Sebastian Balmer Series

=Partner=

=Purpose= The purpose of this lab was to use a constant deviation spectrometer to observe/measure the spectral lines for hydrogen gas in order to calculate the Rydberg Constant. The gas in the tubes are in an excited state and when a transition from a higher state to a lower state takes place, a certain wavelength of light appears as a bright line in the full spectrum. These lines can be observed through the spectrometer, and with a calibration of the spectrometer to known wavelengths, we can measure the wavelengths at which the transitions take place. We also observed the spectral lines for Deuterium, but we did not get to do much outside of the scope of the experiment because we were trying to figure out what we were doing wrong, or what was going wrong with our hydrogen spectra measurements.

=Lab Data= My Lab Notebook Balmer Series Lab Data - September 15, 2010

=Equipment=
 * Spectrometer - Adam Hilger; London, England; Serial: 12610
 * Spectrum Tube Power Supply - Model: SP200 (5000V;10mA; Electro-Technic Products)
 * Mercury Tube
 * Hydrogen Tube
 * Deuterium Tube

=Lab Summary= This lab called for my partner, Matt Cordova, and me to use a spectrometer to measure the spectral lines of a Mercury vapor tube for the calibration of the spectrometer, and then continue on to measure the wavelength of the spectral lines for Hydrogen and Deuterium. Also, the lab manual called for us to try to observe and resolve the Sodium doublet, but due to time constraints we were unable to get to this last part. On the first day of our experiment, my partner and I had some trouble figuring out how to calibrate the spectrometer, as well as reading the Vernier scale on the dial that displays the wavelength (a picture can be found in my primary lab notebook). After resolving these issues and calibrating the spectrometer to the Mercury lines, we began taking data for the Hydrogen tube. We then compared our initial results with a former Physics 307L students data which can be found here. All of our measurements were very similar to the former student's data except for the measurement of the smallest violet (Violet1) wavelength. This issue will be discussed further in my primary lab notebook, but I am making a note of it here because the measurements for Violet1 were not included in our calculations of the average Rydberg constant (the raw data is still in my primary lab notebook, but is not used for any calculations other than finding the average of the measurements). My Partner Matt suggested first that we ignore these measurements, and then Prof. Koch also suggested that we ignore the measurements. On the second day, we were able to record a second trial of the Hydrogen measurements, as well as two trials for the Deuterium measurements. We also tried to figure out why we were getting what appeared to be wrong data. It was very strange though since all the other wavelengths we close to the accepted values. Prof Koch also tried to observe the wavelength in question, Violet1 (n1=2 to n2=6), but he reported a value that was a few tenths of a nanometer away from our measurements. He tried repositioning the crystal and I think he also tried recalibrating to the Mercury tube, but this did not fix our problem. The final part of this lab was to simply calculate an experimental value for the Rydberg constant for both the Hydrogen spectra and the Deuterium spectra.

=Calculations and Results=

From our data, we calculated the following values for the Rydberg constant: $$ R_{calc Hydrogen} = (10976969 +/- 7304)m^{-1}\ \ $$ $$ R_{calc Deuterium} = (10989761 +/- 1736)m^{-1}\ \ $$

Accepted Values
$$R_{\infty}= 1.097\;373\;156\;852\;5\;(73) \times 10^7 \ \mathrm{m}^{-1}$$ $$R_{Hydrogen}= 10967758.3406 m^{-1}\ \ $$ $$R_{Deuterium}=10970746.1986 m^{-1} \ \ $$
 * Note: These Accepted values were calculated using the reduced mass equation for the Rydberg constant which can be found here (more about this calculation can be found in my primary lab notebook).

Comparison
I think that our data and calculations were fairly accurate for this lab considering the spectrometer that we were using.
 * We were within 2 SEM's for the $$R_{calc Hydrogen}$$ calculation compared to the accepted value for Hydrogen.
 * We were withing 11 SEM's for the $$ R_{calc Deuterium}$$ calculation compared toe the accepted value for Deuterium.

Error
The error in this lab would most likely come from errors in the calibration or the spectrometer, misreading the value on the dial, and the width of the slit opening. The calibration was kind of hard because a slight movement of the crystal would result in a drastic change in position of the line being viewed. Also, if the screw on the crystal is tightened too much, it can skew the position of the dial. Reading the dial is also difficult because there are not fine divisions. Because of this, we had to round every wavelength to the tenth of a nanometer. As mentioned in the lab manual (which can be found in the "Procedure section"), we had to find a decent slit width that would allow for an intense enough viewing, but also for a fine resolution. Opening the slit too much would result in a very thick line, which would obviously increase our error when we tried to put the cross hairs on the center of the line, while too narrow of a slit width would decrease the intensity of the lower wavelengths to a point at which that are almost not viewable. All of the preceding topics would result in systematic error.Overall I feel like we recorded decent data considering the instruments we were using.

=Conclusions= Although this lab was very simple to set up and the data collection was not very difficult, I did learn a great deal about the error analysis portion of analyzing data. I am still not too sure about whether I analyzed the Standard error of the mean correctly, but I did my best with what we have done in lecture.