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?

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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?
Transcribed Image Text: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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