For a molecule to give rise to Raman scattering, the vibrational mode must exhibit a change in polarizability. (a) Determine the total number of vibrational modes that should exist for carbon tetrachloride. (b) Use the following character table for a tetrahedral molecule to determine which modes are Raman active (state whether each is polarized or depolarized), which are IR active and state the degeneracies of each mode. B Td Β΄ / B B V₁ A₁ (Rp) 1/2 E (Rdp) V3 V4 F2 (IR, Rdp) F2 (IR, Rdp) "Only one of two E or three F modes in the respective degenerate sets is shown for the AB, and AB4 cases. Each mode of a degenerate set oscillates at the same frequency, and the description of the nuclear motion associated with each component of a degenerate mode is somewhat arbitrary. Rp indicates an allowed Raman band that is polarized; Rdp indicates an allowed depolarized Raman band. (c) The natural abundances of the two isotopes of chlorine are 76% 35 Cl and 24% 37C1 such that CCl4 has several isotopomers. The v₁ vibrational mode is totally symmetric such that it is possible to resolve the peaks that result from the isotopomers. Show the peaks for each isotopomer in order from lowest to highest energy. (d) The relative intensities of the isotopomers in the v₁ vibrational mode can be estimated from the product of the nominal probability and the number of arrangements. Show the relative peak heights for each isotopomer.
For a molecule to give rise to Raman scattering, the vibrational mode must exhibit a change in polarizability. (a) Determine the total number of vibrational modes that should exist for carbon tetrachloride. (b) Use the following character table for a tetrahedral molecule to determine which modes are Raman active (state whether each is polarized or depolarized), which are IR active and state the degeneracies of each mode. B Td Β΄ / B B V₁ A₁ (Rp) 1/2 E (Rdp) V3 V4 F2 (IR, Rdp) F2 (IR, Rdp) "Only one of two E or three F modes in the respective degenerate sets is shown for the AB, and AB4 cases. Each mode of a degenerate set oscillates at the same frequency, and the description of the nuclear motion associated with each component of a degenerate mode is somewhat arbitrary. Rp indicates an allowed Raman band that is polarized; Rdp indicates an allowed depolarized Raman band. (c) The natural abundances of the two isotopes of chlorine are 76% 35 Cl and 24% 37C1 such that CCl4 has several isotopomers. The v₁ vibrational mode is totally symmetric such that it is possible to resolve the peaks that result from the isotopomers. Show the peaks for each isotopomer in order from lowest to highest energy. (d) The relative intensities of the isotopomers in the v₁ vibrational mode can be estimated from the product of the nominal probability and the number of arrangements. Show the relative peak heights for each isotopomer.
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 58AP
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Transcribed Image Text:For a molecule to give rise to Raman scattering, the vibrational mode must exhibit a change in
polarizability.
(a) Determine the total number of vibrational modes that should exist for carbon tetrachloride.
(b) Use the following character table for a tetrahedral molecule to determine which modes are
Raman active (state whether each is polarized or depolarized), which are IR active and state
the degeneracies of each mode.
B
Td
Β΄ / B
B
V₁
A₁ (Rp)
1/2
E (Rdp)
V3
V4
F2 (IR, Rdp)
F2 (IR, Rdp)
"Only one of two E or three F modes in the respective degenerate sets is shown for the AB, and AB4 cases. Each
mode of a degenerate set oscillates at the same frequency, and the description of the nuclear motion associated
with each component of a degenerate mode is somewhat arbitrary.
Rp indicates an allowed Raman band that is polarized; Rdp indicates an allowed depolarized Raman band.
(c) The natural abundances of the two isotopes of chlorine are 76% 35 Cl and 24% 37C1 such that
CCl4 has several isotopomers. The v₁ vibrational mode is totally symmetric such that it is
possible to resolve the peaks that result from the isotopomers. Show the peaks for each
isotopomer in order from lowest to highest energy.
(d) The relative intensities of the isotopomers in the v₁ vibrational mode can be estimated from
the product of the nominal probability and the number of arrangements. Show the relative
peak heights for each isotopomer.
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