# Physics307L F09:People/Ritter/Notebook/071001

## Millikan Oil Drop

DH 1
1
A good writeup. You may need some additional organization and don't forget to put your errors in your numbers
SJK 01:03, 10 October 2007 (CDT)
01:03, 10 October 2007 (CDT)
It appears that all of your raw data are in Antonio's notebook, correct? You should say that and link to those specific pages next time

Refer also to Antonio Rivera's page Physics307L_F09:People/Rivera/Notebook. For photographs of our specific setup.

## Purpose

DH 2
2
Maybe cite where you got that number

The purpose of the Millikan oil drop experiment is to measure the charge of an electron. This value is found by balancing the electric and gravitational forces on tiny oil drops sprayed in between two charged plates. By measuring the travel speeds of the oil drops both in an electric field and when left only to gravity, one should find values that are always integer multiples of a given amount. This amount is the charge of an electron (1.602 x 10^-19 C).

## Equipment and Setup

SJK 00:44, 10 October 2007 (CDT)
00:44, 10 October 2007 (CDT)
I can see that focusing, though, would be a big problem. I wonder, though, whether you are introducing systematic error by not focusing on the wire? I say that because I know that Millikan in his original experiments had to worry a lot about where he was looking, because he needed to know the magnification to know the distance.

This particular version of the experiment utilized the PASCO Millikan oil drop apparatus. See link given at the top of the page for illustrations and a detailed description of this particular piece of equipment. The setup for this experiment was fairly straight forward. The only modification made to the instructions was to place the apparatus on top of a stack of books to make long viewing sessions a little more comfortable.

One issue did arise in the focusing of the viewing lens. The manufacturers suggested method for properly focusing the magnifying lens was slightly vague, and in the end completely useless. For the purposes of our experiment we found it to be much easier, and necessary, to focus the lens as we introduced oil drops into the chamber.

## Data Collection

Data collection did prove to be slightly tricky as there was a definite learning curve associated with the use of this particular instrument. Initially oil drops were hard to find at all. Once this was accomplished, however, the trick was to pick out a quality drop in which good measurements could be taken. It seemed early on that the drops movements were erratic and unpredictable. It was from this that we discovered an error that we had been making in our data collection procedure. Because of this, I have broken my data into two sections based on how the data was taken.

#### Trial 1: Measurements 1-8

In measuring the rise and fall times of our oil drops it was necessary to set the oil chamber as to allow for positive pressure that would in turn "suck" selected drops into the viewing chambering in between the electrodes. This was done using a selector switch on the left side of the chamber. Once drops were viewed it was necessary to flip the switch down into the off position to begin the experiment. However, for our first set of numbers we were setting the switch instead in to the on position which served the purpose of introducing the chamber to a radioactive source, and introducing our oil drops to released alpha particles.

#### Trial 2: Measurements 1-9

These measurements were taken using the outlined procedure given in the PASCO operating manual

## Calculations

DH 3
3
Some of the theory can be given before taking data because they provide readers with motivation for your techniques
SJK 01:04, 10 October 2007 (CDT)
01:04, 10 October 2007 (CDT)
I think the value you wrote down in Antonio's notebook for the spacer width is different than the one you're using from Bradley...why?

Values need for calculations

Known (given to as many significant figures as are reasonably certain):
*$d=7.59\times 10^{-3} m$  (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

Measurment # / q (per electron)

#### Trial 1

SJK 01:21, 10 October 2007 (CDT)
01:21, 10 October 2007 (CDT)
I do realize that you had an Excel sheet that you weren't able to upload (probably because of the server switch over the weekend), so that's probably where some explanation is (please do upload this when you get a chance). Nevertheless, you should have some more explanation of why and what you're doing here (though I could figure it out). See Antonio's notebook for comments about his excel workbook, which maybe is similar to yours.

That said, once I figured out what you're doing, it looks like you're doing great work! I think your formulas for standard error of the mean are correct, and I was very impressed with the data you and Antonio took! Great work!

Another comment comes to mind: if you knew how to do weighted averages, this is a situation where that would be good...more on that later, or you can ask me about it.

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

Mean for Trial 1 = 1.6605E-19

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

Standard Deviation = 1.0205E-20

• $SE = \frac{s}{\sqrt{N}}$

Standard Error = 3.6080E-21

#### Trial 2

9 1.68785E-19

10 1.7939E-19

11 1.5606E-19

Mean for trial 2 = 1.68078E-19

Standard Deviation = 1.16717E-20

Standard error = 6.7387E-21

## Conclusions

SJK 01:25, 10 October 2007 (CDT)
01:25, 10 October 2007 (CDT)
Thank you for putting in this discussion! It is very important to report problems and describe possible solutions!

Very true about error propagation, and I do remember discussing this with you. One "easy" way we discussed doing it is to use Excel or some software to plot the function (q?) and then tweak the various values (viscosity, rise time, etc.) and see how it affects the final value. Effectively, you're looking at approximate partial derivatives. For the rise time specifically, you can see what value you get for the (rise time - error) and (rise time + error) and then this is the error bar on your q value.

Where is your final answer, though??!!! You need to report a value + / - something.

1.) Issues with process - At one point I believe that Antonio and myself had figured out the best possible methods for taking data in this experiment (measurements 9 and 10). However, difficulties with the apparatus itself prevented more such data sets from being taken. This is to say that at one point our apparatus all together stopped working. Oil drops would no longer find there way into the chamber and the instrument would actually begin to smoke. I believed this to be some sort of possible clog in our system somewhere. This seemed to not be the case. It did appear that after prolonged use a cool down and wipe down might be necessary to keep the system functioning.

2.) Error Calculations - In the end I calculated the average charge per electron found from each measured oil drop. From this I calculated the mean, standard deviation, and standard error for the two individual trials. This seemed most appropriate for my current understanding of error calculation, but it does seem fairly insufficient. Our measurements only really concerned the oil drop velocities. This, however, is a small part of the final equation used in calculating the charge of the oil drops. It would seem that larger percentages of error would be possible in our measurements then there would be in the rest of the variables involved in our calculations. Discussing this with Prof. Koch brought up the subject of error propagation. I hope to eventually learn more about this and possibly extend it later on to the data I collected for this experiment.