# Physics307L:People/Meyers/Formal Report

Steve Koch 04:11, 17 December 2010 (EST):Very nice, except for the unrefined "results and discussion" section.

# Repeating the Millikan Oil Drop Experiment to Measure the Electron Charge

Author: Richard T. Meyers

Experimenters: Richard T. Meyers & Nathan Giannini

Location: Junior Laboratory, 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].

we found an experimental value for the fundamental charge as:

$q=1.636*10^{-19}\pm 6.6*10^{-21}C\,\!$

Compared to the accepted value of:

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

This shows that the experiment calculates the elementary charge rather well while using anachronistic methods.

## 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 even though the concept of a fundamental charge was put for before.[12] Since then the experiment has been cited in some journals as a display of misuse of academic ethics.[5]

Millikan preformed his experiment 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] [11] Millikan also needed 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] [11] 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] Since the apparatus is thoroughly cleaned and the temperature in the building where this experiment took place is relatively constant the variations on the pressure through humidity and outside temperature are relatively low. So we used the above mentioned equation that is a function of altitude solely.

I used Millikan's equation to calculate the charge on each particle: $q={4/3 \pi \rho g}{\Bigg[}{\sqrt{\bigg({\frac{b}{2p}}\bigg)^2+\frac{9ηv_f}{2g\rho}}-\frac{b}{2p}}{\Bigg]^3}\frac{v_f+v_r}{Ev_f}\,\!$

Then I plotted the calculated charge versus the expected number of charges, the process of determining which is listed in the Millikan PDF.[8]

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.

## Methods

SJK 04:01, 17 December 2010 (EST)
04:01, 17 December 2010 (EST)
These methods are outstanding. It would have been good to equally thoroughly describe the analysis methods as well, in this section. The instrumentation figures and captions are excellent.

### 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 the experiment we disassembled the capacitor on the Millikan Oil Drop Apparatus Model# AP 8210 . That is the copper device shown on the top left of Figure 1. We removed the top clear plastic plate, the black cylindrical shielding device and the small cylindrical black cap. We cleaned all three of the above and inspected them for oil or water residue. Next we separated the top capacitor plate and the clear plastic separator plate, we measured and recorded the thickness of the clear plastic separator with the SMIEC Micrometer (0-25mm) , from the capacitor assembly. We also cleaned and inspected these as well. With the plastic separator plate we unintentionally removed the lens, we easily replaced the lens. Then we made sure that it is clear of water or oil. After all pieces of the capacitor assembly were clean, note the bottom plate can not be removed, we just cleaned it with a paper rag, we reassembled the capacitor setup as it was before.

### Calibrating the Apparatus

Figure 2: Various Equipement From left to right the equipment is, a bottle of Roberts mineral oil - NDC 54092-417-06 (ρ=886 kg/m^3) , The Oil applicator and a multimeter, above is the micrometer and it's container.
Figure 3:TEL- Atomic 50V & 500V Supply - UNM 195232

The first thing we adjusted was the bubble level to insure that the entire device was level. We adjusted the three legs on the bottom of the device to their shortest extension; then one by one we adjusted the legs so that the bubble in the bubble level was 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 we calibrated was the scope. This is located on the bottom left hand side of Figure 1. This device points towards the capacitor assembly and allowed us to observe the inside of the capacitor. There are two lens here we adjusted. First we adjusted the lens furthest from the capacitor assembly. To do this we removed the top clear plastic plate from the capacitor assembly and the small black cylindrical piece from atop the top capacitor plate. We Replaced the aforementioned black cylindrical piece with similar one located at the center of the apparatus, this black piece had a rigid wire attached at it's bottom, see Figure 1. We fed the wire through the small hole in the top of the top capacitor plate, the black piece rested on the capacitor the same as it's counterpart. Next we attached the power source for the light and turned the light on, on the apparatus, this is to the top right in Figure 1. To get a good view inside the capacitor we turned off the lights to the room. Then viewed the inside of the capacitor camber. We adjusted the furthest lens until we saw the light reflecting off the left side of the wire, clearly. Once this is done we did not touch this lens adjustment.

Next we adjusted the second lens. We removed the black cylindrical piece with the attached wire and replaced with it's counter part. We replaced the top clear plastic disc and returned the black cylindrical piece with the attached wire to it's original place. Once this was done we viewed again through the scope. We saw a black grid of lines, the distance from one major grid line to another is 0.5mm. We then adjusted the second lens, the one closest to the capacitor, until the grid was as clear to us as possible.

Next we set up the voltage source. We plugged in the TEL- Atomic 50V & 500V Supply - UNM 195232, see Figure 3 and attached the leads to the the upper most channels on the top left of Figure 1. We used the voltage setting and adjusted the source until it read 500 volts. We verified this result with a multimeter and recorded this reading.

Lastly we determined the temperature inside the chamber. We took a multimeter and recorded the resistance along the capacitor by attaching the lead to the channels just below the voltage channels in Figure 1. We recorded the corresponding reading and then used that to estimate the temperature on the chart in the middle of Figure 1.

### Applying Oil

After all systems of the apparatus were calibrated, we learned to apply the oil to the chamber. The clear container with the attached rubber hollow ball is the applicator, see Figure 2. We found the best way to apply the oil was, first make sure that the nozzle was clean then squeeze the ball rapidly and into a paper rag until it began to emit a steady spray of oil drops. Then when applying this to the chamber we put the nozzle through the hole in the top clear plastic plate, then we squeezed slowly, so only a few drops were emitted.

### Time Delay

We found it useful to measure the time delay between Nathan and myself because of reaction time. We then incorporated this time difference in our data, see below. To do this we used two separate timers, one on computer in the lab and one on a cell phone. Nathan started both timers as near to synchronous as he could. Then he handed the cell phone to me and at his mark I stopped my timer and he stopped his. Using the difference between these two we were able to calculate my reaction time, if only primitively. We believed that because Nathan was giving warning to starting the reading and because of the abrupt signal to the ending of the reading that this measure of the reaction time could yield positive results in reduction of error.

### Measuring

Before applying the oil, as stated above, we moved the switch, located at the bottom and left side of the capacitor chamber, to it's middle position. This allowed the oil drops to enter. Then we applied the oil. After a few squeezes of the rubber ball, two to three, we saw drops, they appeared as glowing specs of light. We then returned the switch,located a the bottom of the chamber, to off. Then we toggled the capacitor's switch, which was attached to the apparatus via a wire. While toggling the capacitor's switch and viewing through the scope we located a slow moving particle. We tried to locate a particle that moved at near the same speed upwards as downwards.

Once a particle was found we began to measure. We recorded the time it took for the particle to traverse from one major grid line to another. We repeat the measurements for as many rise and fall times as we could. Then we found a second particle and did the same. We repeated this process for multiple particles.

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

## Data

SJK 04:06, 17 December 2010 (EST)
04:06, 17 December 2010 (EST)
As with the rough draft, this section (replacing "Results and Discussion") is unrefined. It is easier to follow your analysis methods than last time. And nice added graph, but no caption. Of course, for a paper to be submitted for peer-reviewed publication, this section would need to be overhauled.

### Raw Data

plate separation=7.59-7.60mm

view through the scope a vertical yellow band of light

The Raw data is stored here

• Side note for the data

In particle 13 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 11 because they were obviously bad points.

### Analyzed Data

The MATLAB program that I wrote to analyze the data is here

plate separation:7.6mm

oil density:886 kg/m^3

pressure:8.3327*10^4 Pa

I used the above mentioned MATLAB program to analyze the above mentioned raw data.

The process of analysis is as follows.

I took the raw time data and the average of the differences of the time correction data and subtracted them to obtain the corrected times for all of the rises and fall of the various. From there I found the rise and fall velocities from know that the distances traveled in each instance was 0.5 mm.

After calculating the corrected velocities I calculated the associated energies by using the laws for capacitance and knowing both the plate separation, which was unchanged for all of the particles, and the voltages which were measured through out the experiment and logged in for each individual particle.

Then I found the air viscosity for each of the particles. We had measured the resistances along the capacitor for each of the droplets and from a table located on the apparatus we determined the associated temperatures. With the temperatures I found the air viscosity for each particle with a graph located in the Millikan PDF.[3]

The last constant that I needed to determine was the barometric pressure in the lab. I used an equation I found on an online engineering cite.[7]

Knowing all of these things I was able to use this equation:

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

to calculate q. I used the standard error function in MATLAB to produce a matrix of q values and SEMs that returned the each particles average q value and it's upper and lower SEM value.

I then plotted the calculated q versus expected number of charges in the particle and overlay a regression to get my final result.

## 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:

$%error=\frac{(1.636*10^{-19}C)-(1.602*10^{-19}C)}{1.602*10^{-19}C}x100%=2.12%\,\!$

As per getting the error that was incurred (i.e. the $\pm 6.6*10^{-21}\,\!$). The deviations in the times that we incurred are listed in the above mentioned MATLAB program.

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.

I decided to use the regression slope of the [Figure 4] because it naturally incorporated all fifteen data points and while showing the number of charges versus the calculated charges the regression provided the ideal method in coming to a final number.

## 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. SJK 04:10, 17 December 2010 (EST)
04:10, 17 December 2010 (EST)
This result is not discussed in the above section. Typically results are not exclusively discussed in the conclusions section.

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.

Also similar to the above mentioned experiment is one that involves an automated detection system to find fractional charges in Meteoric Material.[10] This is similar because it is a search for fractional charges, or qwark-like charges in stellar material.

## 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.

## References

[1] "Millikan oil-drop experiment." Encyclopædia Britannica. 2010. Encyclopædia Britannica Online. 13 Dec. 2010 http://www.britannica.com/EBchecked/topic/382908/Millikan-oil-drop-experiment
[2] "Robert Andrews Millikan." Encyclopædia Britannica. 2010. Encyclopædia Britannica Online. 13 Dec. 2010 http://www.britannica.com/EBchecked/topic/382902/Robert-Andrews-Millikan
[3] Millikan, Robert A. "On the Elementary Electrical Charge and the Avogadro Constant." The Physical Review, vol II., Series II.,108 (1913)
[4] "The Millikan Oil Drop Experiment." Cornell University. 1997. Cornell University Online. 1997 http://people.ccmr.cornell.edu/~muchomas/8.04/Lecs/lec_Millikan/Mill.html
[5] Segerstråle, Ullica. "Good to the Last Drop? Millikan Stories as “Canned” Pedagogy" Science and Engineering Ethics, vol I #3.,197 (1995)
[6] "NIST: The elementary charge" physics.nist.gov. 2010. nist.gov. 2010 http://physics.nist.gov/cuu/Constants/historical1.html
[7] "Elevation above sea level - in feet and meter - with barometric and atmospheric pressure - inches mercury, psia, kg/cm2 and kPa" The Engineering Toolbox. 2010. EngineeringToolBox.com. 2010 http://www.engineeringtoolbox.com/air-altitude-pressure-d_462.html
[8] "Millikan Oil Drop Apparatus" PASCO. pasco.com. 2010 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" AIP Conference Proceedings. 2000. AIP.org. 2010 http://scitation.aip.org/getabs/servlet/GetabsServlet
[10] Kim, Lee, Lee, Perl, Halyo, Loomba. "Search for Fractional-Charge Particles in Meteoritic Material" Physical Review Letters, vol 99 iss 16.,(2007)
[11] Gilchrist, Lachlan. "An Absolute Determination of the Viscosity of Air." The Physical Review, vol I., 124 (1913)
[12] Stoney, G. "Of the "Electron," or Atom of Electricity." Philosophical Magazine, Series 5, Volume 38, 418 (October 1894)