a frequency, but, instead, ²7/1₁ The "wavenumber" is the inverse wavelength, or ū = . 2 the familiar equation = c Linear frequency, v, is given by V 1 == C 2 so the angular frequency in terms of the wavenumber is @= 2лv = с@ = 2лсi As an example, for H35CI, the fundamental vibrational frequency is obs= 2.886 x 10³ cm-¹, so the harmonic oscillator force constant for ¹H35Cl is k =(2nci)² μ = 4.78 x 10² N/m. Here u is the reduced mass for the molecule, i.e.,
a frequency, but, instead, ²7/1₁ The "wavenumber" is the inverse wavelength, or ū = . 2 the familiar equation = c Linear frequency, v, is given by V 1 == C 2 so the angular frequency in terms of the wavenumber is @= 2лv = с@ = 2лсi As an example, for H35CI, the fundamental vibrational frequency is obs= 2.886 x 10³ cm-¹, so the harmonic oscillator force constant for ¹H35Cl is k =(2nci)² μ = 4.78 x 10² N/m. Here u is the reduced mass for the molecule, i.e.,
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Question
The infrared spectrum of 75Br19F consists of an intense line at 380. cm-1. Calculate its force constant, k, in units of N/m. (You can use the example as a sanity check.)
Transcribed Image Text:just one line whose frequency is given by
transitions, so this model predicts that the spectrum consists of
This prediction is in good accord with experiment, and this line is called the fundamental
vibrational frequency. For diatomic molecules, these lines occur approximately at 1014 Hz,
which is in the infrared region. It is customary in vibrational spectroscopy to use units of cm-1.
which, confusingly, is not really a frequency, but, instead, Linear frequency, v, is given by
1
V
====
2
C
Question:
@obs =
1
1
the familiar equation = c. The "wavenumber" is the inverse wavelength, or
m₁
k
√№
so the angular frequency in terms of the wavenumber is @ = 2лv = с@ = 2лсi
As an example, for H³5CI, the fundamental vibrational frequency is obs = 2.886 x 10³ cm-¹, so
the harmonic oscillator force constant for ¹H35Cl is k = (2лci)² μ = 4.78 x 10² N/m.
Here u is the reduced mass for the molecule, i.e.,
1
μ
+
2πV obs
1
2
m₂
The infrared spectrum of 75Br19F consists of an intense line at 380. cm-1. Calculate its
force constant, k, in units N/m. (You can use the example as a sanity check.)
Transcribed Image Text:4. Vibrational energy states associated with a Born-Oppenheimer potential energy surface (i.e.,
an individual molecular orbital) can be approximated as energy levels in a harmonic oscillator.
This works extremely well for the lowest energy vibrational states. Recall that the energy states
of a harmonic oscillator are separated by the same energy,
= hv (v + ²)
v = 0, 1, 2, ...
AE = Eu+1-E, = hv
v=4
v=3
U=2
AE = huobs = hw obs
AE is the same for all allowed transitions, so this model predicts that the spectrum consists of
just one line whose frequency is given by
@obs
U=1
v=0
= 2πVobs
This prediction is in good accord with experiment, and this line is called the fundamental
vibrational frequency. For diatomic molecules, these lines occur approximately at 1014 Hz,
which is in the infrared region. It is customary in vibrational spectroscopy to use units of cm-1.
Linear frequency, v, is given by
V 1
which, confusingly, is not really a frequency, but, instead,
1
the familiar equation = c. The "wavenumber" is the inverse wavelength, or ==
C
2
2
1
2
so the angular frequency in terms of the wavenumber is @= 2πv = c = 2лсi
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