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i) Calculate the energy of the ground, first and second excited rotational levels, expressed as a wavenumber in units of cm-1, assuming a rigid-rotor model.

i) Calculate the energy of the ground, first and second excited rotational levels, expressed as a wavenumber in units of cm-1, assuming a rigid-rotor model.

Principles of Modern Chemistry
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 9P
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Please only answer part ii

a) The rotational spectrum of carbon monoxide, *CYO where x and y indicate isotopes, with bond length of 1.13 Á, has two adjacent absorption lines at 15.36 and 19.20 cm-1, respectively. The centrifugal distortion constant, D, and vibrational frequency of the bond, , have values of 6.2 × 10-6 cm-1 and 2170 cm-1, respectively. Use the equations below to answer the following: h3 D : cm-1 32n412r2 kc k = 4@²n?c?µ i) Determine the origin of the rotational level giving rise to the two observed resonance lines. Calculate the energy of the ground, first and second excited rotational levels, expressed as a wavenumber in units of cm-1, assuming a rigid-rotor model. ii) ii) Calculate the relative populations of the first and second excited rotational levels at 300 K. iv) Using the spectroscopic data, calculate the reduced mass of XCYO.
Transcribed Image Text:a) The rotational spectrum of carbon monoxide, *CYO where x and y indicate isotopes, with bond length of 1.13 Á, has two adjacent absorption lines at 15.36 and 19.20 cm-1, respectively. The centrifugal distortion constant, D, and vibrational frequency of the bond, , have values of 6.2 × 10-6 cm-1 and 2170 cm-1, respectively. Use the equations below to answer the following: h3 D : cm-1 32n412r2 kc k = 4@²n?c?µ i) Determine the origin of the rotational level giving rise to the two observed resonance lines. Calculate the energy of the ground, first and second excited rotational levels, expressed as a wavenumber in units of cm-1, assuming a rigid-rotor model. ii) ii) Calculate the relative populations of the first and second excited rotational levels at 300 K. iv) Using the spectroscopic data, calculate the reduced mass of XCYO.
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