Calculate the standard deviation of the bond length ox of the diatomic molecule 'H1ºF when it is in the ground state and first excited state using the quantum harmonic oscillator wavefunctions. The fundamental harmonic vibrational frequency of HF is 4,460 cm-1 and the equilibrium bond length is 0.091nm. How do you interpret the change in the ratio of average bond length to ox as a function of energy in the vibration?

Calculate the standard deviation of the bond length ox of the diatomic molecule 'H1ºF when it is in the ground state and first excited state using the quantum harmonic oscillator wavefunctions. The fundamental harmonic vibrational frequency of HF is 4,460 cm-1 and the equilibrium bond length is 0.091nm. How do you interpret the change in the ratio of average bond length to ox as a function of energy in the vibration?

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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Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.

Question

Calculate the standard deviation of the bond length \( \sigma_X \) of the diatomic molecule \(^1\text{H}^{19}\text{F}\) when it is in the ground state and first excited state using the quantum harmonic oscillator wavefunctions. The fundamental harmonic vibrational frequency of HF is \(4,460 \, \text{cm}^{-1}\) and the equilibrium bond length is \(0.091 \, \text{nm}\). How do you interpret the change in the ratio of average bond length to \( \sigma_X \) as a function of energy in the vibration?

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