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 9/25/2017 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 e = F N A ; F- Faraday constant, N A - Avagadro constant. Best uncertainty ~1.6 ppm. 4. From Josephson (K J = 2e ) and von Klitzing R h K = h e 2 constants 5. Recommended by NIST value 1.602 176 565(35) 10-19 C 9/25/2017 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 9/25/2017 4
ROBERT ANDREWS MILLIKAN 1868-1953 Diagram and picture of apparatus 9/25/2017 5
Motivation: Measurement of the magnitude of the electron charge! Demonstrate that the electron charge is quantized! Measure the charge of an electron to ±3% Picture of the PASCO setup 9/25/2017 6
d atomizer Oil drops ~1m telescope ρ air V g 500V + V - Forces on the oil drop: 1) Gravity + buoyant force (air displaced by oil drop) 2) Drag force of the oil drop in the air 9/25/2017 7
d atomizer Oil drops ~1m telescope ρ air V g 500V + V - 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 9/25/2017 8
telescope 135-170 o atomizer eyepiece oil mist oil Light source P 1 P 1 Q,m P 2 500±1V oil drop spacer scale 9/25/2017 9
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Allow drop to undershoot here before starting next rise time experiment rise time measurement stops here fall time measurement starts here fall time t g rise time t rise x x = fall distance = rise distance. x must be the same for all drops! rise time measurement starts here fall time measurement stops here 9/25/2017 11
E FE QE F F g drag mgzˆ ( 1) 6av (2) Fdrag 6av Fg mgzˆ F E QE (3) a : radius of drop ρ : density ρ = ρ oil ρ air v : velocity of oil drop Q : charge of oil drop E : electric field E=V/d V : Voltage across plates η : viscosity of air g : gravitational const. Particle reached terminal velocity Fg Fdrag FE 0 dv dt 0 dv F m Fg Fdr ag F dt 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 1m size particle reaches the terminal velocity in ~10-5 s 9/25/2017 12 E
Fdrag 6av George Gabriel Stokes (1819-1903) For small particle radius (a<15m) Stokes law need to be corrected. This correction was derived by E. Cunningham. F drag a 6 f c v Ebenezer Cunningham (1881-1977) a C fc 1 A B e, A 1.246, B 0.42, C 0.78 a a 5 r c -6 6. 18 10 fc 1 A 1 1. 1, for a 10 m, rc a a p[mmhg] Here a particle radius; λ mean free path of the gas molecules negligible term -8 760 [m] 6. 53 10 p[mmhg] 9/25/2017 13
Allow drop to undershoot here before starting next rise time experiment rise time measurement stops here fall time measurement starts here fall time t g rise time t rise x x = fall distance = rise distance. x must be the same for all drops! rise time measurement starts here fall time measurement stops here 9/25/2017 14
Project: T measurement.opj 9/25/2017 15
f c can be found from Newton law equation in the case of V=0 (falling drop) 4 a F F a g 6 v 0 g 3 drag 3 fc (see write-up) 1 2 t g x 1 2 g 2 g gr 3 c c 5 1 2 6. 18 10 ; ; rc[ m] p[ mmhg ] f 9/25/2017 16
3 3 1 9d 2 x 1 1 1 Q n e 3 f 2 V g t t t c g g rise Q : charge of oil drop n : number of unpaired electrons in drop e : elementary charge d : plate separation V : Voltage across plates ρ : density ρ = ρ oil ρ air η : viscosity of air g : gravitational constant x : drift distance for oil drop t g : fall time t rise : rise time 9/25/2017 17
2 5 1 t g 2 x 6. 18 10 1 ; ; [ ] g rc m 3 2 g grc p[ mmhg ] 2 f c 1 3 3 1 9d 2 x 1 1 1 Q F S T 32 fc V g t t g g t rise F 1 t g 1 32 f c g 1 2 S 9d 2 x V g 3 3 T 1 1 1 t t g g t rise 9/25/2017 18
Project: Millikan_raw data.opj Locations: \\engr-file-03\phyinst\apl Courses\PHYCS401\Students\1. Millikan Oil Drop experiment\millikan_raw data.opj 9/25/2017 19
Locations: \\engr-file-03\phyinst\apl Courses\PHYCS401\Students\1. Millikan Oil Drop experiment Please make a copy (not move!) of Millikan1.opj and Millikan_raw data.opj in your personal folder and start to work with your personal copy of the project 9/25/2017 20
Project Millikan1.opj Plugin your data here Constants calculations Parameters of the experiment. Depend on exact setup and environment conditions r c [m] = index 6. 18 10 5 p[mmhg] P(mmHg) Col( Par )[7] 9/25/2017 21
Project Millikan1.opj 9/25/2017
3 3 1 9d 2 x 1 1 1 Q F S T 32 fc V g t t g g t rise Follow correct order of calculations: r c g (F,S,T) Q n Project Millikan1.opj 9/25/2017 23
Project Millikan1.opj Follow correct order of calculations: r c g (F,S,T) Q n Indexes for parameters in Col( Par ) Actual air viscosity should be calculated manually before any other calculation 9/25/2017 24
7 n 6 5 4 n=q/e 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 Drop number 9/25/2017 25
n=q/e 4.5 4.0 3.5 3.0 2.5 2.0 counts 50 40 30 20 Data: Bin1_Counts1 Model: Gauss Equation: y=y0 + (A/(w*sqrt(PI/2)))*exp(-2*((x-xc)/w)^2) Weighting: y No weighting Chi^2/DoF = 34.42645 R^2 = 0.81797 y0 0 ±0 xc1 0.92997 ±0.01884 w1 0.27612 ±0.0381 A1 13.76998 ±1.65786 xc2 1.87091 ±0.05159 w2 0.60549 ±0.11582 A2 16.60884 ±2.56952 1.5 1.0 10 0.5 0 1 2 3 4 5 6 7 8 9 10 11 Drop number 0 1 2 Q/e 9/25/2017 26
Choice of Oil Drops for the Analysis: rise and fall times t r (s) 60 55 50 45 40 35 30 25 20 15 10 5 n=5 n=4 n=3 n=2 0 0 5 10 15 20 25 30 35 40 45 50 55 60 t g (s) n=1 Difficult to separate n=3,4,&5 9/25/2017 27
Drop generation rate 1 Hz Fluid - Dow Corning silicon oil Number of drops - 17 million Mass - 70.1 milligrams Duration - 8 months 9/25/2017 28
Modern experiments at 9/25/2017 29
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. 9/25/2017 30