# Physics307L F07:People/Le/Formal

## The Search for Charge, Milikan Oil Drop Experiment

SJK 16:39, 18 November 2007 (CST)
16:39, 18 November 2007 (CST)
I like the title, even though it's a little informal. This title has the flair of, say, a review article. Since we are practicing research papers, you should come up with new, descriptive title.

Linh Le, Cary Dougherty

Physics and Astronomy Department, Junior Lab 307, University of New Mexico, Albuquerque, New Mexico

Email: linhle@unm.edu

SJK 17:14, 18 November 2007 (CST)
17:14, 18 November 2007 (CST)
Make sure to spell check! Firefox can spell check for you, not sure about Internet Explorer

## Abstract

SJK 16:37, 18 November 2007 (CST)
16:37, 18 November 2007 (CST)
The first sentence is a little informal. Replace it with something about why the charge of the electron is so important. Include uncertainty on your value instead of saying "about ___". Otherwise, it's a good start on the abstract!

The fundamental charge of an electron has stumped many scientists for many years. To find the charge of an electron, we charged oil droplets with excess electrons, then suspended them within an electric field. By measuring their rate of fall, we could find their mass, and by measuring the rate of rising in the field, we can measure the amount of charge stored within the oil droplets. We measured the charge to be about 1.5x10 − 19 Coulombs, very close to the accepeted value of 1.60217733x10 − 19[1].

## Introduction

SJK 17:06, 18 November 2007 (CST)
17:06, 18 November 2007 (CST)
This introduction is much too short, and also too informal. See this page. You will also need to add references to original research articles, as opposed to websites.

The concept of charge has been around long before a number was put to it. Finding a numerical number for the fundamental charge has eluded many scientists for many years (JJ Thomson found a number, but Milikan's apporach was much better) [1]. It was also uncertain if these charges came in discrete intervals (ie. 1q, 2q, 3q..., not 1.23q). This experiment answered both those questions.

The idea that Milikan came up with was to charge oil droplets, suspend them in an electric field, and balance the weight of the droplets and the force of the charges keeping the droplets up to find a value of the charge.[1]

## Methods and Materials

SJK 17:13, 18 November 2007 (CST)
17:13, 18 November 2007 (CST)
This looks like you have enough information here, but it is not quite in the formal style. You should switch to past tense for the procedure. Also, need the make and model numbers for the accessory power supplies, etc. You should make a schematic of how to hook things up. Also, in your methods, you should describe your data analysis methods, including the confusing method for deducing the elementary level of charge.

We used "Millikan Oil Drop Apparatus" by PASCO Scientific Model AP-8210. The manual could be of use and can be found here

A basic drawing of the apparatus

Here is the basic design of the apparatus: It is a parralel plate capacitor that allows oil droplets to enter, attactched to an alpha particle generator, to force the oil droplets to become ionized. The capacitor itself can have it's plate polarities to be switched and has a thermistor hooked up to it, allowing the temperature inside to be determined. Mounted to the right of the plates is a light source, and in the front is a microscope for you to view and measure the droplets from.

The apparatus is almost built for "plug and play" and did not require any extensive setup. We attached a power supply to the capacitor to charge the plates and the ionizer. We attached a multimeter to the supply so we could accurately measure the voltage accross the plate. We also placed a second multimeter to the thermistor to allow us to measure its resistance, and from the, the temperature inside the capacitor. We leveled the whole apparatus, focused the light source and the microscope with a needle inside the capacitor, and filled a ionizer spray bottle with mineral oil.

### Procedure

After calibrating the microscopeSJK 17:07, 18 November 2007 (CST)
17:07, 18 November 2007 (CST)
How did you calibrate the microscope?
, we cover the capacitor with its cylindrical housing. AFfter dimming the lights and plugging all the power supplies in, we place the nozzle of the oil filled sprayer into a small hole in the top of the housing. There is a lever to the left of the capacitor that we turned to open, to allow the oil to enter. One quick spray and a few slower ones, forces the oil into the capacitor. While looking through the microscope, you will see a cluster of "sparkles" come into view. When a good amount comes into view, we switch the lever to close.

With oil inside the apparatus, we now turn the lever to on. This starts the bombardment of the oil droplets by alpha particles. After a few seconds, reset the lever to close. Using the switch to change the polarity of the plates, we are able to move the droplets that were charged up and down. We tried to pick out one that rose and fell slowly. There is a grid in the eyepice of the microscope that gives us a scale for measurements. With our drop found, we measured how long it took for it to fall about .5mm due to gravity, and to rise the same amount due to the force of the electric field created by the plates.

After taking a few measurements, we turn the lever back to on for a few seconds, to re-bombard our droplet again. This allows us to remasure the same droplet with a new amount of charge. We now repeat the expieriment with the rising and fall times.

## Results

We measured, and remeasured, the same droplet as many times as possible, gathering fall times and rise times.

### Raw Data

SJK 22:01, 18 November 2007 (CST)
22:01, 18 November 2007 (CST)
I think you should put your raw data in an appendix, to make results easier to read.

Spacing of plates (as computed by the average of the data above): 8.10mm

Density of Squibb's Mineral Oil: 886kg/m^3

Atmospheric Pressure in Abq (as looked up on the internet): 8.33X10^4 Pa [2]

##### Set 1
SJK 17:18, 18 November 2007 (CST)
17:18, 18 November 2007 (CST)
I want you to discuss seeming outliers (such as 18.38 s), and decide whether removing those data points is justfied, and then explain why or why not.

Voltage: 501V Resistance: 1.9982 M(ohms) Distance: .5mm

Fall Time (s) Rise Time (s)
18.38 3.31
14.38 3.15
14.11 5.14
13.7 5.7
13.8 5.19
14.72 5.52
14.5 5.23
13.13 5.27
15.37 5.37
Avg Fall Time Avg Rise Time
14.67s 4.877s

In this set, we were able to change the charge on the droplet and remeasure

Voltage=501.9V Resistance=1.976M(ohms)

Fall Time (s) Rise Time (s)
13.28
13.86 2.19
14.58 2.21
13.09 2.70
14.38 2.46
13.94 2.24
Avg Fall Time(s) Avg Rise Time(s)
13.855 2.36
##### Set 2

Voltage: 500V Resistance: 1.923M(ohms)

Fall Time(s) Rise Time(s)
15.97 2.99
14.50 3.13
13.80 2.95
15.50 2.69
15.17 2.75
15.36 3.36
Avg Fall Time(s) Avg Rise Time(s)
15.05 2.97

We changed the charge of the oil droplet in this set as well, but the droplet moved so fast, that it was very hard to sync Cary's observations and oral commands with my data collecting. As that is the case, we only took 2 data points.

Fall Time (s) Rise Time(s)
9.70 .72
10.32 .73
##### Set 3

Starting Voltage: 501.0 V Resistance: 2.07 M(ohms) Ending Voltage:501.8 V 2.041M(Ohms)

FALL TIME (s) RISE TIME (s)
14.87 4.81
17.53 4.87
17.17 4.85
18.67 4.57
17.89 4.53
17.77 4.37
15.93 4.56
16.49 4.90
18.97 4.61
18.41 5.11
19.24 2.50
Avg Fall Time(s) Avg Rise Time(s)
17.54 4.52
##### Set 4

Starting Voltage:501.4 V Resistance:1.945 M(Ohms)

Fall Time (s) Rise Time (s)
16.13 2.23
14.29 2.14
14.85 2.47
15.96 1.93
16.49 1.99
14.79 2.25
Avg Fall Time(s) Avg Rise Time(s)
15.42 2.17

### Calculations

Using the fall and rise times, we were able to determine a few things about the droplets and the charge.

To find the fall and rise times, we said that $V=\frac{d}{t}$. We use this simple formula since the droplets reach terminal velocity very quickly and travel at a constant rate after that.

The chart from the manual used to find the temperature of the air in the capacitor from the resistance in the thermistor
The chart from the manual used to find the viscocity of the air in the capacitor from the temperature of the air

To find the charge stored in the electron:

$q = {\frac{4}{3}}\pi \rho g[\sqrt{(\frac{b}{2p})^2 +\frac{9 \eta v_f}{2g\rho}}-\frac{b}{2p}]^3\frac{v_f + v_r}{Ev_f}$

A nice detailed derivation of this formula can be found in the manual, linked above.

q- the charge of the electron

p-barometric pressure-8.334Pa

d-distance between capacitor plates

g- acceleration due to gravity- $9.8 \frac{m}{s^2}$

b- constant 8.20E( − 3)Pa * m

a- radius in drop measured in meters

ρ-density of the oil which is $886 \frac{kg}{m^3}$

η- viscosity of air (found by the comparing temp inside the capacitor with chart in manual appendix A)

V- potential difference across the plates in Volts

vr- rise velocity (dividing .5mm by rise time)

vf- falling velocity (dividing .5mm by rise time)

E electric field (found by $\frac{V}{d})$

After a good amount of number crunching, we came up with some final values for the charges in the oil droplets

##### Set 1A
SJK 17:32, 18 November 2007 (CST)
17:32, 18 November 2007 (CST)
You should consolidate these data into a table, like the one I'm showing in "example table"

Voltage: 501V

Resistance: 1.9982 M(ohms)

Temp=25C

$\eta=1.8480\frac{Ns}{m^{2}}x10^{-5}$

$v_favg=3.408E-5 \frac{m}{s}$

$v_ravg=1.025E-4 \frac{m}{s}$

E= V/d= 61851.85 V/m

Plug everything into the formula: q=3.39E-19 C

##### Example table
Trial Temp Viscosity Vave fall Vave rise droplet size charge other values ... charge
1A
##### Set 1B

Voltage=501.9

Resistance=1.976M(ohms)

Temp=25.5C

$\eta=1.8480\frac{Ns}{m^{2}}x10^{-5}$

$v_favg=3.608E-5 \frac{m}{s}$

$v_ravg=2.118E-4 \frac{m}{s}$

E= V/d= 61886.56 V/m

Painstakenly plug and chug into the formula and get q= 6.38E-19C

##### Set 2

Voltage: 500V

Resistance: 1.923M(ohms)

Temp= 26C

$\eta=1.8520\frac{Ns}{m^{2}}x10^{-5}$

$v_favg=3.225E-5 \frac{m}{s}$

$v_ravg=1.683E-4 \frac{m}{s}$

E= V/d= 61652.28 V/m

Another round of math and I get q=4.84E-19

##### Set 3

Voltage: 501.0 V

Resistance: 2.07 M(ohms)

Temp: 24C

$\eta=1.8440\frac{Ns}{m^{2}}x10^{-5}$

$v_favg=2.855E-5 \frac{m}{s}$

$v_ravg=1.106E-4 \frac{m}{s}$

E= V/d= 61775.59 V/m

Insert values into the formula and get q=3.08E-19C

##### Set 4

Voltage:501.4 V

Resistance:1.945 M(Ohms)

Temp:26C

$\eta=1.8520\frac{Ns}{m^{2}}x10^{-5}$

$v_favg=3.243E-5 \frac{m}{s}$

$v_ravg=2.304E-4 \frac{m}{s}$

E= V/d= 61901.23 V/m

Last but not least, calculations yield q as 6.34E-19C

##### Final
Graph of Rise Velociy vs Q, notice the grouping

By looking at the data, we can see that a faster rise time lead to a higher value for q. There looks to be some kind of trend, leading me to believe that charges are quantized. With that in mind, I will take the minimum value for q as my base. If we look at set 1A and set 3, their charges are about even, sets 1B and 4 are about twice as big, and set 2 is about 1.5times as big.

SJK 17:02, 18 November 2007 (CST)
17:02, 18 November 2007 (CST)
It looks like you are following Bradley's method, but from the way you write it, it is not at all clear what you are doing! Also, how can you have a charge of 1.5? Fractional charge still hasn't been detected. See this paper, which you can talk about in your introduction if you like.]

So now, we can take the avg of them and find some value for this "Q"

$Q= \frac{1+1+2+2+1.5}{5} x10^{-19}$

Q = 1.5x10 − 19C

## Conclusion

SJK 19:15, 18 November 2007 (CST)
19:15, 18 November 2007 (CST)
Most of this belongs somewhere besides the conclusions. Discussion of error analysis method would go in "Methods" and the results of the error analysis in "results and discussion".

This lab is not perfect, but I was very surprised with the results. There are systematic errors that, all added up, will affect the data.

Below, I estimated how far off errors skewed certain measurements we made:

• Human Error in timing: 10%
• Barmoetric pressure off internet: 5%
• Trying to find viscosity off a chart: 5%
• Brownian motion of particles, skewing measurements: 5%
SJK 19:13, 18 November 2007 (CST)
19:13, 18 November 2007 (CST)
It's great that you are using error propagation here. However, you did not get it quite right, as the formula you use is only valid for simpler relations, such as f = x / y. In this much more complicated case, you need to compute the partial derivatives and use the formula as shown here. Alternatively, instead of computing analytically, you can do it numerically. For example, just manually change the barometric pressure and see how your charge answers change.

$error.propigation =\sqrt{x^2 + y^2 +z^2...}$

$ep=\sqrt{10%^2 + 3x(5%^2)}$

ep = 13.2%

Since the data is not 100% accuate, I would surmise the answer lies within the limits set by the error propigation.

Q = (1.5 + / − .1984)x10 − 19C

We can compare our results with that of the accepted value: 1.602x10 − 19C

$%error= \frac{|Actual-Experimental|}{|Actual|}x100$

$%error= \frac{|1.60217646 x 10^{-19}-1.5 x 10^{-19}|}{|1.60217646 x 10^{-19}|}x100$

%error = 6.37

### Sources of Error

There is plenty of room for error in this lab.

• I went on the internet to find the barometric pressure in Albuquerque, but that is probably an estimated quanity and changes with specific altitude of your area and the weather at the timeSJK 17:50, 18 November 2007 (CST)
17:50, 18 November 2007 (CST)
You can look up the air pressure for that day on this site, and then have to convert to actual pressure at this altitude (see: wikipedia article on sea level pressure). You can also examine how much error is introduced by pressure uncertainty simply by putting in different values and seeing how the charge changes.

Also, I learned that "barometric pressure" means "corrected to sea level" so you actually want to use "absolute pressure" (which is what you're using). Altitude is a much bigger factor than weather in this case.
• The viscosity of the air inside the capacitor is measured by the temperature inside the capacitor. That value is determined by measuring the resistance in a thermistor and then finding values on a chart.
• The temperature is estimated off a chart, but when you get a value for the resistance that falls between values, you have to round
• Once the temperature is found, you look at a graph to find the value, and as above, you have to round
• While measuring the fall and rise times of the droplets, it is uncertain how close or far the droplets are, so adjusting the microscope might change the distance that they travel (although it is assumed the apparatus is calibrated to prevent this)
• There is also "lag time" between measurements as one of us stared into the scope and the other was running the stopwatch
• In the calculations, I rounded the values we found as 2 times greater than or 3 times greater than ect. instead of using an acutal ratio

## Acknowledgements

I would like to thank the following people:

• My lab partner Cary, for helping take measurements
• The lab professor, Dr. Koch, for getting this all working
• Milikan, for discovering this in the first place

## References

SJK 20:59, 18 November 2007 (CST)
20:59, 18 November 2007 (CST)
You will need to have many references to original scientific research papers (as opposed to websites). You will cite these mostly in the introduction and methods.

| [1 Milikan's Orignal Experiment]

| [2 Barometric Pressure in ABQ]