The correct order in which the O-O bond length increases in the following is

Options

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

Answer

To determine the correct order of O-O bond lengths in ozone (O₃), hydrogen peroxide (H₂O₂), and molecular oxygen (O₂), we can analyze the bond types and bond orders of these molecules.

### Step-by-Step Solution:

1. **Identify the Bond Types**:
- **O₂ (Molecular Oxygen)**: The structure is O=O, which indicates a double bond between the two oxygen atoms.
- **O₃ (Ozone)**: Ozone has a resonance structure with one double bond and one single bond. The resonance structures can be represented as:
- O=O-O (with one double bond and one single bond)
- O-O=O (with the double bond shifting between the oxygen atoms)
- **H₂O₂ (Hydrogen Peroxide)**: The structure is O-O, which indicates a single bond between the two oxygen atoms.

2. **Determine Bond Order**:
- **For O₂**: The bond order is 2 (one double bond).
- **For O₃**: The bond order can be calculated as follows:
- Total number of bonds = 3 (two single bonds and one double bond)
- Total number of resonance structures = 2
- Bond order = Total bonds / Total resonance structures = 3 / 2 = 1.5
- **For H₂O₂**: The bond order is 1 (one single bond).

3. **Relate Bond Order to Bond Length**:
- Higher bond order means a stronger bond and consequently a shorter bond length. Conversely, a lower bond order indicates a weaker bond and a longer bond length.
- Therefore, we can establish the following relationship based on bond order:
- O₂ (Bond order = 2) < O₃ (Bond order = 1.5) < H₂O₂ (Bond order = 1)

4. **Conclusion**:
- The order of increasing O-O bond length is:
- H₂O₂ > O₃ > O₂

### Final Answer:
The correct order in which the O-O bond length increases is: **H₂O₂ > O₃ > O₂**.