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3. Vibrational excitations in a diatomic molecule can be described with a potential energy function of the form U(r) = D(e-2a(r-re) – 2e¬a(r-re)) %3D where r is the interatomic distance, re is the equilibrium bond distance, D is the dissociation energy (a constant), and a is a positive constant.

3. Vibrational excitations in a diatomic molecule can be described with a potential energy function of the form U(r) = D(e-2a(r-re) – 2e¬a(r-re)) %3D where r is the interatomic distance, re is the equilibrium bond distance, D is the dissociation energy (a constant), and a is a positive constant.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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3. Vibrational excitations in a diatomic molecule can be described with a potential energy function of the form U (r) = D(e-2a(r-re) – 2e¬a(r-re)) where r is the interatomic distance, re is the equilibrium bond distance, D is the dissociation energy (a constant), and a is a positive constant. a) What are the dimensions of re, D, and a? Express your answer in terms of products LªT'M°, where L is length, T is time, M is mass, and a, b, and c are rational numbers. b) What is the value of the potential at arbitrarely large separations (r > re). c) Find the value of r for which U is a minimum. d) What is the minimum value of U? e) Show that for very small displacements x = ergy can be approximated to (r – re) << 1, the potential en- U (x) – U (0) ka where k 2a? D.
Transcribed Image Text:3. Vibrational excitations in a diatomic molecule can be described with a potential energy function of the form U (r) = D(e-2a(r-re) – 2e¬a(r-re)) where r is the interatomic distance, re is the equilibrium bond distance, D is the dissociation energy (a constant), and a is a positive constant. a) What are the dimensions of re, D, and a? Express your answer in terms of products LªT'M°, where L is length, T is time, M is mass, and a, b, and c are rational numbers. b) What is the value of the potential at arbitrarely large separations (r > re). c) Find the value of r for which U is a minimum. d) What is the minimum value of U? e) Show that for very small displacements x = ergy can be approximated to (r – re) << 1, the potential en- U (x) – U (0) ka where k 2a? D.
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