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GATE 2025 PH – Question 28

Atomic and Molecular Physics · rotational and vibrational spectra of diatomic molecules · 1 mark · Multiple select

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?

Potential energy curves of diatomic molecules P and Q.
  1. The equilibrium inter-nuclear distance of Q is more than that of P
  2. The total energy E= 0 separates bound and unbound states of the molecules
  3. The lowest vibrational frequency of P is larger than that of Q
  4. Dissociation energy of Q is more than that of P

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Show answer and explanation

Correct answer: (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

Explanation

Q has its minimum farther right. Zero energy is the dissociation asymptote. P has larger curvature at its minimum, hence larger vibrational frequency, and its deeper well gives the larger dissociation energy.