Vibrational States in a CO2
Laser
Phillip Stewart
Partner: Jonathan Esten
with direction from W. Christian
3-15-00
Abstract
Experiments were performed using a CO2 laser in a
75% He -10% CO2 - 15% N2 gaseous mixture sent
through a chopper and into a power meter. Observed
and discussed here are the transitions from the (0,0,1)
asymmetric vibrational mode to the (1,0,0) symmetric
vibrational mode and the transitions from the (0,0,1)
asymmetric vibrational mode to the (0,2,0) bending
vibrational mode. The Spring constant of the molecule
was found to be k = 3628 N/m and the distribution of
the P and R peaks looked to be a Boltzmann
relationship.
Why Study the CO2 Laser?
High power and efficiency. Used in
cutting and welding in industry.
Easily shows the molecular properties
of CO2
Apparatus
Water
Power Meter
Mirror
Chopper
Cathode
Laser
Anode
Grating w/Motor
Gas Tank
To drain
Theory
When lasing begins at just under 15,000 Volts, electrons
bombard the N2, but they cannot radiate.
They excite the CO2 molecules to vibrational states,
because their energies are very close to the required
level for the asymmetric vibrational state in CO2
More Theory
The CO2 laser is characterized by the vibrational and
rotational transition states in the CO2 molecule, and the
molecules act like simple harmonic oscillators in three
distinct ways.
Yet More Theory
A molecule in a vibrational state also has associated
with it many rotational states. Those states have
degeneracy 2J+1 and account for the miniature
peaks in the data acquired.
To see all of these miniature peaks, a chopper must
be added to avoid lock-in (Milloni)
 Milloni, Peter W. “Lasers”, New York: 1988.
E0
P-Branch
10.4
R-Branch
9.4
Ratio
Chopper Added
1.8
1.6
1.4
Ratio
1.2
1
Series1
0.8
0.6
0.4
0.2
0
0
500
1000
1500
2000
Grating Tilt
2500
3000
3500
Slice of the Graph
1.8
1.6
Power (W)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
3.8
3.9
4
4.1
Grating Tilt (mm)
4.2
4.3
4.4
Analysis
So once again concentrating on the 10.4 micron state, we can
use well known values for the energies associated with the
transitions from the (0,0,1) state to the (1,0,0) state.
Knowing this equation:
We are able to find the
moment of inertia.
Using values from Eastham at specific J’s, the calculation
proves simple:
E0=959.82 cm-1
I=9.654*10-39 g-cm2
These values are close to last year’s. The small differences
may be accounted to the different operating voltages used.
•Eastham, Derek. Atomic Physics of Lasers. Philadelphia: Taylor and Francis, 1986
Analysis
Another quantity that is important to find is the spring constant,
k. Because
, and
, the equations can be
combined to get k.
E0 = 1388 cm-1 (Milonni)
w = 5.226 * 1014 radians/second
k = 3628 N/m
As expected, this spring constant is huge and thus the
displacement of the stretching is quite small (obviously).
Reference: Jim Nolan, http://www.phy.davidson.edu/jimn/Welcome.html
Conclusions
By examining the vibrational and rotational states of the
CO2 molecule, the spring constant was found to be k =
3628 N/m.
The distribution of the P and R peaks follows a Boltzmann
distribution, where the shape of that distribution is highly
dependant on the moment of inertia– the smaller the
moment of inertia, the more symmetric the peaks.