxygen atom)
- For \(O_2\), the configuration is \((\sigma_{1s})^2(\sigma_{1s}^*)^2(\sigma_{2s})^2(\sigma_{2s}^*)^2(\sigma_{2p_z})^2(\pi_{2p_x})^2(\pi_{2p_y})^2(\pi_{2p_x}^*)^1(\pi_{2p_y}^*)^1\).
- Bond order = 2 (since \(N_b = 10\) and \(N_a = 6\)).

### Step 2: Determine the bond order of \(N_2^+\) and \(O_2^+\)

1. **For \(N_2^+\)**:
- Total electrons: 13 (removing one electron from \(N_2\))
- Bond order = 2.5 (since \(N_b = 9\) and \(N_a = 1\)).

2. **For \(O_2^+\)**:
- Total electrons: 15 (removing one electron from \(O_2\))
- Bond order = 2.5 (since \(N_b = 10\) and \(N_a = 5\)).

### Step 3: Analyze the statements

1. **Statement 1**: "When \(N_2\) is converted to \(N_2^+\), the nitrogen-nitrogen bond weakens."
- This statement is correct. As bond order decreases from 3 to 2.5, the bond weakens.

2. **Statement 2**: "The \(O_2\) bond order increases."
- This statement is correct. The bond order increases from 2 to 2.5.

3. **Statement 3**: "The \(O_2\) bond length decreases."
- This statement is correct. As bond order increases, bond length decreases.

4. **Statement 4**: "\(N_2^+\) becomes diamagnetic."
- This statement is incorrect. \(N_2^+\) has a bond order of 2.5, which is odd, indicating that it is paramagnetic, not diamagnetic.

### Conclusion

The statement that is wrong is **Statement 4**: "\(N_2^+\) becomes diamagnetic."

---