User:Thomas S. Mahony/Notebook/Physics 307L/2009/11/23
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In this lab, we observed various spectral lines emitted from both hydrogen and deuterium gas bulbs. Using a lamp to excite the gas, and a constant deviation spectrometer, we recorded wavelengths for multiple lines, and using these results, determined the Rydberg constant.
We began by noting the hazards of the lamp: there was a risk of electric shock, so it was very important to be certain that the lamp was off when changing out bulbs. The lamp also got very hot, quickly, so one has to be careful when changing out bulbs. Next, we calibrated the spectrometer according to Professor Gold's manual. Calibration was done by aligning the spectrometer to the known mercury wavelengths listed in the manual. First we focused the spectrometer on the on the slit at the end of the optics, until the spectral lines were sharp and narrow. Next, we adjusted the positioning of the prism so that the spectral lines corresponded to their respective wavelengths. The prism was adjusted by hand and locked into position with a screw on top of the prism. During calibration and data collection, it was important to turn the wavelength dial in one direction to avoid systematic error from gear back lash, as the gears had dead spots when the direction was reversed.
The values collected in the data table below were collected from two different gas bulbs, Hydrogen and Deuterium,and we measured wavelengths for 4 different spectral line colors 5 times.
I calculated the Rydberg constant using each spectral line for both Hydrogen and Deuterium. I then took the weighted average of each, since they came from the same light source. For Hydrogen I calculated:
For Deuterium I calculated:
These can be compared to the accepted value from wikipedia:
The Rydberg constant for Hydrogen was 21 SEM's away from the accepted value, and the one for Deuterium was 24 SEM's away.
My uncertainty seemed small, so I plugged in the uncertainties in my measurements in place of the calculated SEM's. This yielded Rydberg constants that were about 10 SEM's away. The details of my analysis can be seen on the data table in the google doc.
Even using the uncertainties I made in my measurements in place of the calculated SEM's I was far enough from the accepted value that I cannot attribute this separation due to random error. It had to be systematic error of possibly one of the following forms:
Though my values were far off, I suspect that I grossly underestimated my uncertainty. The dial is on the spectrometer is not very precise, and it was rare that we ever had values line up direct with an integer increment of nanometers. So, we may not have been as far off as it seems from my calculations.