User:Dan C. Wilkinson/Notebook/Physics 307L/11/24/10

= Balmer Series =

Purpose
The purpose of this lab is to measure the Rydberg constant. This will be accomplished using a constant deviation spectrometer.

Setup and Calibration
The apparatus is fairly simple consisting of a constant deviation spectrometer and a light source. The calibration will be done using a mercury lamp. Note: It was necessary to tweak the slit spacing for the fainter colors (red and deep violet). I had to open the slit slightly to allow enough light to get an accurate measurement. I am not sure if this will result in some small degree of systematic error.
 * I first focused on the 435.8nm line and adjusted the crystal to agree with the dial at ~435.8.
 * After calibrating to 435.8nm I then recorded the other dial readings corresponding to the known wavelengths.
 * The largest deviation from the known value was that of the red line, I was off my 9nm.

Theory
The equation for the Balmer Series is
 * $$\frac{1}{\lambda} = R_\mathrm{H}\left(\frac{1}{2^2} - \frac{1}{n^2}\right) \quad \mathrm{for~} n=3,4,5,...$$

Solving for R $$R_\mathrm{H} = \frac{1}{\lambda} \times \frac{1}{\left(\frac{1}{2^2} - \frac{1}{n^2}\right)}$$ Here n represent the quantum states. The lowest n (starting at 2+1) represents the lowest change in energy (the red lines) the larger the n the larger the energy change.

Data
Day 1  Hydrogen  The first lamp I used was Hydrogen. There must have been some contamination present because an almost continuous spectrum was observed instead of well defined lines. The red and green lines were still visible though the others were not discernible from the background. I had to "cheat" and google search the spectrum lines of hydrogen the contamination was so bad. This also throws off my results because there are lines that appear to be there but do not appear in the known spectrum of hydrogen. Deuterium There looks like some fine splitting in the 657nm line but instrumentation isn't accurate enough to discern. The yellow line(s) were not discernible.

Day 2 The same calibration procedure was done. The only difference was that Tyler took the data. Tyler has far better eyes than me so with his help we were able to pick out all of the spectrum lines in the Deuterium spectrum and use this knowledge to track back and assign the n values to the hydrogen ie we learned which lines had to be "skipped over" because they represented contamination instead of actual hydrogen lines.

Results
The calculated Rydberg Constant for hydrogen was $$ 1093(5)\times10^{4} \frac{1}{m}$$ and for deuterium $$ 1097(1)\times10^{4} \frac{1}{m}$$. Both of these results fall within 1 standard error of the mean of the accepted value of $$ 10973731.6 \frac{1}{m}$$. The respective errors in these calculations were 0.37% and 0.053% respectively.

Error
There was obvious very little error in our calculations. Considering the wavelength could (at best) give 4 significant figures of accuracy we cannot hope to get much better results. Our reported results are to for significant figures of accuracy. It is my believe that within the limits of the equipment we used and considering the contamination in the hydrogen, we did very well.