User:Thomas S. Mahony/Notebook/Physics 307L/2009/11/09
e/m Ratio Lab | Main project page Previous entry Next entry | |||
e/m LabIn this lab Ryan and I tried to find the charge to mass ratio for an electron. We used an apparatus with an electron gun that fired into a helium filled bulb placed inside a magnetic field to excited a ring of Helium atoms. We measured the radius of the ring, and knowing about the Lorentz force, we calculated e/m. SummarySJK Incomplete Feedback NoticeSJK 18:07, 15 December 2009 (EST)Equipment
SetupFirst we connected the HP power supply to the Helmholtz coils on the Uchida apparatus with one of the BK multimeters in series. Next the other BK multimeter was connected to the voltmeter jacks on the Uchida apparatus. The Soar power supply was connected to the heater jacks on the Uchida. Finally, the Gelman was connected to the electrodes on the Uchida. We followed the procedure in Professor Gold's manual, which included letting the heater warm up for 2 minutes before applying voltage to the electrodes on the apparatus. To take data, we let either let the voltage of the electrodes or the current running through the coils be constant, while varying the other parameter. We measured the radius of the rings on the right and the left side using the built in ruler. DataNote: At a current of -1.35A, maximum accelerating voltage is 320V, the minimum is 165V. At -1.05A, the maximum voltage is 200V and the minimum is 100V. 11/16/09 Voltage applied to heater jacks: 6.24 V Raw Data:{{#widget:Google Spreadsheet |
key=0Ajaf_99vseiXdEIyXzJxWGJhLUQ2SE9qNGo4UURmMUE | width=760 | height=300
}} AnalysisGiven that (Thanks Alex and Anastasia!):
We can calculate e/m using either of 2 methods:
Since the uncertainty in the radii measurements was almost uniform, I treated it as uniform. Initially, the value for [math]\displaystyle{ \frac{e}{m}\,\! }[/math] based on constant voltage included the last two data points, but I did not incorporate them into my final calculations. Not only did they not include many data points, but the second to last one was an order of magnitude too big with ridiculous error bars, and the last data point had data points spaced very close giving it an error several orders of magnitude smaller than the rest of the data (causing the weighted average to be based primarily off this single value which was only based off of 3 data points itself). The e/m ratio under constant current and varying voltage was:
The e/m ratio under constant current and varying voltage was:
The accepted value (from wikipedia) is:
The constant current value was 21 SEMs away from the accepted value, and the constant voltage value was 23 SEMs away from the accepted value. The full analysis can be seen here. SJK 17:50, 15 December 2009 (EST)ConclusionsNeither result overlapped with the accepted value, and the distance away from the accepted value vs the number of SEM's away each value was leads to believe my results were off primarily due to systematic error. This doesn't surprise me, as this lab is very error prone. The errors I can think of in this experiment include the following:
However, since there are so many errors, and little way to measure their effects independently, I cannot pinpoint which would be the main culprit behind the large error we encountered in the lab. I can't think of any quick fixes to the experiment that wouldn't require drastically changing the setup. AcknowledgmentsThanks to Ryan, my lab partner, for his help. I used Alex and Anastasia's as well as Paul Klimov's labs for references, so thanks to them for their easy to follow and helpful ideas and explanations. Links
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