Millikan Oil Drop Experiment

Agenda

1. Measuring of the charge of electron. 2. Robert Millikan and his oil drop experiment 3. Theory of the experiment 4. Laboratory setup 5. Data analysis

2/17/2014 2 Measuring of the charge of the electron

1. Oil drop experiment. Robert A. Millikan.. (1909). e=1.5924(17)×10−19 C 2. Shot noise experiment. First proposed by Walter H. Schottky 3. In terms of the Avogadro constant and Faraday constant 풆 =

푭 ; F- Faraday constant, NA - Avagadro constant. Best 푵푨 uncertainty ~1.6 ppm.

ퟐ풆 풉 4. From Josephson (푲 = ) and von Klitzing 푹 = constants 푱 풉 푲 풆ퟐ 5. Recommended by NIST value 1.602 176 565(35) 10-19 C

2/17/2014 3 Robert Millikan. Oil drop experiment The Nobel Prize in Physics 1923. Robert A. Millikan "for his work on the elementary charge of electricity and on the photoelectric effect".

ROBERT ANDREWS MILLIKAN 1868-1953

22nd of March, 1868, Morrison, Ill

University of Chicago 2/17/2014 4 Robert Millikan. Oil drop experiment

ROBERT ANDREWS MILLIKAN 1868-1953

Diagram and picture of apparatus

2/17/2014 5 Oil drop experiment.

Measurement of the magnitude of the electron charge! Motivation: Demonstrate that the electron charge is quantized!

Measure the charge of an electron to ±3%

Picture of the PASCO setup

2/17/2014 6 Oil drop experiment.

atomizer Oil drops ∅~1m

telescope + V Vg d 500V - 흆풂풊풓

Forces on the oil drop: 1) Gravity + buoyant force (air displaced by oil drop) 2) Drag force of the oil drop in the air

2/17/2014 7 Oil drop experiment.

atomizer Oil drops ∅~1m

telescope + V Vg d 500V - 흆풂풊풓

Forces on the oil drop: 1) Gravity + buoyant force (air displaced by oil drop) 2) Drag force of the oil drop in the air 3) Electric force on oil drops which carry charge Q

2/17/2014 8 Apparatus. Schematic Layout

telescope

135-170o

atomizer

oil eyepiece Light source oil mist

P1 P1 Q,m

500±1V spacer oil drop scale

2/17/2014 9 Apparatus: actual setup

2/17/2014 10 What is measured

Allow drop to “undershoot” here before starting next rise time experiment rise time measurement stops here fall time measurement starts here

fall time tg

rise time trise x = fall distance = rise x distance. x must be the same for all drops!

fall time measurement stops here rise time measurement starts here

2/17/2014 11 Balance of Forces: Newton’s Law

푬 Fmgz  ˆ (1) FQEE  g

Fadrag  6 v (2)

Favdrag 6 Fmgzg  ˆ FQE  E (3)

a : radius of drop ρ : density ρ = ρoil – ρair dv v : velocity of oil drop FmFFF  gdr ag  E Q : charge of oil drop dt E : electric field E=V/d V : Voltage across plates Forces on the oil drop: η : viscosity of air g : gravitational const. (1) Gravity + buoyant force (air displaced by oil drop) dv (2) Drag force of the oil drop in the Particle reached terminal velocity  0 air dt (3) Electric force on oil drops which carry charge Q FFFg drag  E  0 2/17/2014 12 Modification to Stokes Law

Favdrag 6

For small particle radius (a<15m) Stokes law need to be corrected. This correction was derived by E. Cunningham. a George Gabriel Stokes Fvdrag 6 Ebenezer Cunningham (1819-1903) (1881-1977) fc

a C  Here a – particle fc 1  A  B e , A  1.246, B  0.42, C  0.78 aa radius; λ – mean  r 6. 18 105 free path of the gas f1  A  1 c  1 . 1 , for a  10-6 m , r  cca a p[mmHg] molecules

760 negligible term  [m] 6. 53 10-8 p[mmHg]

2/17/2014 13 We measure: tg and trise

Allow drop to “undershoot” here before starting next rise time experiment rise time measurement stops here fall time measurement starts here

fall time tg

rise time trise x = fall distance = rise x distance. x must be the same for all drops!

rise time measurement starts here fall time measurement stops here

2/17/2014 14 Solving Newton’s law: Q(tg, trise) fc can be found from Newton law equation in the case of V=0 (falling drop)

4 3 a FFagvgdrag  60 3 fc

(see write-up)

1 2 5 126 18t 10g x .  1  ; ; [ ] rm 2 gc2 [] 3 gcgrp mmHg fc

2/17/2014 15 Solving Newton’s law: Q(tg, trise)

1 92111dx33  Qne 3  2 Vgttt  fc ggrise

Q : charge of oil drop ρ : density ρ = ρoil – ρair n : number of unpaired η : viscosity of air electrons in drop g : gravitational constant e : elementary charge d : plate separation x : drift distance for oil drop V : Voltage across plates tg : fall time trise : rise time

2/17/2014 16 Route of charge calculation Q(tg, trise).

1 2 5 126 18t 10g x .  1  ; ; [] rm 3 gc2 [] 2 gcgrp mmHg fc

192111dx33  QFS T 32  fVgtt   cgrise tg 

1 33  2 92dx 111 1 tg F  1  S  T  32  t tt fcg Vg g grise

2/17/2014 17 Route of charge calculation. Origin projects. Data collecting. Projects Section L1.opj … Section L4.opg Locations: \\engr-file-03\PHYINST\APL Courses\PHYCS401\Common\Origin templates\Oil drop experiment \\engr-file-03\PHYINST\APL Courses\PHYCS401\Students\1.Millikan Oil Drop experiment

2/17/2014 18 Route of charge calculation. Origin projects. Data analysis.

Project: Millikan1.opj Locations: \\Phyaplportal\PHYCS401\Common\Origin templates\Oil drop experiment \\Phyaplportal\PHYCS401\Students\1. Millikan Oil Drop experiment

Please make a copy (not move!) of Millikan1.opj in your personal folder and start to work with your personal copy of the project

2/17/2014 19 Route of charge calculation. Origin project. Data analysis.

Project Millikan1.opj

Plugin your data here

Constants

calculations

Parameters of the experiment. Depend on exact setup and environment ퟔ. ퟏퟖ × ퟏퟎ−ퟓ conditions 풓 [풎] = 풄 풑[풎풎푯품] P(mmHg)→Col(“Par”)[7] 2/17/2014 20 index Route of charge calculation. Origin project. Data analysis. Project Millikan1.opj

1 921dx 1133  QFST   32  fVgt t   cg rise tg 

Follow correct order of calculations: rc →g →(F,S,T) →Q →n

2/17/2014 21 Route of charge calculation. Origin project. Data analysis. Project Millikan1.opj

Indexes for parameters in Col(“Par”) Follow correctActual orderair viscosity of calculations should be: r ccalculated→g →(F,S,T) manually→Q →n before any other calculation 2/17/2014 22 Charge calculation. Origin project.

n 7

n=Q/e

0 0 1 2 3 4 5 6 7 8 9 10 11 Drop number

2/17/2014 23 Expected results

4.5 50 Data: Bin1_Counts1 Model: Gauss Equation: y=y0 + (A/(w*sqrt(PI/2)))*exp(-2*((x-xc)/w)^2) 4.0 Weighting: y No weighting

40 Chi^2/DoF = 34.42645 R^2 = 0.81797 3.5 y0 0 ±0 xc1 0.92997 ±0.01884 w1 0.27612 ±0.0381 3.0 A1 13.76998 ±1.65786 30 xc2 1.87091 ±0.05159 w2 0.60549 ±0.11582 A2 16.60884 ±2.56952 2.5

n=Q/e 2.0 counts

1.5 10

1.0

0.5 0 0 1 2 3 4 5 6 7 8 9 10 11 1 2 Drop number Q/e

2/17/2014 24 Choice of Oil Drops for the Analysis: rise and fall times

n=5 60 55 n=4 50 45 n=3 40 35 30 n=2 (s) 25 r Difficult to

t 20 separate n=1 n=3,4,&5 15 10 5 0 0 5 10 15 20 25 30 35 40 45 50 55 60

tg (s)

2/17/2014 25 Modern experiments at

•Drop generation rate 1 Hz • Fluid - Dow Corning silicon oil •Number of drops - 17 million •Mass - 70.1 milligrams •Duration - 8 months

2/17/2014 26 Modern experiments at

2/17/2014 27 Modern experiments at

“No electric charges were measured in the range of an integer charge 1/3 e or 2/3 e.” (SLAC–PUB–7357 August 1996)

2/17/2014 28 Appendix #1

. Traditional reminder: L1_Lab3_student name.pdf Report-exp2.pdf Please upload the files in proper folder! This week folders: Pulses in transmission lines_L1 Pulses in transmission lines_L3 Pulses in transmission lines_L4 Pulses in transmission lines_L5

This week you have the last chance to submit “Transients in RLC” report

2/17/2014 29 Appendix #2

. Transmission line. Unknown load simulation

Load parameters

Function generator parameters X-axes scaling Line characteristic impedance

Expected load

Location: \\Phyaplportal\PHYCS401\Common\Transmission line software

2/17/2014 30 Appendix #2

. Transmission line. Unknown load simulation

Location: \\Phyaplportal\PHYCS401\Common\Transmission line software

2/17/2014 31 Appendix #3 Graphs

Data?

2/17/2014 32 Appendix #3 Graphs

Figure 15: Odd harmonic amplitudes plotted against 1/n

2/17/2014 33