# User:Manuel Franco Jr./Notebook/Physics Lab 307/2008/11/26

Millikan Oil Drop Lab Main project page
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SJK Incomplete Feedback Notice
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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 15:05, 17 December 2008 (EST)
15:05, 17 December 2008 (EST)
Also see David's notebook for a couple comments. Very nice job with this lab--excellent notes and summary...though I do think you still had a mistake in the analysis.

# Millikan Oil Drop

Lab Partner: David

## Objective

• Compute the charge of an electron using the Millikan oil drop apparatus.

What to record:

• The thickness of the plastic separator in the housing chamber
• The plate potential
• The resistance
• The oil density
• The viscosity of the air at the room temperature
• The barometric pressure for each set of velocity measurements
• The rise and fall times of the individual drops

## Materials

• Millikan drop apparatus
• 12 V DC power adapter for Halogen lamp
• Atomizer
• Non-volatile oil (Squibb #5597 Mineral oil)
• A Micrometer Kit: SMIEC China National Machinery Imp. & Exp. Corp./ Shanghai Branch.
• 50/500 V power supply TEL-Atomic
• A Digital Voltmeter
• A Computer
• A Stop Watch
• A Paper Towel
• Instead of using support rods to hold up the apparatus, we used 3 really thick books.
Display of equipment used above.

## Connections

The connections are simple. We adjust the height of the Millikan Drop apparatus, and leveled it using the level on the apparatus. Instead of using rods, we used three really big books to have it at eye level. I connected the power supply to an outlet, and connected the power supply and apparatus using the banana plugs. I also plugged the 12 V adapter to the halogen lamp. I connected the digital voltmeter to the thermistor connector as well.

## Procedure

Millikan Oil Drop Housing Chamber

We took the housing section of the apparatus apart, and measured the plastic plate separator in the housing. After measuring it, we cleaned inside the housing area, and reassembled it.

After making sure all the connections were fine, we turned on the power supply. The power supply was set at approximately 500 V. We then focused the viewing scope using the focusing wire by inserting the focusing wire on top of the capacitor plate. We also focused the halogen filament.

We measured the resistance and the voltage across the plate (see below). We were now ready to spray the oil with the atomizer in to the chamber. (Care! We squeezed the pump an nothing was visible on the screen. It was not until Aram told us that when you spray it there are two distinct sounds. One sounds like nothing but air, which is the one you don't want. And the second sound like something is coming out, which is the oil.) We then collected the data for the fall and rise times.

## Data

Day 1

Data taken roughly at 3:41 PM (Mountain Time, DLST) on my cell phone clock.

• Plastic Separator: 10.56 mm 7.59 mm (We incorrectly measured the thickness, Koch showed us how to use it correctly)
• Power Supply: 500 V
• Measured Resistance: 2.01 MΩ
• Mineral Oil Density: 886 kg/m^3
• Viscosity of Air: 1.847 X 10^-5 N*s/m^2 (Using Appendix A from the manual) Day 1
• Temperature: 25°C (Using the ohm a table) Day 1
• Major Reticle Lines .5 mm
• A Constant (b): 8.20 x 10-3 Pa*m
• Barometric Pressure: 1000.0 mbar/ 1.00 x 10^5 Pa (I just used Google to convert)
• Gravity: 9.80665 m/s^2
• Resistance: 2.09 MΩ

Collected data:

Oil Drop Fall time (s) Rise time (s)
1 9.37 11.83
1 8.11 7.40
2 4.20 18.94
3 6.86 9.52
3 7.28 3.11
3 7.90 2.92
4 9.80 2.62
4 11.08 3.28
5 10.17 1.05
5 10.14 .98
5 10.02 .98
6 12.34 1.48
6 11.73 .64
6 11.61 .62
7 22.17 2.46
7 21.84 .70
7 17.28 1.27
Day2 Day 2 Day 2
8 34.67 4.73
8 30.59 .77
9 12.50 1.21
9 13.84 0.95
9 11.40 1.02
10 26.36 0.83
10 29.81 0.77
11 26.23 3.00
11 22.96 7.36
12 20.64 12.05
13 26.05 2.33
14 13.70 3.21
15 14.48 1.37
16 32.34 2.40
17 20.36 2.18
18 29.12 2.78

## Data Analysis

"The definitions of the symbols used, in SI units:

• q – charge, in coulombs, carried by the droplet
• d – separation of the plates in the condenser in m
• ρ – density of oil in kg/m3
• g – acceleration of gravity in m/s2
• η – viscosity of air in poise ( Ns/m2) (Appendix A)
• b – constant, equal to 8.20 x 10-3 Pa · m
• p – barometric pressure in pascals
• a – radius of the drop in m
• $V_f$ – velocity of fall in m/s
• $V_r$ – velocity of rise in m/s
• V – potential difference across the plates in volts
• e – 1.60 x 10-19 coulombs." Lab Manual P.9

Equation For Finding the Radius of the Oil Drop:

$a=\sqrt{\left(\frac{b}{2 p}\right)^2+\left(\frac{9\eta v_f}{2g\rho}\right)}-\frac{b}{2p}$

Equation For Finding the Mass of the Oil Drop:

$m=\frac{4}{3}\pi\rho a^3$

Equation For Finding the Charge of the Oil Drop:

$q=mg \frac{(v_f + v_r)}{E v_f}$

All derived equations can be found in the Lab Manual P.9

All of my data analysis is done in this excel sheet. $E$ (Electric Field) is the voltage across the plastic plate over the space of the plate. We calculated $E$ = 4.73 x 10^4 V/m. After calculating the radius, then the mass, and the charge of the oil drop, in the excel sheet, I multiply the charges by 1 X 10-19 for convenience of notation in the sheet. Also, in the sheet I group the values of the charges. This is done because charge is quantized at the atomic level. So there are clusters in the values. The groups are those clusters. Below in the picture I have taken the mean of those groups/clusters and graphed them based on their charge. The slope of this graph gives the experimental value of the electron.

SJK 15:02, 17 December 2008 (EST)
15:02, 17 December 2008 (EST)
I don't think you did the grouping "correctly." It appears that you just numbered them from 1 to 15, which coincidentally worked out OK. Check David's sheet to see what he did.

My experimental value is 1.503(.069) x 10^-19 C.

## Acknowledgments

I followed Jessy's data analysis format for this lab. I would like to give him the recognition of his work: Jessy's Data Analysis Excel Sheet. I would also like to thank Dr. Koch for the suggestion on my data analysis, and teaching David and I how to use the micrometer.