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

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The accepted value from NIST is <math>R=1.09737\times 10^{-7}  m^{-1}</math>
The accepted value from NIST is <math>R=1.09737\times 10^{-7}  m^{-1}</math>
My values both had error percenta




Revision as of 17:06, 6 December 2009

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Balmer Series

In this lab, we observe various spectral lines emitted from both hydrogen and deuterium gas bulbs. Using a lamp to excite the gas, and a constant deviation spectrometer, we can record wavelengths for multiple lines, and using these results, determine 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 begin my noting the hazards of the lamp, there is a risk of electric shock, it is very important to be certain that the lamp is off when changing out bulbs. The lamp also gets very hot, quickly, so one has to be weary of that when changing out bulbs. Next, we calibrated the spectrometer according to Professor Gold's manual. Calibration is done by using a mercury bulb and known mercury wavelengths listed in the manual. First we focused the spectrometer on the mercury spectrum by adjusting the slit width on the spectrometer, when the spectral lines are sharp and narrow, we then adjust the positioning of the prism. The prism is adjusted by a screw which rotates the prism until the given values of wavelength from the manual match up with the colors listed. During calibration and data collecting, it is important to turn the screw in one direction to avoid systematic error from gear back lash, as the gears have dead spots, when the direction is 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. {{#widget:Google Spreadsheet

key=tTvLAZPMkm8iJOfkRVvlnFw width=760 height=300

}}

Analysis

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

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

Using excel, I averaged the wavelengths for each color line, then used that value for [math]\displaystyle{ \lambda }[/math] 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 [math]\displaystyle{ R=1.09421\pm .01821\times 10^{-7} m^{-1} }[/math]


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


The accepted value from NIST is [math]\displaystyle{ R=1.09737\times 10^{-7} m^{-1} }[/math]

My values both had error percenta



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