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
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 52AP
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Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4034ead-a81c-474d-bc26-2bb6a2dec46f%2Fc4a0378b-3ea1-46ae-8306-02406bc48b02%2Fdwmeazm_processed.png&w=3840&q=75)
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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