User:Ryan P. Long/Notebook/Physics 307L/2009/11/23

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Balmer Series

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. Click here for the summary.

SJK Incomplete Feedback Notice
Incomplete Feedback NoticeMy feedback is incomplete on this page for two reasons.  First, the value of the feedback to the students is low, given that the course is over.  Second, I'm running out of time to finish grading!
Incomplete Feedback Notice
My feedback is incomplete on this page for two reasons. First, the value of the feedback to the students is low, given that the course is over. Second, I'm running out of time to finish grading!
SJK 17:40, 18 December 2009 (EST)
17:40, 18 December 2009 (EST)Very good primary notebook.
17:40, 18 December 2009 (EST)
Very good primary notebook.

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

The values collected in the google doc below are collected from two different gas bulbs, Hydrogen and Deuterium, we measured wavelengths for four different spectral line colors five times.

View/Edit Spreadsheet

Analysis

In order to calculate my value for R, I used the equation given by professor Gold's manual:

\frac{1}{\lambda }=R(\frac{1}{2^2}-\frac{1}{n^2}), n=3,4,5,..\,\!

Using excel, I averaged the wavelengths for each color line, then used that value for λ in the equation above, I then averaged the R values and calculated the standard error of the mean for those values of R:

From Hydrogen spectra, my value is R=1.09421\pm .01821\times 10^{-7} m^{-1}


From Deuterium spectra, my value is R=1.09416\pm .01746\times 10^{-7} m^{-1}


The accepted value from NIST is R=1.09737\times 10^{-7}  m^{-1}

My values both had error percentages of about .003% as compared to the accepted value from NIST.

My excel file can be downloaded here.

Conclusions

SJK 17:39, 18 December 2009 (EST)
17:39, 18 December 2009 (EST)I share your amazement at the precision of optical spectroscopy!  Interestingly, your uncertainty is much larger than Tom's (thought still small)...Tom worried that his was too small, so comparing your methods could address that question.
17:39, 18 December 2009 (EST)
I share your amazement at the precision of optical spectroscopy! Interestingly, your uncertainty is much larger than Tom's (thought still small)...Tom worried that his was too small, so comparing your methods could address that question.

Although at first I was weary about using the old school spectrometer, the values I calculated were very close to the accepted value, in fact they seem too close, as such I'm skeptical that I may have inadvertently missed something. If I were to re-do this experiment, I would probably collect more data, and perhaps experiment with other methods of calibrating the spectrometer, maybe with other gas tubes. I'd like to thank my partner Tom for being a joy to work with as always.



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