# Physics307L:People/Giannini/Formal

Steve Koch 03:05, 15 December 2010 (EST):This is a good report. A few things were not addressed from the rough draft. Also, I couldn't determine if you included any data from the "extra data" week?

# Electron Charge Measurement Using Millikan Oil Drop Method

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

Millikan Apparatus [3]

## 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.[4] 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, it was found that you could measure their rise and fall times and determine the charge necessary to create these rise and fall times. From there, a pattern was formed, as it was noticeable that the droplets had integer multiples of a value. This value has since been designated the elementary charge e = 1.602 * 10^-19 Coulombs.

In our experiment, which followed this method, we found that:
$\displaystyle e\approx1.645 \cdot 10^{-19} +/- 2.7 \cdot 10^{-21} Coulombs$

The currently accepted charge is $\displaystyle e=1.602 176 487 x 10-19 C +/- 0.000 000 040 x 10-19 C$ [9]

Future work could go along the lines of having a computer replace all parts that humans had in this experiment, measuring rise/fall times and charging the plates until the particle passes a major line (this can be done easily done through programming the computer to turn off the power supply to the capacitors once a particle that you have 'locked on' to crosses a defined point, where the particle is viewed by the computer through a camera).

## 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 consideration of atomic particles that had some form of 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.[6][2] 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, etc. times as fast as other particles were observed, but no rates along the lines of any number except integers.[14] 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]SJK 02:54, 15 December 2010 (EST)
02:54, 15 December 2010 (EST)
Still, you are mixing two kinds of units here, making it very tough to compare
Nowadays, we have experiments that give us that e = 1.6 * 10^{-19}C as the charge of an electron. One such experiment was 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] The current values for an electron's charge come from Faraday's Method, $\displaystyle e=F/N_A$ , where $\displaystyle N_A$ is Avogadro's Number and $\displaystyle F$ is Faraday's Constant.[12][13]
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, where we will measure the rise and fall times of oil droplets between two capacitors[5].

## Methods

Figure 1: This is the bottle of oil (density=886kg/m^3) we used, as well as our multimeter, micrometer and sprayer.
Figure 2: This is our power supply, which we used to supply 500V to our Millikan Apparatus. It was apparent after the experiment that our power supply slowly increased the amount of energy it supplied to our Millikan Apparatus, and could have been a source of error in our experiment.

### Equipment

SJK 02:56, 15 December 2010 (EST)
02:56, 15 December 2010 (EST)
While I agree it's easy to read, this section should have been paragraph form, to be consistent with current-day publications.
• Millikan Oil Drop Apparatus
• Tel-Atomic (50V and 500V power supply)
• Oil of density 886 Kg/m^3

### Set-Up

• First we leveled the plateform for the Oil Drop Apparatus.
• We measure the width of the plastic spacer with a micrometer. This is the plate separation.
• Then we focused the viewing scope by using the focusing wire and adjusted the light.
• We connected the power supply to the plate voltage connectors using bannana plug patch plugs and applied 500V. We also connected a multimeter in parralel with the apparatus and power supply to better monitor the voltage.
• We connected another multimeter to the thermistor connectors to measure the resistance in the thermistor. This gave us the temperature within the viewing chamber.
• We used the atomizer to introduce oil drops into the chamber. This was done with the ionization source lever in the Spray Droplet Position, which allowed air to escape the chamber.
• Once there were droplets in the chamber we moved the ionization source lever to the Off Position. We tried to find a droplet with a fall velocity between 7 and 15 seconds. This was one of the hard parts of the experiment.
• When we chose a drop we measured as many fall and rise times as we could. The fall times are the times it takes the drops to fall from one major reticule line to the next. The major reticule lines are 0.5 mm apart. The rise times are the same, but with the voltage applied between the plates so that the drops rise against the force of gravity.
• For the last oil drop we measured several fall and rise times and then moved the ionization lever to the ON position and measured several more fall and rise times.

### 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 apparatus' 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. This final calibration was found to be necessary as the calibration we did with the wire did not provide a good view once we were looking at the droplets. This was probably due to the wire we used being slightly bent.

### 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

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

## Data

I was originally planning on showing a possible error in time, since I would say go and Richard would begin and there was a possible lag. Then I realized that this lag is canceled out when Richard stops the stopwatch, so I am using my data found here (For a look at what I was planning to do please look here. This includes the estimate of our time error per start/stop, which was found to be 0.397133seconds).

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.

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This figure, click on Chart 1 in the above figure, shows the charge we suspected to be on our particle versus what was actually on it.

## Analysis

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

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
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, 1.60*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. Yet another 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. Afterward, checking that the plates we used, to measure the distances our particles traveled over, are straight along with a more accurate determination of the air pressure, ours came from an equation which we checked with a report about Albuquerque's air pressure, use rulers to more accurately find the viscosity on the chart displayed in Gold's Manual, and an test to determine possible timing errors for the stopwatch on Richard's phone.
Future experiments could involve positively charged molecules or even atoms to determine the charge of a proton, and can use the set-up found in Millikan's Oil Drop as well, with molecules of some kind instead of oil.

## Acknowledgments

I thank Richard T. Meyers for having patience when we repeatedly obtained an entire chamber full of neutral particles and for some of the references I used.I'd also like to thank Steve Koch for allowing us to redo the Millikan Lab so that we could obtain better data. Finally, I thank Alexandra S. Andrego for the format of this Final Report.

## References

[1] 'Millikan Oil Apparatus', PASCO Scientific, used at University of New Mexico Dept. of Physics and Astronomy PHYSICS 307L:'Image:Pasco millikan manual.pdf' http://openwetware.org/images/e/ea/Pasco_millikan_manual.pdf
[2] 'Search for Free Fractional Electric Charge Elementary Particles Using an Automated Millikan Oil Drop', V. Halyo, P. Kim, E. R. Lee, I. T. Lee, D. Loomba, Stanford Linear Accelerator Center, Stanford, California 94309, 1999 and M. L. Perl Techniquehttp://prl.aps.org/abstract/PRL/v84/i12/p2576_1
[3] 'The electron and the light-quant from the experimental point of view', Robert A. Millikan, Nobel Lecture, May 23, 1924 http://labdid.if.usp.br/~estrutura/Experimentos/Millikan/millikan-lecture.pdf
[4] 'Millikan Oil Drop Experiment', Encyclopædia Britannica http://www.britannica.com/EBchecked/topic/382908/Millikan-oil-drop-experiment
[5] 'Robert Andrews Millikan', http://www.britannica.com/EBchecked/topic/382902/Robert-Andrews-Millikan
[6] 'Millikan pdf', http://www.aip.org/history/gap/PDF/millikan.pdf
[7] 'Millikan Oil Drop', http://people.ccmr.cornell.edu/~muchomas/8.04/Lecs/lec_Millikan/Mill.html
[8] 'Good to the Last Drop' http://www.physics.emich.edu/mthomsen/sege.htm
[9] 'NIST: The elementary charge' http://physics.nist.gov/cuu/Constants/historical1.html
[10] 'The Engineering Toolbox' http://www.engineeringtoolbox.com/air-altitude-pressure-d_462.html
[11] 'A Search for Free Quarks in the micro gravity environment of the international space station' http://scitation.aip.org/getabs/servlet/GetabsServlet
[12] 'Elementary Charge', http://en.wikipedia.org/wiki/Elementary_charge#Experimental_measurements_of_the_elementary_charge