P7E.5 In infrared spectroscopy it is common to observe a transition from the v = 0 to v = 1 vibrational level. If this transition is modelled as a harmonic oscillator, the energy of the photon involved is ħo, where o is the vibrational frequency. (a) Show that the wavenumber of the radiation corresponding to photons of this energy, v, is given by v=@/2nc, where c is the speed of light. (b) The vibrational frequency of 'H*Cl is w = 5.63 x 10“s"; calculate v. (c) Derive an expression for the force constant k, in terms of v. (d) For "C"O the v = 0 →1 transition is observed at 2170 cm. Calculate the force constant and estimate the wavenumber at which the corresponding absorption occurs for "C*O. Use integer relative atomic masses for this estimate.

P7E.5 In infrared spectroscopy it is common to observe a transition from the v = 0 to v = 1 vibrational level. If this transition is modelled as a harmonic oscillator, the energy of the photon involved is ħo, where o is the vibrational frequency. (a) Show that the wavenumber of the radiation corresponding to photons of this energy, v, is given by v=@/2nc, where c is the speed of light. (b) The vibrational frequency of 'HCl is w = 5.63 x 10“s"; calculate v. (c) Derive an expression for the force constant k, in terms of v. (d) For "C"O the v = 0 →1 transition is observed at 2170 cm. Calculate the force constant and estimate the wavenumber at which the corresponding absorption occurs for "CO. Use integer relative atomic masses for this estimate.

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 49P

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