`O_(2)F_(2)` is an unstable yellow change solid and `H_(2)O_(2)` is a colourless liquid, both have `O-O` bond and `O-O` bond length in `H_(2)O_(2)` and `O_(2)F_(2)` respectively is `:`

Options

A. 16
B. 24
C. 8
D. 20

Explanation

To solve the problem regarding the bond lengths of the O-O bond in \( H_2O_2 \) and \( O_2F_2 \), we will follow these steps:

### Step 1: Understand the Structures
- **Hydrogen Peroxide (\( H_2O_2 \))**: This molecule has a structure where two oxygen atoms are connected by a single bond, and each oxygen is also bonded to a hydrogen atom.
- **Dioxygen Difluoride (\( O_2F_2 \))**: This molecule consists of two oxygen atoms connected by a single bond, with each oxygen also bonded to a fluorine atom.

**Hint**: Draw the Lewis structures for both \( H_2O_2 \) and \( O_2F_2 \) to visualize the bonding.

### Step 2: Analyze the Bonding
- In \( H_2O_2 \), the O-O bond is influenced by the presence of the hydroxyl (OH) groups, which can affect the electron distribution.
- In \( O_2F_2 \), the O-F bonds are highly electronegative due to fluorine, which influences the character of the O-O bond.

**Hint**: Consider how the electronegativity of the surrounding atoms (H in \( H_2O_2 \) and F in \( O_2F_2 \)) affects the bond character.

### Step 3: Apply Bent's Rule
- According to Bent's rule, the hybridization of the central atom (oxygen in this case) is influenced by the electronegativity of the surrounding atoms.
- In \( O_2F_2 \), the presence of highly electronegative fluorine atoms increases the p-character of the O-F bonds, leading to more s-character in the O-O bond.

**Hint**: Recall that more s-character in a bond typically leads to shorter bond lengths.

### Step 4: Compare Bond Lengths
- The bond length of the O-O bond in \( H_2O_2 \) is approximately 1.48 Å.
- The bond length of the O-O bond in \( O_2F_2 \) is approximately 1.22 Å.

**Hint**: Look up the typical bond lengths for O-O bonds in similar compounds to reinforce your understanding.

### Step 5: Conclusion
- The O-O bond length in \( H_2O_2 \) is greater than that in \( O_2F_2 \) due to the greater s-character in the O-O bond of \( O_2F_2 \) compared to \( H_2O_2 \).

**Final Answer**: The bond length of the O-O bond in \( H_2O_2 \) is greater than that in \( O_2F_2 \).