# Physics307L:People/Callow/millikanoildrop

## Millikan Oil Drop Summary

I worked with Johnny Gonzalez for this lab.

SJK 14:31, 30 October 2009 (EDT)
14:31, 30 October 2009 (EDT)
You did a truly excellent job on this lab (provided you correct typos! :) ). I love the data analysis method you came up with. Your primary notebook is spectacular, and it looks like you and Johnny took really careful and precise data. Great job!

## Links to lab notebook and manual

Link to lab manual used

Link to my lab notebook

## Purpose of the lab

The purpose of the Millikan oil drop experiment is to find the charge of a single electron.

## Summary of my data

The charge of 4 different oil drops are found using their rise time in an electric field and their fall time due to gravity. 2 of these oil drops are also ionized to give them different charges giving a total of 6 different charges q found.

${\displaystyle q_{1}=4.74(17)*10^{-9}e.s.u.}$

${\displaystyle q_{2}=9.17(17)*10^{-9}e.s.u.}$

${\displaystyle q_{3}=9.74(46)*10^{-9}e.s.u.}$

${\displaystyle q_{4}=6.74(17)*10^{-9}e.s.u.}$

${\displaystyle q_{5}=5.35(19)*10^{-9}e.s.u.}$

${\displaystyle q_{6}=5.83(16)*10^{-9}e.s.u.}$

and using the matlab script shown in my lab notebook found the charge of an electron to be

${\displaystyle e=2.785*10^{-10}e.s.u.}$ (Steve Koch 14:04, 30 October 2009 (EDT): As we discussed in class, this is actually an error resulting from the typo)

After fixing the script we found

${\displaystyle e=4.839(20)*10^{-10}e.s.u.}$ usign 10,000,000 steps.

From the lab manual the accepted value is

${\displaystyle e=4.803*10^{-10}e.s.u.}$

So we were off by about .5%. I didn't manage to find the standard error for e but based on the size of the standard error for the charge on the oil drops it's very likely our experiment agrees with the accepted value. The methods for measuring the fall and rise time are likely the major source of error. We also forgot to check the temperature between measuring drops but the thermistor read about 1.9 at the beginning and end of the lab so that likely didn't contribute to much. Other problems are not knowing the barometric pressure inside the chamber and estimating it to be the pressure outside the building at the time, human reaction time using the stopwatch, and just that it is very difficult to keep track of an oil drop for an extended period of time.

As seen in the labview files on the notebook page thanks to professor Koch the function seems to be able to pull out the correct value of e from simulated data as long as the noise in the data for n values is less than .2. So because our data led to a very good estimate of e, our data was likely very good.

## What I learned

SJK 14:02, 30 October 2009 (EDT)
14:02, 30 October 2009 (EDT)
I thought your method was really clever and a ton of fun to see! I'm amazed at how few droplets are needed to get a very precise answer. If you do pursue this further, I'd like to know if other people have used this method, either for the Millikan experiment, or perhaps other unrelated areas that happen to have a similar issue. Also, it'd be interesting to use simulated data (like we were doing with LabVIEW) to see which kinds of situations will kill the method and how robust it is. E.g., will one "bad" measurement ruin everything. Finally, I don't think it'd be too hard to include a weighting factor based on your uncertainty. Also, I wonder if you could derive something similar to what you did, based on some kind of maximum likelihood principle and some of the assumptions you made?

This lab really had me thinking on how to find the charge of a single electron, specifically because our drops all had 10+ charge. But even not knowing the accepted value of the charge I wanted to find an algorithm that would approximate e based on some assumptions. My algorithm may not be the best (it doesn't account for uncertainty and may be incorrect in general) but it at least has me thinking of a way to solve problems where there are more variables than equations but some variables are limited to being natural numbers (or limited in general to a set other than the reals).

## Other notes

I'd like to thank Johnny Gonzalez for being my lab partner. The photos in the lab notebook are all thanks to him and the experiment wouldn't have been possible without him. Also I'd like to say thanks for making sure I feel involved in taking measurements and setting the experiment up.