Physics307L:People/Giannini/Rough

= Millikan Oil Drop =

Author: Nathan Giannini

Experimentalists: Nathan Giannini & Richard T. Meyers

Junior Lab, Department of Physics and Astronomy, University of New Mexico

Albuquerque, NM 87131

ngiann01@unm.edu





Abstract
In 1909, Robert A. Millikan embarked on the quest to discover the charge of an electron, and to convince those that electron theory was sound. In a Nobel talk in 1924, Millikan described his experiment, named the Millikan Oil Drop for simplicity.[3] This experiment used an electric field to suspend oil droplet inside a small chamber which could be viewed by a microscope. These oil droplets needed to have very small diameters, so that the warping in their dimensions as they accelerated upwards or downwards would be kept to a minimum. By applying an electric field to these droplets, you could measure their rise and fall times and determine the charge necessary to create these rise and fall times. From there, a pattern is formed, as it is noticeable that the droplets had integer multiples of a value. This value has since been designated the elementary charge e = 1.6 *10^-19 Coulombs. In this experiment, which followed this method, we found that:


 * $$e\approx1.645 \cdot 10^{-19} +/- 2.7 \cdot 10^{-21} Coulombs$$

Introduction

 * In 1750, Benjamin Franklin stated that, "The electrical matter consists of particles extremely subtle since it can permeate common matter, even the densest, with such freedom and ease as not to receive any appreciable resistance." This was the first conception of atomic particles that had a charge. From there, Wilhelm Weber theorized about the charge of such a particle in 1871, and the increments of charge that would be detected. In 1897 J.J. Thomas and Zeeman both determined e/m of an electron and started the boom in electron theory. However, many physicists still doubted the theory. In 1909, Robert A. Millikan designed an experiment that was based of the model for a pith ball, he would use oil droplets of such size as to have a diameter of less then one thousandth of a millimeter, so that they maintained a spherical shape while they moved through an electric field. This electric field would accelerate these oil droplets, due to the distribution of charges on them that are created by being squirted out of a sprayer. This electric field was generated by two plates that could have a voltage potential applied to them. Here he measured the time it took a particle to go 1 cm. Upon determination of the charge the electrons would need to obtain these rise rates, he found that they had rates corresponding to integer multiples of each other. Rates of even 1, 2, 3, 4, and higher times as fast as other particles were observed, but no rates along the lines of any number except integers. However, despite this brilliant experiment, he was unable to achieve the now known correct result, he found that e = 4.774 (± 0.005) * 10^{-10}.[3] Nowadays, we have experiments that give us that e = 1.9 * 10^{-19}C as the charge of an electron. One such experiment with was one conducted in 1999 at Stanford. This experiment found the charge of an electron to within 0.16e of the accepted charge of an electron.[2]


 * In this experiment, I will be using a set-up close to the one that can be found to be used by Robert A. Millikan, but with particles of diameter near a micro-meter. This will give us much better results than those obtained by Millikan in his own experiment, due to less surface for charges to populate on, allowing for the observation of smaller charges.



Calibration of the Millikan Apparatus

 * Before we started the experiment, it was necessary to calibrate the Millikan Apparatus. To begin with, we adjusted the leveling of our apparatus until the bubble was located in the middle of a circle located on top of the bubbles holder, which indicates where the bubble should be for the apparatus to be at 90 degrees to the gravitational field vector. From here, we cleaned the chamber of the Millikan Apparatus, which contained a removable capacitor plate, spacer, and a cap with a hole, who's purpose it was to reduce the amount of oil drops which enter our aparatus' chamber. Next, we inserted a wire into the hole located in the removable capacitor to aid us in the calibration of the light source. We first adjusted the microscope to bring the wire into focus. Afterward, we began to adjust our light source so that the right side of our wire was brighter then the left side [1]. Then, we removed the wire and replaced the cap on the capacitor. The final step in calibrating our apparatus occurred when we were viewing our droplets. We adjusted the "Droplet Focus" on our microscope so that we could see the droplets as well-defined (not blurry) pinpoints of light.



Measuring the Rise and Fall Time of the Oil Drops

 * To measure the rise and fall times of our oil droplets, it was necessary to go through a certain procedure to limit the interactions between our droplets. We, first, applied a potential difference to our capacitor plates, to accelerate most of our particles out of the chamber. Afterward, we searched for a particle that would fall .5mm(one major line on our grid) in approximately 10-15 seconds. Next, we tested our found particles to make sure that they did not have a charge of 5e or more (by accelerating them upwards and timing how long it took to get to one of the major lines). Finally, we would then begin measuring the rise and fall rates of our particles. Our method was to wait until the oil droplet was on one of the major lines and then begin timing it as it either rose (with an applied potential) or fell. We tried to do this 10 times for each particle, but we found that our particles had a tendency of dying before this point. Luckily, we were able to obtain a few particles that would last long enough. For one of the particles we were able to get over 10 runes with, we exposed it to Thorium for 10 seconds and then proceeded to measure the droplets rise and fall times again. It was apparent that the Thorium changed the charge on our particles, due to the fact that they accelerated upwards at a highly increased rate (about 3 times as fast by our own estimates).

Table 1
 * {| border="1"

!Particle !Average Fall Time (s) !Average Rise Time (s)
 * 3
 * 12.80
 * 5.76
 * 4
 * 16.47
 * 4.41
 * 5
 * 16.26
 * 4.88
 * 7
 * 13.91
 * 3.93
 * 8
 * 15.87
 * 12.99
 * }
 * 8
 * 15.87
 * 12.99
 * }
 * }

Analysis and Results

 * Our results for this experiment can be seen in Table 2 below. "a" refers to the radius of our droplet, "m" refers to the mass of our droplet, and "q" refers to the charge on our droplet.


 * The charges shown above were calculated using the following equations:
 * $$a=\sqrt{(b / 2 p)^2+9 n v_f/2 g \rho}{-b/2p}\,\!$$
 * $$m={4/3 \pi a^3 \rho}\,\!$$
 * $$q=\frac{mg(v_f+v_r)}{(V/d)v_f}\,\!$$


 * We separately determined the results for our data. I decided to use circular logic to determine the charge of 1 electron. I did so by using the already readily available quantity for the value to determine the charge on each droplet. The values I determined are shown in Table 3 below. The charges are in 10^-19C.

Table 3
 * {| border="1"

!Particle !Charge of one Electron
 * 3
 * 1.672 +/- 0.199
 * 4
 * 1.635 +/- 0.382
 * 5
 * 1.636 +/- 0.194
 * 7
 * 2.067 +/- 0.578
 * 8
 * 1.635 +/- 0/202
 * }
 * 2.067 +/- 0.578
 * 8
 * 1.635 +/- 0/202
 * }
 * }


 * This data shows that our data has high precision, with the exception of particle 7. This also means that there is a high probability that there must have been some kind of systematic error in our experiment that would cause our results to be off, as the human error represented in the measurements would to, at least, be minimal.

Discussion and Conclusion

 * To give a good comparison as to the accuracy of our results, it is good to consider the accepted value for the charge of an electron, 1.6*10^-19C. As you can see, most of our data is off by 1 SEM, with two for Particle one (here I neglect Particle 7 due to the results). I mainly believe, as I have stated above, that most of our error was systematic. Examples of probable systematic error are: the increase in voltage supplied by our power supply with time and/or the device was not entirely level. I believe most of this error could be eliminated by using a power supply that does not provide an increased voltage over time, since this probably provided the greatest source of error. Another, slightly less ideal idea would be to reset the voltage to the original amount for each particle. Finally, the last way to reduce our systematic error would be to use a type of level that will bring our apparatus to a completely level state, such as that used in the Michelson Interferometer.



Acknowledgments

 * To Richard T. Meyers for having patience when we repeatedly obtained an entire chamber full of neutral particles.
 * To Steve Koch for allowing us to redo the Millikan Lab so that we could obtain better data.
 * To Alex Andrego for the format of this Rough Draft.

Overall Koch Comments
Steve Koch 00:51, 28 November 2010 (EST): This is a very good first draft! There is no really big thing that needs to be done, but a bunch of things throughout. Thanks for redoing the experiment and doing a great job! For the "extra data session" I want you to fight the urge to be sick of the experiment and see if you can get more data. I'd also like you to explore further analysis methods, a good example being John Callow's 2009 method. Finally, looking into the charge differences quantitatively when doing the thorium exposure would be very nice.