The decreasing `(O -O)` bonf length order in the following is .

Options

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

Explanation

To determine the decreasing order of (O-O) bond lengths in the compounds O2 (dioxygen), H2O2 (hydrogen peroxide), and O3 (ozone), we will analyze the bond order of each compound. The bond order is inversely related to bond length; that is, a higher bond order corresponds to a shorter bond length.

### Step-by-Step Solution:

1. **Identify the Compounds**: We have three compounds to analyze: O2, H2O2, and O3.

2. **Determine the Bond Order**:
- **O2**:
- O2 has a double bond (one sigma bond and one pi bond).
- Bond order = 2.
- **H2O2**:
- H2O2 has single bonds between the oxygen atoms.
- Bond order = 1.
- **O3**:
- O3 has resonance structures, which means it has partial double bonds.
- The bond order for O3 can be considered as 1.5 (since it has characteristics of both single and double bonds).

3. **Relate Bond Order to Bond Length**:
- Higher bond order means shorter bond length.
- Therefore, we can rank the bond orders:
- O2 (bond order = 2) has the shortest bond length.
- O3 (bond order = 1.5) has a longer bond length than O2 but shorter than H2O2.
- H2O2 (bond order = 1) has the longest bond length.

4. **Establish the Order of Bond Lengths**:
- From the bond orders, we can conclude:
- O2 < O3 < H2O2
- In terms of bond lengths, this translates to:
- H2O2 has the longest bond length, followed by O3, and O2 has the shortest bond length.

### Final Answer:
The decreasing order of (O-O) bond lengths is:
**H2O2 > O3 > O2**