Data and Analysis:
Here are the two emission bands we observed; each has a P branch
and an R branch.
To gather the emission spectrum of the laser, we used a thermocouple power gauge and a
strip-chart recorder. All data was taken with a potiential of 18,000 Volts across
the plasma. Due to the slow response time and the thermocouple, the emission peaks
are smeared into one large emission mountain. The top picture is the band
corresponding to transitions from the (001) asymmetric vibrational mode to the (100)
symmetric vibrational mode. The left hump is the P branch and the right hump is the
The next photo is the band corresponding to transitions from the (001)
asymmetric vibrational mode to the (020) bending vibrational mode. Again, we see the
P branch on the left and the R branch on the right. Although it is difficult to tell
from the small photo, the separation of the peaks increases as we move farther from the
band center (v0).
Notice that in both bands, the P branch has a higher intensity than the R
branch. This results from a quantum mechanical effect whereby the wave functions
overlap in such a way to make P branch transitions more probable than R branch
transitions. The following data was taken by hand-- it is the R branch of the
transitions from (001) to (020). We see that R(12) is right in the center of the
For the sake of time, we did not set up the equipment needed to
measure the exact wavelengths corresponding to these molecular transitions. So, we use
well known data to discuss the analysis of the emission spectrum as if we were able to
know the exact values in our data. According to Eastham, peaks in the first band
have been observed from R(0) at 10.39 microns to R(62) at 10.02 microns as well as P(2) at
10.42 microns to P(68) at 11.18 microns. The lasing transition with maximum
intensity P(22) at about 10.6 microns (Eastham 205).
Knowing that the difference between rotational levels is , we can use a little algebra to calculate the E0
energy difference between the ground state (001) and the ground state of (100): E0=
1.91077 *10-20 J = 962.54 cm-1. For the rotational inertia, we
calculate a value of:
I=9.766*10-39 g-cm2 (compare to HCL, for which I=2.60*10-40
g-cm2 (Shankland 153)).
The force constant and vibration frequency for the CO2 symmetric stretch
mode can be calculated if we know the ground state energy for the symmetric stretch:
1388 cm-1 (Milonni 438)
, where mr is the reduced
mass of the system
For the Symetric Stretch mode:
w = 5.226 * 1014 rad/s. This
is about 83 trillion cycles per second, which is quite faster than most people can run.
For the H2 molecule, the frequency of vibration is even larger at
8.295*1014 rad/s (Sandin 254).
k = 3628.00 N/m. If a 200 pound person were to hang from a large
metal spring with this same force constant, the spring would stretch about 25 cm.
Similar analysis may be performed with other diatomic and triatomic systems.
Molecular spectroscopy is a very useful tool to learn much about the
interaction of molecules in a plasma.
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