Physics307L:People/Meyers/Formal

= Millikan Oil Drop Experiment =

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
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
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].

I used Millikan's equation to determine the fundamental charge:

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

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
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) 

Cleaning the Apparatus


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
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
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

Rise Time Thorium Irradiated Particle:

[1.37,1.01,1.12]s

Fall Time Thorium Irradiated Particle:

[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.

Mean fall velocity: $$3.918*10^{-5}m/s$$
 * Particle 3:

Mean rise velocity: $$8.66*10^{-5}m/s$$ Mean fall velocity: $$3.036*10^{-5}m/s$$
 * Particle 4:

Mean rise velocity: $$1.134*10^{-4}m/s$$ Mean fall velocity: $$3.269*10^{-5}m/s$$
 * Particle 5:

Mean rise velocity: $$1.026*10^{-4}m/s$$ Mean fall velocity: $$3.595*10^{-5}m/s$$
 * Particle 7:

Mean rise velocity: $$1.271*10^{-4}m/s$$ Mean fall velocity: $$3.150*10^{-5}m/s$$
 * Particle 8:

Mean rise velocity: $$3.85*10^{-5}m/s$$ Mean fall velocity: $$3.6250*10^{-5}m/s$$
 * Particle Thorium:

Mean rise velocity: $$4.2860*10^{-4}m/s$$

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
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
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.

Steve's overall comments
17:54, 27 November 2010 (EST): Overall, the parts that are complete are very nice w/ good writing. See all the specific comments above. By far, the most work remaining is in the "results and discussion" section, which you need to turn into a formal report style, along with making some figures and tables. Extra data session: I would like you to get some more drops, of course. I'd also like you to see if you can measure the specific charge change when using ionizing radiation. Finally, I'd like you to think more about the data analysis method and check out John Callow's method (2009) and Dan Wilkinson's follow-on.