Physics307L F08:People/Barron/labsum~Balmer
Balmer Series Lab Summary
Here is the lab manual page.
Here are my lab notes.
Partner: Justin Muehlmeyer
Introduction
In this lab, we ascertain the value of the Rydberg constant, R, using a constantdeviation spectrometer. Do to photoelectric effect, hydrogen gives off light in the visible spectrum through electrons jumping from energy levels with principle quantum number (n) higher than two to n=2. The relation of R to wavelength (λ) and n is given through this expression:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{1}{\lambda}=R(\frac{1}{2^{2}}\frac{1}{n^{2}}), }
discovered empirically by Swiss high school teacher Balmer in 1885. Rydberg and Ritz later modified the above equation, giving rise to the possibility of other spectra series.
Approach
Matching colorspecific spectra to values of the principal quantum number n gives many different values of R. The key is to find find the specific quantum numbers which reveal a fairly constant R over each color spectra. Using datavisualization tools in MATLAB, generating and comparing many Rs is a breeze. After ascertaining the proper values of n, one can generate an experimental value for R with a weighted mean.
Final Results
inal R computed as a weighted mean, with error bars corresponding to the extrema of all the relevant data.
File:FinalRcomp.tif 
Hydrogen [1/m]  Deuterium [1/m] 
R_{final} = 1.088e+07

R_{final} = 1.101e+07

The accepted Rydberg constant is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle R=1.0967758\cdot 10^{7} m^{1},}
and doesn't appear to correlate with my uncertainty. Not a good showing overall.
Looking at the trends in R with increased wavelength readings, I believe this experiment has large systematic error  so much so that I didn't compute a statistical confidence interval on the final value. I believe this is the same situation as was discussed in the last lab lecture, where error bars generally disagree. With that in mind, I set my error to the extrema of the data errors.
In my data analysis, I saw fit to throw out information from yellow spectra in both Deuterium and Hydrogen. My thought process is in my notes.