Molecular Spectroscopy

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 R branch.

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 maximum.

    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:

    E₀ = 1388 cm^-1   (Milonni 438)

, where m_r 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.

Table of Contents:

Return to Jim's homepage  or  Davidson Physics.