# Physics307L:People/Rivera/Notebook/Millikan Oil Drop

## Millikan Oil Drop Experiment

### Purpose

DH 1
1
Good lab. A little better organization and maybe more introduction/motivation would help

The purpose of this experiment is to find the charge of an electron, using the charge on a drop of oil drop. We assume that this charge is a multiple of a constant that is equated with the charge of one electron.

### Equiptment and Setup

The setup can be found in the Pasco manual for the Millikan Experiment, Pasco Model AP-8210

### Data Collection

SJK 23:57, 9 October 2007 (CDT)
23:57, 9 October 2007 (CDT)
I suppose it is not impossible to have positively charged droplets, right? It is a mystery to me why things tend to get negatively charged when you spray them, or at least oil does.

We found that it takes a few practice runs to get the hang of timing the drops correctly. Sometimes the drops don't do what you want them too. They will jump the wrong way when an electric field is applied. After a few tries me and Brian got the timing down and began to be able to manipulate the drops better. After we got it down we seemed to get better numbers and more measurements per drop.

Our data from the first day and the second day show that as we went along we were able to get more numbers per drop.

### Calculations

DH 2
2
It might be better to put some of the theory before your data and even before your setup to give some motivation
SJK 00:16, 10 October 2007 (CDT)
00:16, 10 October 2007 (CDT)
Great data! In particular, that one data set by itself was awesome (I think the 9th?). Data analysis for this experiment is not easy. I took a look at your Excel sheet and noticed a few things: (1) Some errors near the top of the basic calculations page (3 order of magnitude error in #electrons) (2) probably your life would be a lot easier with some Excel tricks that I could show you, or maybe you are learning them already.

A major critique is that while it is great that you found a way to measure q, it wasn't completely independent of using the known value. That is, you use it in your calculations page to deduce the number of electrons. I think you could probably do this another way without relying on that.

Here are our calculations. I had to upload them to my web page because for some reason every time I tried to upload to wiki I got an error. Below are our numbers the formulas and data can bee seen on our calculations page. There are 2 sheets one with the data and basic calculations and the other with our values for e, std. deviation, errors and experimental differences.

#### Values need for calculations

##### Known (given to as many significant figures as are reasonably certain):
SJK 00:18, 10 October 2007 (CDT)
00:18, 10 October 2007 (CDT)
isn't this spacer distance different than what you measured?
• $d=7.59\times 10^{-3} m$ (plastic spacer width using micrometer)
• $\rho=8.86\times 10^2 \frac{kg}{m^3}$ (density of oil given on bottle)
• $g=9.8 \frac{m}{s^2}$ (gravitational acceleration)
• $b=8.20\times10^{-3} Pa\cdot m$ (some stupid constant)
• $l=1.0\times10^{-3} m$ (length droplet will be measured over)
##### To be found when taking data:
• p (air pressure in Albuquerque. Changes by day will be read each day data taken)
• T (temperature from thermistor in °C)
• V (Voltage between plates in viewing chamber in volts)
• tf (time droplet takes to fall in no field in seconds)
• tr (time droplet takes to rise in field in seconds)
##### To be calculated later:
• η (viscosity of air as a function of T found in a table in Pa*s)
• $v_f=\frac{l}{t_f}$ (average velocity of oil droplet falling in no field in m/s)
• $v_r=\frac{l}{t_r}$ (average velocity of oil droplet rising in a field in m/s)
• $a=\sqrt{\left(\frac{b}{2p}\right)^2+\frac{9\eta v_f}{2g\rho}}-\frac{b}{2p}$ (radius of droplet in meters)
• $q=\frac{4}{3}\pi\rho g d\frac{a^3}{V}\frac{\left(v_r+v_f\right)}{v_f}$ (charge of oil droplet in Coulombs)

#### Final Numbers

SJK 00:27, 10 October 2007 (CDT)
00:27, 10 October 2007 (CDT)
Very nice final numbers! Excellent job with the calculations: you used the correct statistics (standard error of the mean, including N-1, etc.). I have some comments: (1) It's not important that the accepted value is within your standard deviation, but rather that it is within or reasonably close to the range set by your standard error of your mean. When you report that final value, you're saying you think there's a 68% chance that the true value is within the range you're stating. So, 32% of the time it will be outside that range. So, it's not a tragedy that the "accepted value" is outside your range. If 30 students did this experiment, 10 of them should be outside the accepted value, otherwise, errors are not being estimated correctly.

(2) Here is how I would state your final result:
(1.67 +/- 0.19) * 10^-19 C
You technically had the units in the wrong place, and also too many digits.
Measurement # / q (per electron)
1 1.60183E-19
2 1.60013E-19
3 1.60054E-19
4 1.77331E-19
5 1.93057E-19
6 1.7327E-19
7 1.84478E-19
8 1.20668E-19
9 1.68785E-19
10 1.7939E-19
11 1.5606E-19

Mean 1.66663E-19

Standard Deviation 1.92246E-20

• $s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2}$

Standard Error 5.79644E-21

• $SE = \frac{s}{\sqrt{N}}$

Accepted Value 1.60E-19

Experimental difference (|accepted-mean|) 6.66E-21 (within our standard deviation)

Relative Error (|accepted-mean|/|accepted|) 4.16%

Our Number 1.66663e-19 C (+/- 1.92246E-20)

#### Error Explanation

We had a pretty small error. I feel that most of it is from human error such as hitting the timer start and stop at the right times and calling the start and end times exactly when watching the drops going up and down. Also barometric pressure was taken from the National Weather Service web site, it is taken at the Albuquerque Sunport, and can differ as you move farther from that point. Air viscosity was taken from a chart in the back of the manual and wasn't exact by number so it did have to be estimated on the graph. Temperature also was taken from a chart where we had to estimate the temp based on a voltage reading that didn't exactly match the numbers for the thermoresistor so we had to estimate it as the next closest number.

These are the most likely causes of error in our experiment.

### Lessons Learned

SJK 00:29, 10 October 2007 (CDT)
00:29, 10 October 2007 (CDT)
Great lab! I am glad that you are excited by your success...it's amazing that you're able to detect / measure the charge on a single electron, isn't it?

First thigh I have learned is not to throw out data. I thought that our data from the first day wasn't very good but after doing the analysis those numbers seem to fit quite well with all the rest of our data and give us a better argument for our number since we have more numbers to work with making our estimate better. I was very excited when I saw the results from our data.

It took a lot of practice to get our data collection down but once we got it there were not many problems. We did find that we had to clean out the apparatus after each set of drops and sometime couldn't get usable drops into the viewing area each time. It took patience to get it right and to keep a drop in place doing what we wanted it to do.