ABSTRACT:
In this lab we calculated the vibrational constants
and Morse parameters of the diatomic iodine molecule
by examining the spectrum emitted by
argon-ion-laser-pumped iodine vapor. We found the
Morse parameters to be De = ne2 (4nexe)-1 cm-1 and b
= (2p2cm(Deh)-1)1/2ne cm-1. These values differ from
the accepted values of De and b by 28% and 18%,
respectively.
INTRODUCTION:
An examination of the vibrational spectra of the
diatomic iodine molecule can, through several
measurements and calculations, yield the molecules
Morse parameters. This is accomplished by examining
the spacing of the peaks of the wavelengths fluoresced
by iodine vapor that has been excited through laser
pumping, from which the vibrational constants and
therefore the Morse parameters can be calculated.
THEORY:
A diatomic molecule such as I2 can have many different
potential energies due to the varying energy levels
created by the interplay between magnetic and strong
forces as the interatomic separation of the molecule
varies. Therefore, when an electron in the molecule is
excited to a higher energy band, many energy gaps of
different distances exist for the electron to drop
down. Each transition has a particular wavelength of
light associated with it. By examining the spacing
between these wavelengths vibrational constants can be
determined, through the following method:
For a harmonic oscillator E=hf(v+1/2), so for an
enharmonic oscillator we can take the first two terms
of a Taylor series expansion; ne(v+1/2)- nexe(v+1/2)2.
Thus wave number of a photon transitioning from
vibrational level v to vibrational level v has wave
number equal to the difference of energies:
n(v, v) = nel + ne(v+1/2) - nexe(v+1/2)2 -
ne(v+1/2) + nexe(v+1/2)2
Equation 1
The spacings of wavelength peaks represent the
difference between two adjacent transitions, so the
difference of photon energies W(v) can be written:
W(v) = n(v, v) - n(v, v+1)
Equation 2
Which, through algebraic calculations that can be
found in Appendix A, becomes the equation:
W(v) = (ne 2xene) (2xene)v
Equation 3
The equation describes the linear relation between W
and v. Thus by graphing this data the vibrational
constants xe and ne can be determined. From these,
the Morse parameters of the diatomic molecule can be
calculated as follows:
De = ne2 (4nexe)-1
b = (2p2cm(Deh)-1)1/2ne Equation 4
Equation 5
PROCEDURE:
In this lab we used the 514.5 nm output of an
argon-ion laser to pump iodine vapor contained in a
glass chamber from vibrational energy level 0 to
vibrational energy level 43. A PC-mounted spectrometer
collected wavelength and intensity data from the
fluorescing iodine vapor. This data was compiled in a
spreadsheet for examination of wavelength peak
separation, from which the vibrational constants and
Morse parameters were calculated.
RESULTS:
The wavelength and intensity data we collected can be
found in Appendix B. The peaks were identified and
converted to wave number in Appendix C, from which
values for W are calculated. Appendix D contains the
graph of W vs. v from which we determined the
vibrational constants.
We found the vibrational constants to be xe = 0.0031
ne = 214.45
These correspond to Morse parameters De = 17421.35
cm-1
b = 1.576 x 108 cm-1
Our value for De is off of the accepted value of 12410
by 28%, while our value for b is off of the accepted
value of 1.858 x 108 by 18%.
CONCLUSION:
That our calculated values landed within 28% and 18%
of the accepted values shows that our experimental
methods and calculations are sound. However,
improvement on the quality of our Morse parameters
could be achieved by collecting better data. A better
alignment of the fiber optic cable with the beam of
fluorescing iodine would yield truer peaks which would
reduce the uncertainty in peak spacing. This would
result in a more accurate, straighter graph from which
to calculate vibrational constants and Morse
parameters.