# Millikan Oil Drop

• Please note that I worked with Ginny for this lab.

## Purpose

The purpose of this lab is to determine the charge of a single electron based on the measurements of the charge on several drops and compare the result to the accepted value.

## Equipment

Millikan setup
Millikan power supply
• Two Wavetek 85XT multimeters
• TEL-Atomic 50V and 500V supply
• PASCO scientific Model AP-8210
• Banana plug connectors
• Stop-watch (We used an online stop-watch)
• Mineral Oil
• SMIEC Micrometer
• Atomizer
• Halogen lamp
• Thermistor
• Viewing scope
• Thorium-232
• Spacer and Capacitor

## Safety

• The most dangerous apparatus is the TEL-Atomic 50V and 500V supply. There is the chance of getting shocked.
• The thermistor connectors should not have a voltage applied across them.
• The halogen lamp should be monitored to prevent overheating in the chamber.

## Setup

• WE looked at the PASCO Manual for the setup.
• We first measured the spacing of the capacitor plates using the SMIEC Micrometer.
• The spacing of the capacitor plates was $7.57 mm \,\!$.
• In order to start calibrating the setup, we cleaned and rinsed the capacitor plates and the spacer.
• We then measured the voltage across the capacitors and got a reading of $499.5 V \,\!$ from the multimeter.
• We used the focusing wire to try and get the right focus of the wire and the background grid so that we can have a good picture of the drops later in the lab.
• We sprayed some droplets into the viewing chamber and chose drops that were not too heavy and too light.
• We then timed the droplets rise and fall times for a variety of distances.
• We recorded the thermistor resistance at each new set of times

## Measurements and Data

• Finding the drops was the hardest part of the lab for us. We did not realize that we could clean out a small lens that is on the clear spacer. The lens was pretty dirty, therefore this was one of the reasons that we could not see the oil drops.
• We recorded our data using a google docs spread sheet and we measured the resistance every time we finished measuring the rise time and fall time of a drop that we chose to measure. Some of the drops were not good to use because they were either too heavy or too light; the light drops would just stay in one place and float the whole time.
• we also took measurements when we irradiated the drops with the thorium.
• Please see our data below.
• We found that you have to be careful with how hard you spray the drops from the atomizer because some drops will fall really fast and sometimes we got a lot of drops in one are and this made it hard for us to keep track of the one we chose to measure.
• This lab required that we work in the dark.
• Please see our data below

## Calculations and Analysis

• We looked up the pressure at our altitude.
• The density of our mineral oil was $.886kg/m^3 \,\!$.
• Using the equations from the PASCO kit manual and the data from our spreadsheet we were able to calculate the charge of the drops.
• According to wikipedia the accepted value of the electron is $e=1.602176487(40)*10^-19C \,\!$.

Useful Equations for Calculating the Charge

• These were the three equations that were useful for me to calculate the charges
$a=\sqrt{(b/2p)^2+9nv_f/2gp_d}{-b/2p}\,\!$
$m=4*pi*a^3*p_d\,\!$
$q=\frac{mg(v_f+v_r)}{(V/d)v_f}\,\!$
• $a \,\!$ is the radius, $d \,\!$ is the separation of the plates, $b\,\!$ is a constant, $v_{f} \,\!$ is the fall velocity, $v_{r} \,\!$ is the rise velocity, $n \,\!$ is the viscosity, $p \,\!$ is pressure, $V \,\!$ is the potential difference across the plates, and $p_{d} \,\!$ is the density of the oil.

Calculated Charges

• $e_{1}= 3.3479*10^-11 C \,\!$
• $e_{2}= 4.0373*10^-11 C \,\!$
• $e_{3}= 2.376*10^-11 C \,\!$
• $e_{3,Ionized}= 9.807*10^-12 C \,\!$
• $e_{4}= 1.6*10^-14 C \,\!$
• $e_{4,Ionized}= 1.5*10^-15 C \,\!$
• $e_{5}= 1.2*10^-14 C \,\!$
• $e_{6}= 1.4*10^-14 C \,\!$
• These results were not so good and I was pretty sure I had made a mistake so I recalculated the charges.

Recalculated Charges

• $e_{1} = 1.0897 \cdot 10^{-20} +/- 3.6766 \cdot 10^{-20}$C
• $e_{2} = 6.2910 \cdot 10^{-21} +/- 3.7180 \cdot 10^{-21}$C
• $e_{3} = 4.8342 \cdot 10^{-20} +/- 6.9860 \cdot 10^{-21}$C
• $e_{3,Ionized} 7.0758 \cdot 10^{-20} +/- 1.0487 \cdot 10^{-20}$C
• $e_{4} = 2.0642 \cdot 10^{-17} +/- 3.0899 \cdot 10^{-18}$C
• $e_{4,Ionized} = 4.1899 \cdot 10^{-17} +/- 2.8041 \cdot 10^{-18}$C
• $e_{5} = 4.6468 \cdot 10^{-17} +/- 1.1432 \cdot 10^{-17}$C
• $e_{6} = 4.6110 \cdot 10^{-17} +/- 1.2955 \cdot 10^{-17}$C
• Please note that these results are the average of the drops +/- the standard error of the mean.
• As you can see, these results are much better than the previous results but it is still obvious that there is some systematic error. Please see the section on the error below to see why we might have had an error with our results.

## Error

• We made measurements with our eyes, therefore it is highly possible that our data is not accurate because we are looking through the microscope.
• Human error in timing the droplets. There is probably a better technique of timing the droplets.
• Error in measuring the plate separation with the micrometer.
• Made a mistake somewhere in my calculations.
• Possibly wrong conversions of units or pressure.
• Halogen lamp was not very affective for us. I think that we could have made better measurements with a better light source.

## Acknowledgements

• Ginny, my lab partner for coming in an extra day to get a few more measurements for our data.
• Thanks to Dan Wilkinson and Tyler Wynkoop for the suggestions with the setup.
• Emran Qassem for the help with finding the oil drops.
• Professor Koch and Katie Richardson.