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CHEM4591 T 911:50am
Feb 8th
Weifeng Wang
Partner: Zheng Zheng
TA: Samuel Park
VibrationRotation Spectrum of HCl
Abstract
The vibrationRotation spectrum of HCl was measured by the fundamental
spectrum and overtone spectrum. The fundamental spectrum was run on the FTIR
instruments, and the overtone spectrum was run on the Cary 17 instrument. The B’ we
obtained for Cl
35
was 9.82 cm
1
, with an error of 6%. The B” for Cl
35
was 10.42 with an
error of 2%; the B
e
was10.55, with an error of 0.4%; the r
e
was 1.28, with an error of
0.7%;
ϖ
e
χ
e
was 49.5 cm
1
, with an error of 6%; the D was 44910 cm
1
, with an error of
25.7%.
Introduction
When a molecule absorbs light, its internal energy increases by the photon energy
hv. The energy that the molecule obtained is used to excite the molecule’s electronic,
vibration, and rotation state. In this experiment HCl molecules are used for analysis of
their vibrationrotation spectrum. Two methods were employed to obtain the spectrum:
one is the Cary 17 spectrophotometer for the first over tone spectrum, and the other is the
FTIR instrument for the fundamental spectrum.
Two basic theoriesrigid rotor and harmonic oscillator are always used to
approach the ideal light absorption.
For diatomic molecules, the energy of rotation is calculated by
1
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J
= BJ(J+1)
J = 0,1,2.
..
(1)
Here B is the rotational constant, and J is the rotational quantum number.
B is described as,
B = h/(8π
2
cμr
2
)
(2)
In this equation, h is the Planck constant; c is the velocity of light; r is the HCl bond
length; μ is the reduced mass, given by,
μ = M
1
M
2
/(M
1
+ M
2
)
(3)
According to Hook’s law and Schrödinger’s equation, the energy of vibration is
illustrated as,
E
v
= ħω(v + ½) (v = 0, 1, 2, …)
(4)
In this equation, ħ is h/2
π
, and ω is the angular frequency.
Usually, it is convenient to introduce a spectroscopic constant with units of cm
1
.
Dividing the energy by hc, a new equation in terms of ω
e
is used,
E
V
=
ω
e
(v+1/2)
(5)
Where
ω
e
=ħω/hc = ω/2πc.
However, these equations must be corrected before applying them to the real
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 Spring '11
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