# User:David E. Sosa/Notebook/2008/11/26

Millikan Oil Drop Main project page
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SJK 14:46, 17 December 2008 (EST)
14:46, 17 December 2008 (EST)
Excellent job on this lab! It looks like you took really good notes, did very good analysis, and produced a very good final result.

## Purpose

To measure the charge of the electron by balancing the gravitational and electrical forces that interact with the oil drop.

## Background and Useful Quantities

The electron charge is one of the most fundamental constants of natures. That is why its accurante measurment if of great importance. When Millikan devised his experiment there were already different experiments that had measured the electric charge of the electron. Nevertheless...

• Mineral Oil density: $\rho = 886 \;\frac{kg}{m^3}$
• Spacer thickness: $d = 10.56\;mm = 10.56 \times 10^{-3}\;m$
• Barometric Pressure: $P = 1.0 \times 10^5\;Pa$

## Equipment

Millikan Oil Drop Apparatus (PASCO Scientific Model AP-8210).
Millikan Oil Drop Apparatus Viewing Chamber.

Refer to the PASCO manual.

• 500 Volt DC power supply for applying a potential across the plates of the oil drop chamber
• Mineral oil,Squib #5597
• Atomizer for spraying mineral oil into chamber
• Multimeter capable of measuring ohmic resistance around 2 megaohms and DC voltage in the range of 500 volts
• Stopwatch
• Millikan oil drop apparatus (PASCO scientific Model AP-8210).
• DC power supply for halogen light source on Millikan oil drop apparatus

### Manuel's Dairy

#### Day 1 (Nov. 26, 2008)

Manuel 2:34 pm, 26 Nov 2008 (EDT): Here's the Lab Manual Link This might not be in the lab manual: The micrometer SMIEC China National Machinery Imp. & Exp. Corp./ Shanghai Branch. Nor the power supply:

What to record:

• The plate potential
• The oil density
• The viscosity of the air at the room temperature
• The barometric pressure for each set of velocity measurements

Measuring the plastic separator 10.56 mm 7.59 mm. We used the micrometer and the tools in the kit to remove the parts. When measuring the plastic, we did not squeeze the plastic. We just tightened enough, but not enough were the plastic fell if we held it up.

• Barometric Pressure for this day. 101900 Pa

We used paper towels to clean up the plates and the separator.

Note from the Manual: "Viewing will be easier for experimenters who wear glasses if the viewing scope is focused without using the glasses."

For procedure follow the lab manual.

The power supply is set at approximately 500V.

Temperature in side the thingy is approximately 25°C Using the ohm a table. Our measured resistance is 2.01 MΩ at 3:41 PM my cell phone clock.

The mineral oil density is 886 kg/m^3. Refer to manual section 2 above Figure 9.

According to appendix A of the manual the viscosity of the air is 1.847 X 10^-5 N*s/m^s.

#### Day 2 (Dic. 01, 2008)

Resistence 2.09 MΩ Barometric Pressure for this day: 101600 Pa

## Data

Collect data:

Oil Drop Fall time (s) Rise time (s))
1 9.37 11.83
1 8.11 7.40
2 4.20 18.94
3 6.86 9.52
3 7.28 3.11
3 7.90 2.92
4 9.80 2.62
4 11.08 3.28
5 10.17 1.05
5 10.14 .98
5 10.02 .98
6 12.34 1.48
6 11.73 .64
6 11.61 .62
7 22.17 2.46
7 21.84 .70
7 17.28 1.27
Day 2 Day 2 Day 2
8 34.67 4.73
8 30.59 .77
9 12.50 1.21
9 13.84 0.95
9 11.40 1.02
10 26.360.83
10 29.81 0.77
11 26.23 3.00
11 22.96 7.36
1220.6412.05
1326.052.33
1413.703.21
1514.48 1.37
16 32.342.40
1720.36 2.18
1829.122.78

## Results, Analysis and Graphs

I am not going to go trough the lengthy derivation of all the formulas. Instead I am only going to post the formulas that were used during the analysis, which can be seen in my Excel Spreadsheet

In order to get the charge of the electron we used the following formula given in the manual:

$q=mg \frac{(v_f + v_r)}{E v_f}$

Where:

$m=\frac{4}{3}\pi\rho a^3$

And:

$a=\sqrt{\left(\frac{b}{2 p}\right)^2+\left(\frac{9\eta v_f}{2g\rho}\right)}-\frac{b}{2p}$

Putting everything together we get:

$q= \frac{4}{3}\pi\rho g$

When we finally obtain a charge for the for each drop by relating all the constants and previously obtained values, we can relate that charge to a multiple of the charge of the electron. I assigned a multiple of e to each of these measured charges. I also had to change the calculations in order to account for the change in temperature that we measure two different days. Because we made measurements two different days, we have to different temperatures for each day.Since the temperature was not exactly as given in the Thermistor Resistance Table it was necessary to plot that data and the insert our values for the resistance to get the temperature for the two day. Once I had the temperature, I used this fancy Gas Viscosity Calculator to get the viscosity for each day. It is important to take this into account. Also the barometric pressure for each day is going to be different. Using the least squares method I was able to obtain the value $(1.63\pm 0.02)\times 10^{-19}\;C$ with a difference of $2.14%\;$ with the accepted value of $1.602\times 10^{-19}\;C$.

Figure 1: Charge vs. Multiples of e
Figure 2: Temperature Vs Resistance

## A Brief Comment About Millikan's Own Experiment

I cannot help to find the history behind the Millikan's experiment extremely interesting. The way that Millikan selected his data was a bit arbitrary, sometimes ignoring data that did not fit his previously held convictions. I found this interesting and also relevant to us, in this lab. To see how an incorrect result can still provide a Nobel prize is pretty amazing. Anyway I think it is no longer acceptable to make such mistakes.

## References and Aknowledgments

• I would also like to thank Jesse Smith from last year for his invaluable help for this analysis.
• Also thanks to Dr. Koch for teaching us how to measure the milimiter.

## Suggestions for this Lab

It would be a good idea to get one of these:

SJK 14:45, 17 December 2008 (EST)
14:45, 17 December 2008 (EST)
I agree with your above fascination with the Millikan story. I want to learn more! Also I agree this stand would be great. Either it's laying around somewhere, or somebody "borrowed" it.