Physics307L:People/Rivera/Notebook/Millikan Oil Drop

Purpose
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
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
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
From Bradley's page

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)
 * $$t_f$$ (time droplet takes to fall in no field in seconds)
 * $$t_r$$ (time droplet takes to rise in field in seconds)

To be calculated later:

 * $$\eta$$ (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
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
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.