Concept: The relationship between bond order, bond energy, and bond length is fundamental in understanding chemical bonding and molecular stability.

Why (A) is correct:

Bond order is a measure of the number of chemical bonds between a pair of atoms. A higher bond order indicates more electrons shared between the atoms, leading to a stronger and shorter bond.

• Bond order and Bond energy: As the bond order increases (e.g., from single to double to triple bond), the bond becomes stronger. A stronger bond requires more energy to break, hence bond energy increases. Therefore, bond order is directly proportional to bond energy ($\text{Bond order}\propto \text{Bond energy}$).
• Bond order and Bond length: As the bond order increases, the atoms are pulled closer together due to increased electron density between them. This results in a shorter bond length. Therefore, bond order is inversely proportional to bond length ($\text{Bond order}\propto \frac{1}{\text{Bond length}}$).

Combining these relationships, we get: $\text{Bond order}\propto \text{Bond energy}\propto \frac{1}{\text{Bond length}}$.

Option Analysis:

• A) Bond order $\propto$ bond energy$\propto \frac{1}{\text{ bond length }}$: This statement correctly represents the relationships. Higher bond order means stronger bond (higher bond energy) and shorter bond (smaller bond length).
• B) Bond order $\propto$ bond length $\propto \frac{1}{\text{ bond energy }}$: This is incorrect. Bond order is inversely proportional to bond length, and directly proportional to bond energy.
• C) Bond order $\propto \frac{1}{\text{ bond length }}\propto \frac{1}{\text{ bond energy }}$: This is incorrect. Bond order is directly proportional to bond energy, not inversely.
• D) Bond order $\propto$ bond length $\propto$ bond energy: This is incorrect. Bond order is inversely proportional to bond length.

Correct Answer: (A)