Millikan Oil Drop Experiment Professor Jeff Filippini Physics 401 Spring 2020 Today’s Topics 1. History: Measuring the charge of the electron 2. Theory of the Experiment 3. Laboratory Setup 4. Data Analysis Physics 401 2 Motivation: The Dawn of Elementary Particles • 1750s: Benjamin Franklin proposes electricity is flow or surplus/deficit of single electrical fluid • 1881: Hermann von Helmholtz argues for elementary positive and negative electric charges (“atoms of electricity”) • 1897: J.J. Thompson shows particle nature of “cathode rays” emitted in vacuum tubes • Universal negatively-charged particles from vacuum tubes, radioactivity, … • Measured charge-to-mass ratio (e/m) via magnetic deflection • Mass <1/1000 of hydrogen ion (actually ~1/1836) Physics 401 3 Robert Millikan and the 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 University of Chicago Moved to Caltech in 1921 Physics 401 4 Robert Millikan and the Oil Drop Experiment Work with Ph.D. student ROBERT ANDREWS MILLIKAN Harvey Fletcher – not a 1868-1953 coauthor on famous paper. “The father of stereophonic sound” First functional electronic hearing aid Physics 401 5 Oil Drop Apparatus Motivation: 1. Measure the magnitude of the electron charge Apparatus precision ± 3% Millikan original ± 0.1% 2. Demonstrate that electric charge is quantized! Physics 401 6 Oil Drop Experiment atomizer oil drops ∅~1µ telescope + d V Vg 500 V - ���� Forces acting on the oil drop: 1. Gravity 2. Electric force on a charged oil drop Physics 401 8 The Role of Air: Buoyancy and Drag Lowering an object through a fluid means Motion through a fluid opposed lifting an equal volume by drag: friction with and within of the surrounding fluid the surrounding fluid Objects eventually reach terminal velocity at which drag balances accelerating forces Physics 401 9 Oil Drop Experiment atomizer oil drops ∅~1µ telescope + d V Vg 500 V - ���� Forces acting on the oil drop: 1. Gravity 2. Electric force on a charged oil drop 3. Buoyant force (weight of air displaced by oil drop) 4. Drag force on a moving oil drop Physics 401 10 Oil Drop Apparatus: Schematic Layout Light source telescope 135-170o atomizer oil eyepiece Light source oil mist P1 P1 Q,m P2 500±1V spacer oil drop scale Physics 401 11 Oil Drop Apparatus: Schematic Layout Physics 401 12 How the Measurement Looks Allow drop to “undershoot” here before starting next rise time experiment … and stops here Fall time measurement starts here… Fall time tg Rise time trise x x = fall distance = rise distance Must be the same for all drops! … and stops here Rise time measurement starts here… Physics 401 13 Balance of Forces: Newton’s Second Law � Forces on the oil drop: �⃗% � 1. Gravity + buoyancy �� = −�� �+ 2. Drag force ����� = −���� � ⃗ �$ 3. Electric force � = � � �⃗!"#$ � a: radius of drop �� � = � = �� + ����� + �� ρ: net density ρoil - ρair �� Drop v: velocity of oil drop Q: charge of oil drop !+ Terminal velocity: speed at which = 0 E: electric field E=V/d !, V: voltage across plates �� + ����� + �� = � η: viscosity of air Achieved within ~10-5 s by a 1 μm particle Apparatus g: gravitational constant Physics 401 14 Modifications to Stokes’ Law ����� = −���� � For particles of small radii (� ≲ 15 ��), Stokes’ Law must be corrected for the particle nature of air. This correction was derived by E. Cunningham � George Gabriel Stokes � = −��� � Ebenezer Cunningham ���� (1881-1977) (1819-1903) �� Here: • # a = particle radius � � "! � = 1 + � + � � $, � = 1.246; � = 0.42; � = 0.78 • λ = mean free path of gas ! � � "# molecules $ %! "& &.()×(+ , �! ≈ 1 + � = 1 + ≈ 1.1 for � = 10 �, �! = 760 ���� # # - [,,/0] � = 65.3 �� � Physics 401 15 What We Measure: Rise and Fall Times Allow drop to “undershoot” here before starting next rise time experiment … and stops here Fall time measurement starts here… Fall time tg Rise time trise x x = fall distance = rise distance Must be the same for all drops! … and stops here Rise time measurement starts here… Physics 401 16 Measuring the Temperature Project: T measurement.opj Physics 401 17 Solving Newton’s Law: �(�*, �+,-.) � The correction factor �- can be found from Newton’s Law �⃗% � in the case of � = 0 (falling drop) ⃗ - , �!"#$ �⃗$ . �⃗) + �⃗*+,) = � �� − 6�� �⃗ = 0 . /! a: radius of drop ρ: net density ρoil- ρair v: velocity of oil drop See write-up for derivation Drop Q: charge of oil drop E: electric field E=V/d 1 . 23 V: voltage across plates 1 �$ 2�� 6.18×10 � ≈ 1 − ; � = ; � = η: viscosity of air ./0 � $ ���. - � [����] g: gravitational constant �- $ - Apparatus x: drift distance Measured tg, trise: fall, rise times Physics 401 18 Solving Newton’s Law: �(�*, �+,-.) ) % *+ � �⃗ 1 �( 2�� 6.18×10 � % ≈ 1 − ; � = ; � = � %/' � ( ���% $ � [����] �$ ( $ �⃗ ⃗ !"#$ �$ Putting it all together: a: radius of drop ρ: net density ρ - ρ oil air � � v: velocity of oil drop � ��� �� � � � � Drop � = �� = + Q: charge of oil drop �/� � �� � � � �� � � ���� E: electric field E=V/d V: voltage across plates η: viscosity of air F: Stokes’ law correction g: gravitational constant : Stokes’ law force balance Apparatus x: drift distance S Measured tg, trise: fall, rise times T: Your timing measurements Physics 401 19 Origin ProJects: Data Collection Project: Millikan_raw data.opj Location: \\engr-file-03\PHYINST\APL Courses\PHYCS401\Students\1. Millikan Oil Drop experiment\Millikan_raw data.opj Physics 401 20 Origin ProJects: Data Analysis Location: \\engr-file-03\PHYINST\APL Courses\PHYCS401\Students\1. Millikan Oil Drop experiment\ Please make a copy (don’t move!) of Millikan1.opj and Millikan_raw data.opj in your personal folder and work with your personal copy of the project Physics 401 21 Origin Data Analysis Project: Millikan1.opj Your data Constants goes here Calculations Experimental Parameters Depend on exact setup and 6.18×10%& � � = environmental conditions $ � [����] P[mmHg] ⟹ Col(“Par”)[7] Physics 401 22 Origin Data Analysis Project: Millikan1.opj Physics 401 23 Origin Data Analysis Project: Millikan1.opj æö19phdx 233 11æö 1 QFST=••=ç÷32 ç÷ + fVgr ç÷ tt èøctg èø g rise Follow correct dependency sequence of calculations: �$ → �' → �, �, � → � → � Physics 401 24 Origin Data Analysis Project: Millikan1.opj • Indices for parameters in Col(“Par”) • Actual air viscosity should be calculated manually before any other calculation Physics 401 25 Origin Charge Calculation n 7 6 5 4 3 n=Q/e 2 1 0 0 1 2 3 4 5 6 7 8 9 10 11 Drop number Physics 401 26 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 3.5 R^2 = 0.81797 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 20 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 Physics 401 27 Effect of Choice of Oil Drops n=5 60 55 n=4 50 45 40 n=3 35 30 (s) 25 r t 20 15 n=2 n=1 Difficult to separate 10 5 n=3, 4, 5, … 0 0 5 10 15 20 25 30 35 40 45 50 55 60 tg (s) Physics 401 28 Modern Experiments •Drop generation rate: 1 Hz •Fluid: Dow Corning silicon oil •Number of drops: 17 million •Mass: 70.1 milligrams •Duration: 8 months Physics 401 29 Modern Experiments 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 fractionally charged particles was found. Physics 401 30 Measuring the Electron Charge • 1909: Oil drop experiment, Robert A. Millikan e=1.5924(17)×10−19 C (0.1% error) • 1918: Shot-noise proposed by Walter H. Schottky Poisson fluctuations in current across a Barrier appear as noise P Measure noise variance �O = 2�� ∆� over a Bandwidth ∆� • In terms of Avogadro’s constant and Faraday constant (Coulombs per mole, from electrolysis) � = �/�Q; Best uncertainty ~1.6 ppm PS • From superconducting junctions (Josephson constant, �R = ) and T T quantum Hall effect (von Klitzing constant, � = ) U S" Physics 401 31 Modern Definition • SI base units redefined on May 20, 2019 1967 • Move to ground all 7 SI base units in terms of exact defined values of the physical 1983 2019 constants (exactly reproduciBle in laB!) • Response to the “crisis” of infinitesimal variations in the standard kilogram mass 2019 2019 • Modern exact definition: � = 1.602176634×10VWX ������� 2019 1979 Physics 401 32.