# Millikan Oil Drop Experiment

SJK 14:39, 27 November 2010 (EST)
14:39, 27 November 2010 (EST)
Ordinarily, the title is a bit more descriptive. E.g., "Repeating the Millikan Oil Drop Experiment to Measure the Electron Charge. Otherwise, good heading.
Author: Richard T. Meyers

Experimenters: Richard T. Meyers & Nathan Giannini

Location: Junior Laboritory, Physics and Astronomy Bldg, University of New Mexico, Albuquerque, NM

Contact: rmeyers@unm.edu

## Abstract

SJK 14:52, 27 November 2010 (EST)
14:52, 27 November 2010 (EST)
I like your abstract. I would delete the big equation as it is not one of your derivation. I would also add commentary at the end as to whether your result agreed with accepted value. It's not common to have references in abstracts (due to space issues probably) but it's OK for me here.

Since first being published, in 1909, the Millikan Oil Drop experiment has received an acclaim nearly unparalleled in science[1]. It's popularity is a result of both it's brilliance and it's controversy. There exists people who claim that Millikan "cherry picked" his data, whereas other point out the reproducibility of his work as proof to the opposite[5]. Here we make no claim to either camp but we wish to see if an accurate measure of the fundamental charge can be obtained through the use of similar methods, to that of Millikan.

Using an apparatus to mimic the one used by Robert Millikan, we will attempt to measure the charge on oil drops in between a capacitor[3]. By measuring the rise and fall times of the oil drop we will calculate the respective velocities and then after calculating the air temperature, pressure and viscosity, and the Voltage and distance across the capacitor we can then make a measure for the fundamental charge[8]. Using this equation:

$q={4/3 \pi \rho g}{\Bigg[}{\sqrt{\bigg({\frac{b}{2p}}\bigg)^2+\frac{9ηv_f}{2g\rho}}-\frac{b}{2p}}{\Bigg]^3}\frac{v_f+v_r}{Ev_f}\,\!$

we found an experimental value for the fundamental charge as:

$q=1.643*10^{-19}\pm 6.8*10^{-21}C\,\!$

This compared to the accepted value of:

$q=1.602176487(40)*10^{-19}C\,\!$

## Introduction

SJK 15:03, 27 November 2010 (EST))
15:03, 27 November 2010 (EST))
Your introduction is good too. There are a couple improvements needed. For one thing, there are some items brought up in your abstract that aren't mentioned here and elaborated on. Technically, the abstract should only refer to things that are in the full paper. That's since, historically, the abstract has been information abstracted from the paper to help people decide whether obtaining or reading the full paper was worthwhile. Second. You have one citation to original, peer reviewed research (the Millikan review). You should have more than that. You do have good citations, but they're not to peer-reviewed stuff, and that's an exercise we're doing. An example of one you could add would be to the Gilchrist and Rapp paper, if you could find it.

The Millikan Oil Drop Experiment, which was devised by Robert A. Millikan (1868-1953), is set in the pantheon of physics experiments for it's notoriety[2] [4]. Millikan's experiment was the first to attempt to measure the fundamental charge. Millikan did this by measuring the rise and fall times of small oil drops in between the plates of a capacitor under charge and not. By no means was this the only measure that Millikan need to obtain. Millikan needed to obtain the viscosity of the air; Millikan used the combined work of Lachlan Gilchrist and I. M. Rapp to determine the viscosity of air with respect to temperature[3]. Millikan also need to determine the size of the oil drop; Millikan assumed that the oil would act as a rigid sphere and thus made his approximation[3]. This leads the rest of the constants in the theory as known or easily measurable.

I tried to reproduce Millikan's work here, with accepted values for other constants. Going off the original work of Gilchrist and Rapp we have a procedure to determine the viscosity of air[8]. We already work under Millikan's assumption of a rigid sphere; so what is left is an accurate way to find the pressure and to measure the rise and fall times of individual drops. The equation for pressure I found is from an engineering database[7]. SJK 11:51, 27 November 2010 (EST)
11:51, 27 November 2010 (EST)
The equation you use assumes that the sea level air pressure would have been standard pressure. How much do day to day fluctuations matter? You can find them on wunderground for your specific day. You'd have to convert from inches to pascal.]
I used Millikan's equation to determine the fundamental charge: SJK 14:57, 27 November 2010 (EST)
14:57, 27 November 2010 (EST)
technically, this doesn't find the fundamental charge. It finds the charge on the droplet and you need another method to determine how many charges are on each drop.

$q={4/3 \pi \rho g}{\Bigg[}{\sqrt{\bigg({\frac{b}{2p}}\bigg)^2+\frac{9ηv_f}{2g\rho}}-\frac{b}{2p}}{\Bigg]^3}\frac{v_f+v_r}{Ev_f}\,\!$

To finish off the experiment we decided to see the effect of radiation on the movement of the oil drop and the calculation of q. We bombarded an oil drop with radiation from a Thorium isotope after doing this the movement should change while under the influence of the capacitance and the number of charges should also change.

## Equipment

The Equipment we used, listed below, is germane to the University of New Mexico Junior Lab.

### Equipment List

SJK 17:28, 27 November 2010 (EST)
17:28, 27 November 2010 (EST)
formal reports do not typically have equipment lists. Instead the equipment is listed within the prose. For example, "Our main apparatus was a model ___ Millikan Apparatus (Pasco, Inc., [city of company])." That may be antiquated someday, but it's how it's done for now. So, you should move these into your text below, and cite the company/city the first time you talk about the item.

standard multimeter

Millikan Oil Drop Apparatus - AP 8210

TEL- Atomic 50V & 500V Supply - UNM 195232

SMIEC Micrometer 0- 25mm

Roberts mineral oil - NDC 54092-417-06 (ρ=886 kg/m^3)

## Methods

SJK 17:35, 27 November 2010 (EST)
17:35, 27 November 2010 (EST)
The methods should mostly be in past tense, using phrases like "We first adjusted blah blah blah." Currently you have it as a "how to" type of writing. There is actually a point to making it past tense--this gives the reader confidence in knowing exactly how to reproduce your work. If it's "you should do this," then they may wonder how many corners you actually cut. If there were a standard recipe or "how to," then you can certainly link to that (e.g. the Pasco manual) but then use "we did this actually" type of statements. If you have suggestions for future research, then I think it's fair to say "future research may benefit from blah blah blah." See Nathan's rough draft for an example of using the past tense. I haven't looked at it carefully yet but looks like he does a good job.

Other than the style, it looks like your methods are great and your figures are very nice. Actually your figures need brief titles, such as Figure 2 Accessory Equipment.

### Cleaning the Apparatus

Figure 1: The Millikan Oil Drop Apparatus. The golden circular piece is the capacitor assembly. Below this is the viewing scope and to the right is the light source. Below the light source is the bubble level and in between the light source and the capacitor is both the temperature chart and the black cylindrical piece with the attached wire. Above the capacitor assembly are the channels to read the chamber's resistance and the channels for it's voltage, as you read up.

Before beginning anything in the experiment it is useful to dis assemble the capacitor on the apparatus setup. This is the copper device shown on the top left of Figure 1. One should remove the top clear plastic plate, the black cylindrical shielding device and the small cylindrical black cap. All three of the above should be carefully cleaned and inspected for oil or water residue. Next separate the top capacitor plate and the clear plastic separator plate, be sure to measure and record the thickness of the clear plastic separator with a micrometer, from the capacitor assembly. These should be cleaned and inspected as well. With the plastic separator plate be careful with the attached lens, make sure that it is clear of water or oil. After all pieces of the capacitor assembly are clean, note the bottom plate can not be removed, just clean it with a paper rag, reassemble the capacitor setup as before.

### Calibrating the Apparatus

Figure 2: From left to right the equipment is, a bottle of Robert's Mineral Oil, The Oil applicator and a multimeter, above is the micrometer and it's container.
Figure 3: This is the voltage supply

The first thing to adjust is the bubble level. To make sure that the entire device is level, so as to not through of the fall times because of an angle with the gravitational force, adjust the three legs on the bottom of the device to their shortest extension then one by one adjust the legs so that the bubble in the bubble level is at the direct center. The bubble level is located on the right side of the apparatus towards the middle, see Figure 1.

The next device to calibrate is the scope. This is located on the bottom left hand side of Figure 1. This device points towards the capacitor assembly and allows you to observe the inside of the capacitor. There are two lens here to adjust. First adjust the lens furthest from the capacitor assembly. To do this one must remove the top clear plastic plate from the capacitor assembly and the small black cylindrical piece from atop the top capacitor plate. Replace the aforementioned black cylindrical piece with similar one located at the center of the apparatus, this black piece should have a rigid wire attached at it bottom, see Figure 1. Feed the wire through the small hole in the top of the top capacitor plate, the black piece should rest on the capacitor the same as it's counterpart. Now attach the power source for the light and turn the light on, on the apparatus, this is to the top right in Figure 1. To get a good view inside the capacitor turn off the lights to the room that you are in. Now view the inside of the capacitor camber. Adjust the furthest lens until you can see the light reflecting off the left side of the wire, clearly. Once this is done do not touch this lens adjustment.

Now to adjust the second lens remove the black cylindrical piece with the attached wire and replace with it's counter part. Replace the top clear plastic disc and return the black cylindrical piece with the attached wire to it's original place. Once this is done view again through the scope. You should be able to see a black grid of line, the distance from one major grid line to another is 0.5mm. Adjust the second lens, the one closest to the capacitor, until the grid is as clear to you as possible.

Now that the scope is calibrated we need to set up the voltage source. Plug in the voltage source, see Figure 3 and attach the leads to the the upper most channels on the top left of Figure 1. Use the voltage setting and adjust the source until it reads 500 volts. Verify this result with a multimeter and record this reading.

Lastly we must determine the temperature inside the chamber. Take a multimeter and record the resistance along the capacitor by attaching the lead to the channels just below the voltage channels in Figure 1. Record the corresponding reading and then use that to estimate the temperature on the chart in the middle of Figure 1.

### Applying Oil

Now that all systems of the apparatus are calibrated, we should make one note on applying oil to the chamber. The clear container with the attached rubber hollow ball is the applicator, see Figure 2. The best way to apply the oil is, first make sure that the nozzle is clean then squeeze the ball rapidly and into a paper rag until it begins to emit a steady spray of oil drops. Now when applying this to the chamber put the nozzle through the hole in the top clear plastic plate, this time squeeze slowly, so only a few drops are emitted.

### Measuring

Before applying the oil, as stated above, move the switch, located at the bottom and left side of the capacitor chamber as you look in to it, to it's middle position. This allows the oil drops to enter. Now apply the oil. After a few squeezes of the rubber ball, two to three, you should be able to see drops, they should appear as glowing specs of light, return the switch,located a the bottom of the chamber, to off. Now toggle the capacitor's switch, which is attached to the apparatus via a wire. While toggling the capacitor's switch and viewing through the scope locate a slow moving particle. Try to locate a particle that moves at near the same speed upwards as downwards.

Once a particle is found you can begin to measure. Record the time it takes for the particle to traverse from one major grid line to another. Repeat the measurements for ten rise times and ten fall times. Then find a second particle and do the same, you may need to apply more oil. Repeat this process for multiple particles. Once this is done you should have enough data to begin the calculation of q.

• Important note: Remeasure and rerecord the voltage of the the voltage source and the resistance of the capacitor and ultimately the chamber's temperature every ten minutes.

## Data

SJK 17:42, 27 November 2010 (EST)
17:42, 27 November 2010 (EST)
From this point on, your report looks much more like a lab notebook than a condensed formal report. It is great to link to raw data and calculation and what looks like Matlab code or output. However that's not what the reader wants to see first. They want to understand the results in a concise manner. That will require a figure. For example, you cite that wonderful summary from Cornell (currently your ref. 4--in it, they show a nice Millikan plot. You can decide what to plot. One idea would be to plot charge versus drop number. You will need to fix this.

Also, currently I can not understand your methods for analysis. These methods will need to be accurately described and added as a new section in your above methods section--analysis is part of the methods. I can guess, by looking at Nathan's report, that you used a method similar to him, but that is not evident here. I'm also not sure that's the best method, so during "extra data week," I'd like you to think more about the analysis method. John Callow developed a very fun analysis method last year, and this year Dan Wilkinson extended it a bit for error analysis.

This data was taken from Millikan Oil Drop Lab 2.

### Raw Data

plate separation=7.59-7.60mm

view through the scope a vertical yellow band of light

• Side note for the data

We dropped particle one and two because there were not enough data points to get a good set.

Also in particle 3 we dropped the last fall time because it didn't have a corresponding rise time and we dropped point 1, 2, and 7 from particle 5 because they were obviously bad points.

### Analyzed Data

plate separation:7.6/1000mm

oil density:886 kg/m^3

pressure:8.3327*10^4 Pa

Times

Rise Times Particle 3:

[5.34,5.93,5.67,5.94,5.51,5.90,6.13,6,5.34,5.88]s

Fall Times Particle 3:

[13.23,13.27,12.23,12.88,12.48,12.57,11.73,13.7,13.06,13.13]s

Rise Time Particle 4:

[4.26,3.73,3.98,4.08,3.5,6.9]s

Fall Time Particle 4:

[15.27,15.42,16.1,17.72,17.03,17.26]s

Rise Time Particle 5:

[4.87,4.94,4.79,4.96,5.7,4.34,4.53]s

Fall Time Particle 5:

[16.88,14.07,14.07,15.24,15.24,15.83,15.52]s

[1.37,1.01,1.12]s

[15.03,13.69,12.55]s

Rise Time Particle7:

[5.15,3.54,4.85,5.02,2.97,3.71,3.09,3.14]s

Fall Time Particle 7:

[15.27,14.54,12.96,14.26,12.57,11.79,15.62]s

Rise Time Particle 8:

[11.55,11.72,12.93,12.59,13.04,12.93,13.67,15.67,12.39,13.48]s

Fall Time Particle 8:

[16.63,15.74,15.23,16.42,17.17,14.31,15.35,17.10,16.45,14.31]s

Energies

Energies Determined for the Above particles:

[6.6737*10^4,6.6737*10^4,6.6737*10^4,6.6737*10^4,6.6737*10^4,6.7053*10^4]V/m

Air Viscosity (Etas)

Etas of the Above Particles:

[1.842*10^(-5),1.848*10^(-5),1.852*10^(-5),1.852*10^(-5),1.852*10^(-5),1.854*10^(-5)]Ns/m^2

## Calculations

From the Raw data of the Rise and Fall times of the respective particles, we used the fact that the distance traveled each time was $0.5mm\,\!$ to determine the mean rise and fall velocities of the respective particles. The results are below.

• Particle 3:

Mean fall velocity: 3.918 * 10 − 5m / s

Mean rise velocity: 8.66 * 10 − 5m / s

• Particle 4:

Mean fall velocity: 3.036 * 10 − 5m / s

Mean rise velocity: 1.134 * 10 − 4m / s

• Particle 5:

Mean fall velocity: 3.269 * 10 − 5m / s

Mean rise velocity: 1.026 * 10 − 4m / s

• Particle 7:

Mean fall velocity: 3.595 * 10 − 5m / s

Mean rise velocity: 1.271 * 10 − 4m / s

• Particle 8:

Mean fall velocity: 3.150 * 10 − 5m / s

Mean rise velocity: 3.85 * 10 − 5m / s

• Particle Thorium:

Mean fall velocity: 3.6250 * 10 − 5m / s

Mean rise velocity: 4.2860 * 10 − 4m / s

From these velocities we calculated the charge on each respective oil drop using this equation:

$q={4/3 \pi \rho g}{\Bigg[}{\sqrt{\bigg({\frac{b}{2p}}\bigg)^2+\frac{9ηv_f}{2g\rho}}-\frac{b}{2p}}{\Bigg]^3}\frac{v_f+v_r}{Ev_f}\,\!$

As for the pressure we used this equation:

$p=101325(1-2.25577x10^{-5}x h)^{5.2588}\,\!$

Where $p\,\!$ is pressure and $h\,\!$ is altitude. [7]

Using simple algebra we get the following results for $q\,\!$.

Particle 3: $q=1.566*10^{-19}\pm 1.1*10^{-20}C\,\!$

Particle 4: $q=1.539*10^{-19}\pm 5.1*10^{-21}C\,\!$

Particle 5: $q=1.525*10^{-19}\pm 6.7*10^{-21}C\,\!$

Particle 7: $q=1.954*10^{-19}\pm 4.5*10^{-21}C\,\!$

Particle 8: $q=1.534*10^{-19}\pm 6.9*10^{-21}C\,\!$

Thorium Particle: $q=1.5977*10^{-19}\pm 3.1*10^{-20}C\,\!$

Averaged together we get a q of:

$q=1.643*10^{-19}\pm 6.8*10^{-21}C\,\!$

## Error

With the accepted value of q as:

$q=1.602176487(40)*10^{-19}C\,\!$

This is inside my first standard deviation of mean of my calculated q.

Also the percent error is:

$%error=\frac{(1.643*10^{-19}C)-(1.602*10^{-19}C)}{1.602*10^{-19}C}x100%=2.56%\,\!$

As per getting the error that was incurred (i.e. the $\pm 6.8*10^{-21}\,\!$). The deviations in the times that we incurred are listed below: Standard Deviations for Times Particle 3

Rise Time: 0.2815

Fall Time: 0.5789

Particle 4

Rise Time: 1.2496

Fall Time: 1.0178

Particle 5

Rise Time: 0.4291

Fall Time: 0.9874

Thorium Particle

Rise Time: 0.1845

Fall Time: 1.2413

Particle 7

Rise Time: 0.9239

Fall Time: 1.4415

Particle 8

Rise Time: 1.1595

Fall Time: 1.0532

From these we ran the standard deviations through the same calculation for $q\,\!$ and then averaged them together, as we did with the $q\,\!$ values, excluding the Thorium irradiated particle because of it high number of charges.

We decided to average the five different values for the fundamental charge together to obtain an ultimate value for the fundamental charge because even given the one value at $1.954*10^{-19}\,\!$ being larger than the rest we believe that it was still close enough not to be an outlier. Also the fact that this value is a constant, we thought that averaging them together would have little effect on the out come. Indeed this choice of analysis did raise the value slightly but not enough to discourage the use of the mean.

## Conclusions

SJK 17:46, 27 November 2010 (EST)
17:46, 27 November 2010 (EST)
I like your conclusions. Ref9 is a good opportunity to cite a peer-reviewed report. Look for a paper by our own Dinesh Loomba in Physical Review Letters in about 2006 for a wonderful paper about their automated Millikan experiment.

By comparing our final result for the fundamental charge to that of the accepted value we notice a small degree of error. The shear fact that it appears that this experiment is reproducible, i.e. it has produced a similar result to others, shows that the theory around the Millikan Oil Drop Experiment is solid. It appears possible, given enough data, to have a close approximation of the fundamental charge with those of later experiments. Another way to measure the fundamental charge is to use the relationship $q=F/N\,\!$, by calculating both the farad and Avogadro's number[6]. In both methods we see similar results so the question of whether or not Millikan was cherry picking, while not being solved, become less probable. In the very least the theory is plausible. Also we found that once we bombarded the oil drops with radiation from a Thorium isotope, the drop's movement became more rapid and thus had a higher charge. So radiation can increase charge.

Lastly it is interesting to note that a modern day use of Millikan may be used in micro gravity. It has been theorized that reproducing Millikan's experiment in microgravity one could use much larger drops, because of the near zero gravity, thus eliminating the g portion of Millikan's equation. With these larger drops one could find partial charges, i.e. q/3 or the charge of a quark[9]. Experimenters are hoping that they can find partial charges to prove the existence of free quarks in space.

## Acknowledgments

SJK 17:49, 27 November 2010 (EST)
17:49, 27 November 2010 (EST)
Good acknowledgements

This paper would not be possible without the help of my lab partner, Nathan Giannini; he was invaluable during all stages of the experiment. Also our Professor Steven Koch, who gave numerous pointers during lab time. Lastly to a previous year's student, Alexandra Andrego; she has done extraordinary work in her write ups.

## References

SJK 17:50, 27 November 2010 (EST)
17:50, 27 November 2010 (EST)
These are good references. Keep them in there, but as noted, add in a few more to peer-reviewed original research.
[1] 'Millikan Oil Drop Experiment' http://www.britannica.com/EBchecked/topic/382908/Millikan-oil-drop-experiment
[2] 'Robert Andrews Millikan' http://www.britannica.com/EBchecked/topic/382902/Robert-Andrews-Millikan
[3] 'Millikan pdf' http://www.aip.org/history/gap/PDF/millikan.pdf SJK 11:33, 27 November 2010 (EST)
11:33, 27 November 2010 (EST)
This is a good paper to cite, it is an original research (review) paper. You'll just want to switch the reference format to something more standard, which is something like: AuthorLast, AuthorFirstInitial. "Title." JournalName, vol., FirstPage (Year)
[4] 'Millikan Oil Drop' http://people.ccmr.cornell.edu/~muchomas/8.04/Lecs/lec_Millikan/Mill.html
[5] 'Good to the Last Drop' http://www.physics.emich.edu/mthomsen/sege.htm
[6] 'NIST: The elementary charge' http://physics.nist.gov/cuu/Constants/historical1.html
[7] 'The Engineering Toolbox' http://www.engineeringtoolbox.com/air-altitude-pressure-d_462.html
[8] 'Pasco Millikan Manual' http://openwetware.org/images/e/ea/Pasco_millikan_manual.pdf
[9] 'A Search for Free Quarks in the micro gravity environment of the international space station' http://scitation.aip.org/getabs/servlet/GetabsServlet