Optical Pumping: Absorption Cross-Section

Analysis

Error
In the experiment some of the sources of error would have been related to the temperature controller. The controller would after reaching equilibrium still fluctuate about the set value especially at higher temperatures (~70°C). Also the time the system takes to reach an equilibrium varied for each temperature so taking measurements after a fixed time would have introduced some error into the measurements. Uncertainty in reading measurements off the oscilloscope screen and reading vapour pressure off the graph were other sources of error. Finally the background light leaking into measurement chamber would have caused the detected signal to be higher than expected resulting in additional error.

Interpretation of Results
The theory expects an exponential decline of the measured light intensity while the results follow more of a linear fit. The reasons for this would be related to aforementioned error.

There is still a significant amount of light reaching the detector as the density increases. This intensity does not trail to zero because the total absorption area of the Rubidium is much less than the area presented to the incident radiation. This results in a lot of light radiation still passing through the vapour.

The experimental cross-section of Rubidium vapour is on the order of 10^-18 m while the theoretical maximum value for cross-section is 10^-9 m which is roughly the square root of the experimental value. This seems like a large experimental error except when compared to the cross section of the Rubidium atom. Assuming rubidium has a radius of the order of 10^-10 m then its cross section is on the order of the square of the radius, which is 10^-20 m. This value for the physical size of the atom agrees with the experimental value quite well considering the absorption of a certain wavelength is a lot more complex than photons physically 'bouncing' off the Rubidium atoms. Conclusively there must be a problem with the derivation of the theoretical maximum cross-section.