; F- Faraday constant, N A - Avagadro constant. Best. uncertainty ~1.6 ppm. 4. From Josephson (K J = 2e. constants. ) and von Klitzing R h

Transcription

1

2 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

3 1. Oil drop experiment. Robert A. Millikan.. (1909). e=1.5924(17) 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 (35) C 9/25/2017 3

4 The Nobel Prize in Physics Robert A. Millikan "for his work on the elementary charge of electricity and on the photoelectric effect". ROBERT ANDREWS MILLIKAN nd of March, 1868, Morrison, Ill University of Chicago 9/25/2017 4

5 ROBERT ANDREWS MILLIKAN Diagram and picture of apparatus 9/25/2017 5

6 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

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 9/25/2017 7

8 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

9 telescope 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

10 9/25/

11 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/

12 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/ E

13 Fdrag 6av George Gabriel Stokes ( ) 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 ( ) a C fc 1 A B e, A 1.246, B 0.42, C 0.78 a a 5 r c fc 1 A , for a 10 m, rc a a p[mmhg] Here a particle radius; λ mean free path of the gas molecules negligible term [m] p[mmhg] 9/25/

14 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/

15 Project: T measurement.opj 9/25/

16 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 ; ; rc[ m] p[ mmhg ] f 9/25/

17 d 2 x 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/

18 2 5 1 t g 2 x ; ; [ ] g rc m 3 2 g grc p[ mmhg ] 2 f c d 2 x 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 t t g g t rise 9/25/

19 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/

20 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/

21 Project Millikan1.opj Plugin your data here Constants calculations Parameters of the experiment. Depend on exact setup and environment conditions r c [m] = index p[mmhg] P(mmHg) Col( Par )[7] 9/25/

22 Project Millikan1.opj 9/25/2017

23 d 2 x 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/

24 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/

25 7 n n=q/e Drop number 9/25/

26 n=q/e counts 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 = R^2 = y0 0 ±0 xc ± w ± A ± xc ± w ± A ± Drop number Q/e 9/25/

27 Choice of Oil Drops for the Analysis: rise and fall times t r (s) n=5 n=4 n=3 n= t g (s) n=1 Difficult to separate n=3,4,&5 9/25/

28 Drop generation rate 1 Hz Fluid - Dow Corning silicon oil Number of drops - 17 million Mass milligrams Duration - 8 months 9/25/

29 Modern experiments at 9/25/

30 Modern experiments at Summary as of January Total mass throughput for all experiments milligrams of fluid Total drops measured in all experiments million No evidence for fractional charge particles was found. 9/25/