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 \( r_e \), 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 frequency of an equivalent harmonic oscillator. (Suggestion: include higher order terms in the expansion.)(Note: There are no graphs or diagrams in the image.) **The Morse Potential**The harmonic potential, \( V(x) = \frac{1}{2}kx^2 \), is a useful start for modeling molecular vibrations, but it has limitations. A realistic potential between two atoms should accurately represent the sharp increase in the potential as two nuclei come in close proximity, and also have the ability for a bond to break: that is, an asymptote \( V \to 0 \) as \( x \to \infty \).One option, as shown in the figure, is the Morse potential:\[V(r) = D(1 - e^{-\alpha(r-r_e)})^2\]![Graph of Morse Potential](attachment)In the graph, the Morse potential equation is represented. The potential energy \( V(r) \) is plotted on the vertical axis, while the distance \( r \) is on the horizontal axis. As the graph shows, the potential drops steeply to a minimum value before rising again to approach zero.The parameter \( D \) is the well depth (or binding energy) of the potential, \( r_e \) is the bond length, and \( \alpha \) 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

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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