User:Roberto Sebastian Rosales/Notebook/Physics 307L/2010/09/15
|Balmer Series Lab Data - September 15, 2010|| Main project page|
BackgroundSJK 13:23, 22 October 2010 (EDT)
The Rydberg constant is given by the following equation which can be found here:
(which can be found here), where and c are the mass of an electron, the charge of an electron, the permittivity of free space, Planck's constant, and the speed of light respectively. After reading the Wikipedia article about the Rydberg constant, I learned that when dealing with Hydrogen we must use the reduced mass version of the Rydberg constant given by: (which can be found here, where M is the atomic mass of the nucleus. We can use the relation (which can be found here in order to predict the Rydberg constant by measuring the wavelength of emission for known energy state transitions (n1, and n2 are the quantum numbers for the electrons transitioning). For the Balmer series we will be using n1 = 2, and the accepted values for the transitions are (and are from this Wikipedia Page:
NoteWe will be comparing two calculated Rydberg constants, one for Hydrogen and one for Deuterium, to the accepted value obtained from the reduced mass Rydberg constant (not the Rydberg constant for an infinitely massive atomic nucleus).SJK 12:56, 22 October 2010 (EDT)
We used Prof. Gold's lab manual in order to complete this lab manual. We did however have to figure out how to calibrate the spectrometer on our own since the lab manual simply states to calibrate it to the Mercury lines.
SetupSJK 12:58, 22 October 2010 (EDT)
This lab was fairly easy to setup and took only minutes to get up and running. We simply set the spectrometer on the table top, and then positioned the Spectrum Tube Power Supply on top of two books directly in front of the slit opening. The books were used to ensure that the middle part of the tube was being viewed as opposed to the top or bottom parts of the tube. Of course the lights needed to be turned off in order to see the spectral lines through the spectrometer.
CalibrationSJK 12:59, 22 October 2010 (EDT)
Initially we had to figure out how to read the dial that displayed the wavelength, and how the scale, when rotated, changed what was being viewed in the spectrometer. After some inspection of the apparatus, we realized that the crystal (shown below) itself actually rotates as the dial is turned. So, in order to calibrate the spectrometer, we loosened the screw that holds the crystal in place, found whichever spectral line we were calibrating to in the Mercury spectrum and aligned it with the cross-hairs in the eye piece, and then tightened the screw to hold the crystal in place. Throughout this process, as well as the measuring process, we were careful to avoid gear back lash by always starting at a lower wavelength and turning the dial towards the higher wavelength. Also, we decided to calibrate the spectrometer first to the green line for Mercury, and then take measurements for both Hydrogen and Deuterium. We then re-calibrated the spectrometer to the violet line (435.8nm) and took another set of data for both Hydrogen and Deuterium. Finally, we calibrated the spectrometer to the red line for Mercury and took another set of data. We did this hoping that we would eliminate some systematic error in our measurements. The wavelengths we used to calibrate the spectrometer are from Prof. Gold's lab manual and are as follows:
IssuesSJK 13:03, 22 October 2010 (EDT)
As mentioned in the Lab Summary, we experienced some problems when measuring the line for Violet 1 for Hydrogen. We first suspected either a bad calibration or a lack of waiting for the tube to heat up to be the culprit of the misreadings. We re-calibrated the spectrometer, but got the same reading of about 418nm for the Violet 1 line. We then proceeded to calibrate to a different line for Mercury, but the problem persisted. After obtaining reasonable data for all of the other lines for Hydrogen, my partner and I decided to move on and just record the results that we were getting. On the second day of this lab, Prof. Koch asked how we were doing and we made him aware of the issue. Upon taking his own measurement of 417.8 nm (if I recall correctly), he also realized that something had to be wrong. The three of us attempted to reposition the crystal in hopes of correcting the error, but this did not work. I believe that he also calibrated the spectrometer himself, but the same wavelength was observed. I suspect that the tube or the Hydrogen gas in the tube is the reason for the poor data, because we observed the correct wavelength of around 410 nm for the Deuterium tube. We wanted to test a different Hydrogen tube, but the other tube had a note attached that read "Broken," so we did not test it. So, with the suggestion from my lab partner and Prof. Koch, I decided not to include the data for Violet 1 in our RcalcHydrogen calculation. A Rydberg constant for the Violet 1 average wavelength is available in the Google Spreadsheet shown in my "Data and Calculations" section, but it is not a part of any other calculations.
Data and Calculations
All of the raw data can be found in the following spreadsheet, as well as the calculations for our experimental Rydberg constant for both Hydrogen and Deuterium.
For the average wavelength calculations, we simply took an average of all the data for one transition (i.e. all the Blue-Green wavelengths for Hydrogen) for Hydrogen and Deuterium separately. , where xi is one of the measurements and n is the total number of measurements. I was unsure about whether taking the average of the wavelengths was allowed or a good idea, but in class we discussed that if the observations are normally distributedSJK 13:09, 22 October 2010 (EDT)
From our data, we calculated the following values for the Rydberg constant:
ComparisonSJK 13:16, 22 October 2010 (EDT)
I think that our data and calculations were fairly accurate for this lab considering the spectrometer that we were using.
Using the following equation we calculated the percent error: .
ErrorThe 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.SJK 13:18, 22 October 2010 (EDT)
ReferencesSJK 13:18, 22 October 2010 (EDT)
I looked at David Weiss' and Tom Mahony's lab notebooks for some help on calculating the SEM for our Rydberg constants. I referenced Wikipedia multiple times and the links can be found near the information that was obtained from Wikipedia.