Potential Energy Curve

The question presents a potential energy diagram for two diatomic molecules, P and Q. Let's analyze each option based on the provided diagram:

1. Equilibrium Inter-Nuclear Distance:

   The equilibrium inter-nuclear distance corresponds to the minimum of the potential energy curve. From the diagram, the equilibrium inter-nuclear distance for molecule Q is larger than that for molecule P.

   ✓ Option (A) is correct.

2. Energy E = 0 Separates Bound and Unbound States:

   The energy level E = 0 represents the threshold between bound and unbound molecular states. States with energy below zero are bound (stable), and those above zero are unbound (dissociative).

   ✓ Option (B) is correct.

3. Lowest Vibrational Frequency:

   Vibrational frequency is linked to the curvature of the potential energy curve at the minimum. A steeper curve (as in P) indicates stronger restoring forces and thus a higher vibrational frequency compared to a shallower curve (as in Q).

   ✓ Option (C) is correct.

4. Dissociation Energy:

   Dissociation energy is the depth of the potential well. From the diagram, molecule Q has a deeper well, hence a higher dissociation energy than P.

   ✗ Option (D) is incorrect.

Conclusion: The correct options are (A), (B), and (C).