Question

Potential energy of two diatomic molecules P and Q of the same reduced mass is shown in the figure. According to this diagram, which of the following option(s) is/are correct?

• A. The equilibrium inter-nuclear distance of Q is more than that of P
• B. The total energy \( E = 0 \) separates bound and unbound states of the molecules
• C. The lowest vibrational frequency of P is larger than that of Q
• D. Dissociation energy of Q is more than that of P

Hint:

The dissociation energy corresponds to the difference in potential energy at equilibrium and at infinite separation. The equilibrium distance is where the potential energy is minimized, and the lowest vibrational frequency is related to the curvature of the potential energy curve.

Answer 1

The Correct Option is A, B, C

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).