Vibrations of molecules can be approximated by a harmonic oscillator only near the mini-mum of the binding potential curve, i.e., for small amplitudes for vibrations. Much betterdescription is provided by the Morse potential21-h?w² ( n+4DeEn = hw ( n +A) Consider the 39K 35C1 molecule. In the far infrared spectrum, it has an intense line at278.0 cm-1. Assume that it is an ideal quantum harmonic oscillator and estimate theperiod of vibration of the molecule.B) Now consider that 39K 35C1 molecule is described with a Morse potential with De34843.15 cm-1 (this value comes from an experimental fit from the literature). If theexcitation from the vibrational ground state to the first excited state is 278.0 cm-1, howmuch would the period of vibration change? How much would the energy transitionbetween the first and second excited vibrational level differ from 278.0 cm-1?

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A) Consider the 3ºK 35C1 molecule. In the far infrared spectrum, it has an intense line a 278.0 cm-1. Assume that it is an ideal quantum harmonic oscillator and estimate the period of vibration of the molecule.

A) Consider the 3ºK 35C1 molecule. In the far infrared spectrum, it has an intense line a 278.0 cm-1. Assume that it is an ideal quantum harmonic oscillator and estimate the period of vibration of the molecule.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

Vibrations of molecules can be approximated by a harmonic oscillator only near the mini-
mum of the binding potential curve, i.e., for small amplitudes for vibrations. Much better
description is provided by the Morse potential
2
1
-h?w² ( n+
4De
En = hw ( n +
A) Consider the 39K 35C1 molecule. In the far infrared spectrum, it has an intense line at
278.0 cm-1. Assume that it is an ideal quantum harmonic oscillator and estimate the
period of vibration of the molecule.
B) Now consider that 39K 35C1 molecule is described with a Morse potential with De
34843.15 cm-1 (this value comes from an experimental fit from the literature). If the
excitation from the vibrational ground state to the first excited state is 278.0 cm-1, how
much would the period of vibration change? How much would the energy transition
between the first and second excited vibrational level differ from 278.0 cm-1?

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