Physics 309

The Configurations of Carbon Monoxide

The excited states of the diatomic molecule carbon monoxide (CO) can be observed by crossing a beam of electrons with another beam consisting of carbon monoxide. The energy spectrum of the scattered electrons is displayed below. If the potential energy between the two atoms is truly a harmonic oscillator potential, then the energies of the excited states can be represented by

$$E = (n + {1 \over 2}) \hbar \omega_0 \qquad .$$

Outline in careful language how you would test this hypothesis using the data shown below. How would you test the agreement between the theory and the experimental data? How good is the harmonic oscillator hypothesis at reproducing this data? Be quantitative in your answer. How does the spring constant implied by your results compare with typical values of everyday springs? The springs used in the general physics laboratory have spring constants of about 3 N/m.

A rough measure of the range of oscillation of the CO molecule is provided by the classical amplitude. What is the classical amplitude of the molecule we are studying here in the n=2 state? How does your result compare with the typical CO inter-molecular separation of about $\rm 1 \AA$? We often treat molecules as if they were made of atoms rigidly held in place by sticks. For those who took organic chemistry, recall the tinker toys you used to study the configurations of different molecules. What, if anything, do the results here have to say about our tinker toy model?