The lowest O-O bond length in the following molecule is :

Options

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

Answer

To determine the lowest O-O bond length among the molecules O2F2, O2, H2O2, and O3, we will analyze the bond orders of each molecule and how they relate to bond lengths.

### Step-by-Step Solution:

1. **Identify the Structures of Each Molecule:**
- **O2F2 (Dioxygen Difluoride):** This molecule contains a peroxide linkage (O-O bond) and has a single bond between the two oxygen atoms.
- **O2 (Dioxygen):** This molecule consists of two oxygen atoms connected by a double bond (O=O).
- **H2O2 (Hydrogen Peroxide):** Similar to O2F2, it has a peroxide linkage with a single bond between the two oxygen atoms.
- **O3 (Ozone):** Ozone has a resonance structure where the O-O bond is a partial double bond due to resonance between two structures.

2. **Determine the Bond Order:**
- **O2F2:** The bond order is 1 (single bond).
- **O2:** The bond order is 2 (double bond).
- **H2O2:** The bond order is 1 (single bond).
- **O3:** The bond order is approximately 1.5 (due to resonance).

3. **Relate Bond Order to Bond Length:**
- The bond length is inversely proportional to the bond order. This means that a higher bond order corresponds to a shorter bond length.
- Therefore, we can summarize the bond orders:
- O2F2: Bond order = 1 → Long bond length
- O2: Bond order = 2 → Short bond length
- H2O2: Bond order = 1 → Long bond length
- O3: Bond order ≈ 1.5 → Intermediate bond length

4. **Conclusion:**
- Among the given molecules, O2 has the highest bond order (2), which means it has the shortest O-O bond length.
- Therefore, the molecule with the lowest O-O bond length is **O2**.

### Final Answer:
The lowest O-O bond length is found in **O2**.