The correct order of O - O bond length in `O_(2)H_(2)O_(2)` and `O_(3)` is

Options

A. `O_(2) gt O_(3) gt H_(2)O_(2)`
B. `O_(3) gt H_(2)O_(2) gt O_(2)`
C. `H_(2)O_(2) gt O_(3) gt O_(2)`
D. `O_(2) gt H_(2)O_(2) gt O_(3)`

Answer

To determine the correct order of O-O bond lengths in \( O_2 \), \( H_2O_2 \), and \( O_3 \), we need to analyze the bond order and structure of each molecule.

### Step-by-Step Solution:

1. **Identify the Structures**:
- **\( O_2 \)**: This molecule has a double bond between the two oxygen atoms. The Lewis structure shows that each oxygen shares two electrons, resulting in a bond order of 2.
- **\( H_2O_2 \)** (Hydrogen Peroxide): In this molecule, the two oxygen atoms are connected by a single bond. Each oxygen is also bonded to a hydrogen atom. The bond order between the two oxygen atoms is 1.
- **\( O_3 \)** (Ozone): Ozone has a resonance structure where one oxygen atom is bonded to another with a double bond, and the third oxygen is connected with a single bond. The average bond order for \( O_3 \) is 1.5 due to resonance.

2. **Determine Bond Orders**:
- For \( O_2 \): Bond order = 2
- For \( H_2O_2 \): Bond order = 1
- For \( O_3 \): Bond order = 1.5

3. **Relate Bond Order to Bond Length**:
- Bond length is inversely proportional to bond order. This means that a higher bond order corresponds to a shorter bond length.
- Therefore, the order of bond lengths based on bond orders will be as follows:
- **Highest bond length**: \( H_2O_2 \) (bond order 1)
- **Intermediate bond length**: \( O_3 \) (bond order 1.5)
- **Shortest bond length**: \( O_2 \) (bond order 2)

4. **Conclusion**:
- The correct order of O-O bond lengths from longest to shortest is:
\[ H_2O_2 > O_3 > O_2 \]

### Final Answer:
The correct order of O-O bond length is \( H_2O_2 > O_3 > O_2 \).