Millikan Oil Drop Experiment

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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

9/21/2015 2 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

9/21/2015 3 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 9/21/2015 4 ROBERT ANDREWS MILLIKAN 1868-1953

Diagram and picture of apparatus

9/21/2015 5 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

9/21/2015 6 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

9/21/2015 7 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

9/21/2015 8 telescope

135-170o

atomizer

oil eyepiece Light source oil mist

P1 P1 Q,m

500±1V spacer oil drop scale

9/21/2015 9 9/21/2015 10 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

9/21/2015 11 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 (1) Gravity + buoyant force (air g : gravitational const. displaced by oil drop) (2) Drag force of the oil drop in the air dv (3) Electric force on oil drops which Particle reached terminal velocity  0 dt carry charge Q 1m size particle reaches the FFFg drag  E  0 terminal velocity in ~10-5s 9/21/2015 12 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]

9/21/2015 13 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

9/21/2015 14 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

9/21/2015 15 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

9/21/2015 16 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

9/21/2015 17 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

9/21/2015 18 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

9/21/2015 19 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] 9/21/2015 20 index Project Millikan1.opj

9/21/2015 1 921dx 1133  QFST   32  fVgt t   cg rise tg 

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

9/21/2015 Project Millikan1.opj 22 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 9/21/2015 23 n 7

n=Q/e

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

9/21/2015 24 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

9/21/2015 25 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)

9/21/2015 26 •Drop generation rate 1 Hz • Fluid - Dow Corning silicon oil •Number of drops - 17 million •Mass - 70.1 milligrams •Duration - 8 months

9/21/2015 27 Modern experiments at

9/21/2015 28 Modern experiments at

Summary as of January 2007. Total mass throughput for all experiments- 351.4 milligrams of fluid Total drops measured in all experiments - 105.6 million No evidence for fractional charge particles was found.

9/21/2015 29 . 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

9/21/2015 30 . 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

9/21/2015 31 . Transmission line. Unknown load simulation

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

9/21/2015 32