# Millikan Oil Drop

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My feedback is incomplete on this page for two reasons. First, the value of the feedback to the students is low, given that the course is over. Second, I'm running out of time to finish grading!
SJK 18:45, 16 December 2009 (EST)
18:45, 16 December 2009 (EST)
Excellent lab notebook, and looks like some good data.

In this lab we will be trying to determine by experimentation the value for the charge of an electron. We will do this by measuring how an oil drop with a negative charge responds to the force of gravity and the electric force applied through two charged plates.

## Equipment

The equipment is as follows:

Millikan Oil Drop Apparatus (Pasco Scientific AP-8210)
Mineral Oil
SMIEC Micrometer
Multimeter (Wavetek 85XT)
500V DC Power supply (TEL-Atomic)
Atomizer
Stopwatch

## Safety

The following are the safety concerns for this lab:

electrical safety. The main thing to keep in mind is that we are using electrical equipment to produce an electric field between the two plates and there is a danger of electrical shock
equipment safety. Don't do anything that could potentially cause harm to the equipment. Don't drop it for example because the main interment is one solid peace and could be severely damaged due to its solid construction.

## Set Up

The set up is outlined in the operations manual for the Milkman Oil Drop Apparatus.

First you need to take apart the chamber and clean it and measure the spacing which in my case was 7.6 mm. Then put the chamber back together don't forget to make sure the black peace on the top of the chamber has the hole on top facing down if not no oil will be able to get into the chamber. You will need to connect the light source on the oil drop apparatus to a power supply. Once you do that you can calibrate the lens. You will need to take the focusing wire and align it with the grid. The way to do this is to adjust the focus on the eyepiece by turning it. You will need to get the sharpest image of the wire you can and then focus the other focus until the grid is in plan view and sharp. Once you have the focusing done you can connect the DC power supply to the capacitor plates. Measure the voltage across the plates and record it mine was different for the different days that I did the experiment. Once you get the voltage across the plates connect the multimeter to the thermistor holes so you can determine the temperature in the chamber by reading a resistance and converting it using the chart in the operators manual of the oil drop apparatus. Now you are ready to start spraying oil into the chamber.

## Notes

### Day 1

• Worked with Elizabeth Allen
• Went through a safety brief with Dr. Koch and discussed whats going on in this lab
• used several books to get the height just right to view the eyepiece
• Set up the equipment and adjusted the eyepiece suing the focusing wire to get the grid into focus
• Hooked up the multimeter to the what ever to record the current and looked on the chart on the apparatus to find out at what temp that the experiment was being conducted and also found out what voltage is being applied to the capacitor plates
• Put some oil on the plates using the dropper and started to take data by picking out oil drops to watch
• Had some difficulty's in finding the drops and deiced to adjust the focus to find the drops I don't know if this will alter the data but I will calculate the calculations for the first day compared to how using a different way to find the drops on the other day
• Got some data but it was a struggle to find the drops

### Day 2

• Worked with Elizabeth Allen again
• Came in and set up the lab. Took readings on the voltage across the plates which was 501.1 volts. We then took a temperature reading using the multimeter and the attached chart.
• Opened the ionization source lever to allow oil in the spray position and sprayed oil in the chamber.
• Having trouble seeing any drops again cleaned the apparatus where the oil is let in the chamber to try to see if there were any clogs that were preventing any of the oil from coming into the chamber.
• Seeing lots of drops but none of the drops appear on the grid I don't know why but since they are not on the grid I cannot tell where they are in relation and how far they travel in terms of the grid-lines. We got Dr Koch to help us with spraying and focusing the interment again. We started taking data on drops again.
• First try we could not find oil drops. Searched for them with the focus rings, but no luck. Re-calibrated the focus with the probe.and sprayed oil without the small black cover inside. Had Dr. Koch help us adjust the focus and found oil drops. Started to take data on how long a drop takes to fall across one grid line and how long it takes to rise with an applied voltage across the same distance. Took 9 different sets of data for different drops with multiple fall and rise times.

### Day 3

• Worked with Elizabeth Allen
• came in and set up the equipment again, took reading on the voltage across the plates which was 501.1 volts. Then took a temperature reading on the multimeter and the chart.
• Let oil in using the sprayer. Found some drops to measure. Took data on 2 different drops both with multiple fall and rise times.

## Calculations

The formula for the derivation of the charge q is as follows $q=400*\pi *d*\left[ \frac{1}{g\rho }*\left(\frac{9*\eta }{2} \right)^3\right]^{\frac{1}{2}}*\left(\frac{1}{1+\frac{b}{pa}} \right)^{\frac{3}{2}}*\frac{V_{fall}+V_{rise}\sqrt{V_{fall}}}{V}$

• where q is the charge in esu
• d is the separation of the plates in the condenser .808cm
• ρ is the density of the oil in this case is .866g/cm3
• g acceleration due to gravity 981cm/s2
• η is the viscosity of air in pose which is given by the thermistor reading of 1.9*10^6 is about 1.856*10^-4 poise from page 19 of the manual
• b is a constant whose value is 6.17*10^-4 cm of Hg
• p is the barometric pressure 76.0 cm of Hg that I got from John Callow

thanks John

• a is the radius of the drop in cm which can be obtained using the following formula
$a=\sqrt{\left(\frac{b}{2p} \right)^2+\frac{9\eta V_{fall}}{2g\rho }}-\left(\frac{b}{2p} \right)$
• Vfall is the velocity of the falling drop in cm/s
• Vrise is the velocity of the rising drop in cm/s
• V is the voltage difference across the plates

I used the Excel spread sheet to calculate the values of a and of q. The velocity of the drop can be found by knowing that the distance the drop travels is .05 cm. To get the velocity you take the $Velocity=\frac{.05cm}{time}$

I calculated the charge for 7 of my drops

The first drop had a charge of 3.38(19)*10^-9 e.s.u. and it had 7 electrons

The second drop had a charge of 1.545(05)*10^-9 e.s.u. and 3 electrons

The third drop had a charge of 2.27(003)*10^-9 e.s.u. and 5 electrons

The forth drop had a charge of 8.34(06)*10^-9 e.s.u. and 17 electrons

The fifth drop had a charge of 3.59(01)*10^-9 e.s.u. and 7 electrons

The sixth drop had a charge of 4.33(07)*10^-9 e.s.u. and 9 electrons

The seventh drop had a charge of 4.41(07)*10^-9 e.s.u. and 9 electrons

The accepted value from the lab book is 4.803*10^-10 e.s.u.

I got the number of electrons by $\frac{experimental}{calculated}$ and by error from $\sqrt{\left( \frac{dV_{r}}{dt}*\sigma _{r}\right)^2+\left( \frac{dV_{f}}{dt}*\sigma _{f}\right)^2}$ where sigma(f and r) are the SEM of the rise and fall velocity's and dv/dt is a small change in the rise and fall velocity's respectfully of which the step size was .00001.

## Errors

• some possible sources of error can come from the amount of drops inside the chamber so you can lose track of the drop your viewing and think that it is a different drop than it actually is. Another source could be when you open the ionization source lever to allow air to escape when you are putting the initial drops in the chamber and forget to close it allowing air to continue to flow in the chamber which could cause the drops to fall at a higher rate or lower rate.

# References

Milkman Oil drop experiment procedure procedure begins on page 7