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.

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

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.

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