Balmer Series

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Balmer Series

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^{SJK 17:03, 18 December 2009 (EST)}

17:03, 18 December 2009 (EST)
Very good notebook.

Summary

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.

Equipment

Antique “constant-deviation” spectrometer
Spectrum Tube Power Supply (Model SP200)
Mercury Vapor Spectrum Tube (S-68755-30-K)
Hydrogen Spectrum Tube (S-68755-30-G)
Deuterium Spectrum Tube (S-68755-30-E)

Setup

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.

Data

Purple Spectral Line
Turquoise Spectral Line
Red Spectral Line

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. {{#widget:Google Spreadsheet

key=tQ7bmgkpVrGcQq9Z8otGAhQ

width=760

height=300

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Analysis

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:

[math]\displaystyle{ R = 1.09561(8) \times 10^7 \ \mathrm{m}^{-1}, }[/math]

For Deuterium I calculated:

[math]\displaystyle{ R = 1.0948(1) \times 10^7 \ \mathrm{m}^{-1}, }[/math]

These can be compared to the accepted value from wikipedia:

[math]\displaystyle{ R = 1.097\;373\;156\;852\;5\;(73) \times 10^7 \ \mathrm{m}^{-1}, }[/math]

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.

Conclusion

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:

Mis-calibration of the spectrometer: It is possible that in the process of aligning the spectrometer to the spectral lines from a Mercury source, we made an error (tightened the screw which turned the crystal or misread the dial)
Gear Back lash (although we were careful to only measure values turning the gear one direction)
Too large of a slit opening: The slit opens from one side, rather then evenly on both sides, so this may have skewed our data to one direction.

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.

Acknowledgments

As always, thanks to Ryan. Without him, this experiment wouldn't have been half as cool, or successful.

Steve Koch 16:59, 18 December 2009 (EST): Cool! In the first part of the video, it looks like the bullet "splashes" like water droplets do. It reminded me of an interesting result from U. Chicago a few years ago, showing that water doesn't splash in a vacuum. Do bullets "splash" in a vacuum? I guess probably the physics of the two situations aren't the same, but still very cool videos.