The function e(x) where r = R/a (see Molecules Notes on blackboard) describes the total energy of the H molecule in units of -E1 (13.6 eV). The second derivative of ɛ(x) at the equilibrium point, can be used to estimate the natural frequency of vibration of the two protons. If the ground state energy (hw/2) of this oscillator exceeds the binding energy of the system, the protons will become unbound. Estimate the oscillator frequency w and hence the vibrational energy and show that it is small compared to the binding energy of the H, molecule. You may want to consider the following quadratic expansion of the function E(x) around the minimum e(x) - Eo + k(x – xo)² xo – 0.25 < x < xo + 0.25 2 where Eo = 1.13E1, k = -0.126E1 and ro = 2.5R/a. Note Eı is a negative constant (E1=-13.6 eV)

The function e(x) where r = R/a (see Molecules Notes on blackboard) describes the total energy of the H molecule in units of -E1 (13.6 eV). The second derivative of ɛ(x) at the equilibrium point, can be used to estimate the natural frequency of vibration of the two protons. If the ground state energy (hw/2) of this oscillator exceeds the binding energy of the system, the protons will become unbound. Estimate the oscillator frequency w and hence the vibrational energy and show that it is small compared to the binding energy of the H, molecule. You may want to consider the following quadratic expansion of the function E(x) around the minimum e(x) - Eo + k(x – xo)² xo – 0.25 < x < xo + 0.25 2 where Eo = 1.13E1, k = -0.126E1 and ro = 2.5R/a. Note Eı is a negative constant (E1=-13.6 eV)

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter20: Molecular Spectroscopy And Photochemistry

Section: Chapter Questions

Problem 14P

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