Oscillations and Resonance in a Carbon Dioxide Laser


Description of the Experiment:

    This experiment was used as an introduction to the apparatus and mechanics of molecular lasers.  The Carbon-Dioxide laser is a particularly excellent example because it so clearly demonstrates the characteristics of a molecular laser and as well as the dynamics of molecular vibration and rotation.  The apparatus used was similar to that in the Helium-Neon laser experiment.  A discharge tube was continuously pumped with a mixture of Helium, Carbon-Dioxide and Nitrogen and an antiquated power source was used to create a potential difference of 18,000 Volts across the tube.  The frequency of the emitted light was variable by adjusting a Littrow grating located at the back of the laser cavity.  The power of the emission was determined by a thermocouple power meter.  With a motor that rotated the grating and a strip chart recorder we were able to gather the emission spectrum of the laser.

Oscillations and Resonance in the Experiment:

   In this experiment we again encounter resonance in the excitation of Carbon-Dioxide through collisional excitation transfer, however we also encounter resonance at the molecular level.  Molecular lasers function differently than atomic lasers because they involve vibrational and rotational energies as well as electron energies.  Resonance is found in these molecular vibrations which occur because the relative positions and orientations of the atomic nuclei are not absolutely fixed within the molecule.   The energies associated with molecular vibration are quantized just like electron energies so only certain vibrational levels are possible.  The possible forms of resonant vibration are referred to as the vibrational modes of a molecule, and each of these vibrational modes has a series of quantized energy levels.  In order to understand the mechanics of molecular vibration it will help to consider a classical model of resonant vibration.  

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    In a diatomic molecule such as O2, N2 or CO, the individual atoms are bound by a molecular binding force that functions much like the spring constant k of a linear harmonic oscillator.  When excited, the two nuclei will vibrate much like two masses connected by a spring.  While real diatomic molecules are not perfect harmonic oscillators, their potential energy functions approximate those of a harmonic oscillator for a certain value of inter-nuclear separation.   Although Carbon Dioxide is a triatomic molecule, it behaves much like a simple diatomic molecule because its structure is linear.  Such a linear triatomic molecule has three normal modes of vibration, described as the asymmetric stretch mode, the bending mode and the symmetric stretch mode.  Again these vibrational modes occur only at the natural resonant frequencies of the Carbon-Dioxide molecule.

 

vibenergies.JPG (10058 bytes)

 

  Each one of these normal modes of vibration for the CO2 molecule is associated with a characteristic frequency of vibration as well as a ladder of allowed energy levels.  The energy levels of  the three vibrational modes of CO2 are quantized and approximated by the energy expression for the quantum mechanical simple harmonic oscillator.  The energy level diagram to the left depicts the three vibrational modes of  CO2 and their first couple of energy levels.  Notice that the characteristic frequency for the symmetric stretch mode is 1288cm-1 and  for the bending mode it is 667cm-1.  For the asymmetric stretch mode, the characteristic frequency is much higher at  2349cm-1.

 

    Resonance is also encountered in the excitation of the Carbon-Dioxide.  As in the Helium-Neon laser, the Carbon-Dioxide is excited through a collision with excited N2 molecules.  This transfer of energy occurs by a resonant effect.  Since the vibrational energy levels of N2 are metastable and have an energy very close to that of the first energy level of the asymmetric stretch mode of Carbon-Dioxide, they have ample time to transfer their energy and excite the Carbon-Dioxide molecules.  Again this process is analogous to a classical understanding of resonance in which two identical tuning forks in close proximity will vibrate at the same frequency if one is already vibrating.  The lasing occurs when Carbon-Dioxide in the excited asymmetric mode makes the transition to the bending or symmetric stretch modes.  The Carbon-Dioxide then returns to its ground state through another collisional transfer of energy with the Helium atoms.

    To conclude, in this experiment we observed resonant effects in the process of excitation of the molecules and in the vibrational states of the molecules themselves.  While these effects occur on the atomic level they can still be suitably modeled with a classical conception of resonance.  It is also important to note that the oscillations of these atomic systems still behave linearly.   In the case of collisional transfer of energy, the driving periodic force, or excitation, will always produce a corresponding periodic output as long as the energy levels of the two atoms, or molecules, are equivalent.  In the case of molecular vibration, if one atom of a molecule is oscillating with some period then it cause a corresponding oscillation in the other atoms- the same resonant effect observed in the classical system of two masses connected by a spring.


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