Arrange `O _(2) H_(2)O_(2) and O _(3)` in the correct order of decreasing O-O bond length.

Explanation

To arrange \( O_2 \), \( H_2O_2 \), and \( O_3 \) in the correct order of decreasing O-O bond length, we need to analyze the bond order of each molecule. The bond length is inversely proportional to the bond order; that is, a higher bond order corresponds to a shorter bond length.

### Step-by-Step Solution:

1. **Identify the Bond Order of Each Compound:**
- **\( O_2 \)**: Oxygen molecule has a double bond (O=O), which gives it a bond order of 2.
- **\( H_2O_2 \)**: Hydrogen peroxide has a single bond between the two oxygen atoms (O-O), resulting in a bond order of 1.
- **\( O_3 \)**: Ozone has a resonance structure with bonds that can be considered as having a bond order of approximately 1.5 (due to the delocalization of electrons).
...