The correct order of `O-O` bond length in `O_2,H_2 O` and `O_3`.

Options

A. `O_2 gt O_3 gt H_2O_2`
B. `O_3 gt H_2O_2 gt O_2`
C. `O_2 gt H_2O_2 gt O_3`
D. `H_2O_2 gt O_3 gt O_2`

Explanation

To determine the correct order of O-O bond lengths in \( O_2 \), \( H_2O_2 \), and \( O_3 \), we will analyze the bond lengths based on the molecular structure and bonding characteristics of each compound.

### Step-by-Step Solution:

1. **Identify the Compounds**: We have three compounds to consider: \( O_2 \) (dioxygen), \( H_2O_2 \) (hydrogen peroxide), and \( O_3 \) (ozone).

2. **Understand the Bonding**:
- **\( O_2 \)**: It has a double bond between the two oxygen atoms. The bond length is shorter due to the stronger double bond.
- **\( H_2O_2 \)**: This compound has a single bond between the oxygen atoms. The bond length is longer compared to \( O_2 \) because single bonds are generally longer than double bonds.
- **\( O_3 \)**: Ozone has a resonance structure with one double bond and one single bond between the oxygen atoms. The bond length is intermediate between a single and a double bond.

3. **List the Bond Lengths**:
- The bond length of \( H_2O_2 \) is approximately **147.5 picometers**.
- The bond length of \( O_3 \) is approximately **128 picometers**.
- The bond length of \( O_2 \) is approximately **121 picometers**.

4. **Order the Bond Lengths**: Based on the bond lengths:
- \( H_2O_2 \) has the longest O-O bond length (147.5 pm).
- \( O_3 \) has a shorter bond length than \( H_2O_2 \) but longer than \( O_2 \) (128 pm).
- \( O_2 \) has the shortest bond length (121 pm).

5. **Final Order**: Therefore, the correct order of O-O bond lengths from longest to shortest is:
\[ H_2O_2 > O_3 > O_2 \]

### Conclusion:
The correct order of O-O bond lengths is:
\[ H_2O_2 > O_3 > O_2 \]