Explain the observations that the bond length in `N^(+)` is `0.02Å` larger than in `N_(2)` while the bond length in `NO^(+)` is `0.09Å` less than in `NO.`

Explanation

To explain the observations regarding the bond lengths in \( N_2^+ \) and \( NO^+ \) compared to their neutral counterparts, we need to analyze the bond orders of these molecules. The bond length is inversely related to the bond strength, which is determined by the bond order. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the Electron Configuration and Bond Order of \( N_2 \)
- **Electron Count**: \( N_2 \) has a total of 14 electrons.
- **Molecular Orbital Configuration**:
- \( \sigma_{1s}^2 \)
- \( \sigma_{1s}^*^2 \)
- \( \sigma_{2s}^2 \)
...