and can you explain how you got the answer? It helps me understand the math 1) Take the derivative of this function to find the force function associated with it.2) Demonstrate that for values of r close to re, the potential is close to harmonic: i.e., the forceis proportional to displacement and opposite in direction. (Suggestion: expand the exponentialfunction as a power series.)3) Show that for large amplitudes, the vibrational frequency of the oscillator is less than thefrequency of an equivalent harmonic oscillator. (Suggestion: include higher order terms in theexpansion.) The Morse potentialThe harmonic potential, V(x) = ½kx?, is useful start for modelling molecular vibrations, but it haslimitations. A realistic potential between to atoms should accurately represent the sharpincrease in the potential as two nuclei come in close proximity, and also have the ability for abond to break: that is, an asymptote V →0 as x →00.One option, as shown in the figure, is the Morse potential:V(r) = D(1 – e-«(r=re))21510101520The parameter D is the well depth (or binding energy) of the potential, re is the bond length,and a is the anharmonicity constant.

Answered: Image /qna-images/answer/88bcf99f-b7a9-4347-a16f-b795f3a8f8d0.jpg

1) Take the derivative of this function to find the force function associated with it. 2) Demonstrate that for values of r close to re, the potential is close to harmonic: i.e., the force is proportional to displacement and opposite in direction. (Suggestion: expand the exponential function as a power series.) 3) Show that for large amplitudes, the vibrational frequency of the oscillator is less than the

1) Take the derivative of this function to find the force function associated with it. 2) Demonstrate that for values of r close to re, the potential is close to harmonic: i.e., the force is proportional to displacement and opposite in direction. (Suggestion: expand the exponential function as a power series.) 3) Show that for large amplitudes, the vibrational frequency of the oscillator is less than the

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter7: Tunneling Phenomena

Section: Chapter Questions

Problem 1P

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