The O-O bond length is inversely related to the bond order. A higher bond order means a stronger and shorter bond.

Let's analyze the O-O bond order in each species:

• O₂ (Oxygen molecule): The oxygen molecule has a double bond between the two oxygen atoms ($\mathrm{O}=\mathrm{O}$). The bond order is 2. The typical O=O bond length is approximately 121 pm.
• H₂O₂ (Hydrogen peroxide): In hydrogen peroxide, there is a single bond between the two oxygen atoms ($\mathrm{H}-\mathrm{O}-\mathrm{O}-\mathrm{H}$). The bond order is 1. The typical O-O single bond length is approximately 148 pm.
• O₃ (Ozone): Ozone has a resonance structure. The central oxygen atom is double-bonded to one oxygen atom and single-bonded to another, with delocalization of electrons. This results in an average bond order of 1.5 for each O-O bond. The typical O-O bond length in ozone is approximately 128 pm.

Comparing the bond lengths:

• H₂O₂ (bond order 1): ~148 pm
• O₃ (bond order 1.5): ~128 pm
• O₂ (bond order 2): ~121 pm

Therefore, the correct order of O-O bond length is ${\mathrm{H}}_2{\mathrm{O}}_2>{\mathrm{O}}_3>{\mathrm{O}}_2$.

Option Analysis:

• A) ${\mathrm{O}}_3>{\mathrm{H}}_2{\mathrm{O}}_2>{\mathrm{O}}_2$: Incorrect, as H₂O₂ has the longest O-O bond.
• B) ${\mathrm{O}}_2>{\mathrm{H}}_2{\mathrm{O}}_2>{\mathrm{O}}_3$: Incorrect, as O₂ has the shortest O-O bond.
• C) ${\mathrm{O}}_2>{\mathrm{O}}_3>{\mathrm{H}}_2{\mathrm{O}}_2$: Incorrect, as O₂ has the shortest O-O bond and H₂O₂ has the longest.
• D) ${\mathrm{H}}_2{\mathrm{O}}_2>{\mathrm{O}}_3>{\mathrm{O}}_2$: Correct, matching the calculated bond lengths based on bond order.

Correct Answer: (D)