Physics307L:People/Wilkinson/Millikan
Millikan Lab Summary
SJK 00:50, 14 October 2010 (EDT)
This is a great informal lab summary. I like how it reads, and I like seeing the result reported with uncertainty and comparison to the accepted value. See some comments for improvement below.
Discussion
This lab was based on the Millikan Oil Drop Experiment originally performed by Robert Millikan in 1909. The basis of this experiment was to determine the fundamental charge unit i.e. the charge of the electron. This was a controversial topic in the period because the existence of subatomic particles was still hotly contested among physicists. Our experimental setup was very much like the original Millikan setup. We used a prefabricated apparatus meant for undergraduate physics labs. With this apparatus and some clever data interpretation we were able to get a value that is fairly close to the accepted value.
Theory
The basis of this experiment relies on a simple force balance calculation. A spray of oil drops is injected between two charged plates and the drops are observed to fall under the force of gravity and rise under the force of an applied electric field. With the observations one is able to calculate the overall charge on the oil drop. Once this data is acquired a least squares calculation can be applied to find the least common divisor of the data i.e. the fundamental electric charge. Millikan Lab Data
Results
SJK 00:45, 14 October 2010 (EDT)
The information I need is here to see that your measurement is consistent with the accepted value, since the discrepancy is comparable to the standard error you devised. However, you never actually say that, using a little statistics talk, which would be better. Also, to be nit-picky, your answer can be written more cleanly by saying either (1.62 +/- 0.02) E-19 C or 1.62(2) E-19 C. The extra digits and different exponent on the uncertainty make it trickier to read. Finally, I am intrigued by your method for adding uncertainty estimation following John Callow's method. I don't see any description of this in your primary notebook. Presumably any information in your summary would have initially been recorded in your primary notebook as you developed and implemented the method. Then I as a reader would be able to go there and figure out more. Right now I can only just look at the matlab code. Just by reading here, it seems like a clever innovation.
The accepted charge charge of an electron is [math]\displaystyle{ q = 1.60217646*10^{-19} C }[/math] Charge of the Electron. Our determined value after least squares Least Squares approximations is q = 1.62E-19 ± 2.24E-21 C. The error is 1.3%. The standard error of the mean was calculated by dividing the individually calculated charges, dividing them by the determined charge. This value was rounded to get the integer value of how many fundamental charges were in one calculated charge. Knowing these integer values I divided the calculated values by their integer multiples to find how much they differed from the determined fundamental charge. Using this data I took the standard deviation and divided by the square root of the number of charges in question.
SJK 00:58, 14 October 2010 (EDT)
This comment on Tyler's page applies as well: In addition to this result, I also would like to have seen a summary of the charge changes brought upon by thorium irradiation. It looked to me like you got really good results with that, and possibly it'd be a simpler way of seeing fundamental unit of charge.
Conclusion
SJK 00:48, 14 October 2010 (EDT)
I agree, it is amazing! Kudos to you and Tyler for what look like some carefully taken and clean data. It's the best thorium results that I remember seeing, though it's difficult to see how your deltaQ (charge after - charge before) resulted, since I can't see your matlab output. I should note, too, that as an experimentalist I remain skeptical that there isn't a little luck in some systematic errors canceling each other :)
It is amazing that one can determine the charge of an electron simply by watching oil drops fall! I believe that the large amount of data we collected allowed us to get close to the accepted value with relatively small error and deviation.
Acknowledgments
Tyler did all of the staring into the telescope and for that I am very thankful. I also want to thank John Callow for the idea to use least squares to approximate the fundamental charge. Without this idea I wouldn't have been able to analyse the very large amount of data that Tyler and I had collected.
