Experiment 21.Millikan's oil-drop experiment to measurethe charge of the electronThe oil drop experiments performed by famous American physicist Robert A.Millikan from 1909 to 1917 to measure the elementary electric charge, is of greatsignificance in the history of physical development.The beauty of the oil dropexperiment is that it is a simple, elegant hands-on demonstration that charge isquantized. Professor Millikan spent 10 years on the experiment to obtain results ofgreat significance. (1) He proved the discontinuity of electric charge (granular). (2)He measured and obtained the elementary charge (the charge of the electron)withvalue e=1.60x10-19c. It is now recognized that e is the elementary charge and itsmeasuring accuracy has been improved. The best result of the value ise=(1.60217733±0.00000049)×10-19CIn 1923, Millikan won the Nobel Prize in physics, in part because of this experiment.Experimental objectives(1)Measuring thechargeofelectrons.(2) verifying the quantum of chargeExperimental InstrumentsMillikan's oil-drop experiment instrument, monitor and sprayers.Experimental principleThe basic idea to design the oil-drop experiment is to make the charged oildroplet in a state of force equilibrium in the measuring range. Classifying oil dropletsinto two types of motion as uniform motion or static state, the methods to measureelectronic charge by oil drop can be divided into dynamic method and static method.1.Dynamic methodAn oil droplet with mass m and charge is located between two parallelmetal plates. When there is no voltage on the plates, the droplet falls rapidly by
Experiment 21. Millikan's oil-drop experiment to measure the charge of the electron The oil drop experiments performed by famous American physicist Robert A. Millikan from 1909 to 1917 to measure the elementary electric charge, is of great significance in the history of physical development. The beauty of the oil drop experiment is that it is a simple, elegant hands-on demonstration that charge is quantized. Professor Millikan spent 10 years on the experiment to obtain results of great significance. (1) He proved the discontinuity of electric charge (granular). (2) He measured and obtained the elementary charge (the charge of the electron) with value 19 e 1.60 10 C − = . It is now recognized that e is the elementary charge and its measuring accuracy has been improved. The best result of the value is 19 e 1.602177 33 0.000 000 49 10 C − = （ ） In 1923, Millikan won the Nobel Prize in physics, in part because of this experiment. Experimental objectives (1) Measuring the charge of electrons. (2) verifying the quantum of charge. Experimental Instruments Millikan’s oil-drop experiment instrument, monitor and sprayers. Experimental principle The basic idea to design the oil-drop experiment is to make the charged oil droplet in a state of force equilibrium in the measuring range. Classifying oil droplets into two types of motion as uniform motion or static state, the methods to measure electronic charge by oil drop can be divided into dynamic method and static method. 1. Dynamic method An oil droplet with mass m and charge q is located between two parallel metal plates. When there is no voltage on the plates, the droplet falls rapidly by
gravity. Since the viscous drag caused by air on the droplet f, is proportional to thevelocity, the viscous resistance and gravity become balanced (buoyant force in the Airis ignored) and the droplet falls at a constant speed after it speeds up to velocity ygAs shown in the Fig.21-1, by the Stokes law we get(21-1)6元ay,=mgwhere n is the viscous coefficient of the air, a is the radius of the droplet (Thedroplet can be treated as a ball approximately because of the surface tension).mgFig.21-1:The force of oil droplets in the gravitational fieldWhen the voltage U is added to the parallel plates, the droplet is in theelectrostatic field with strength E,Assume the electric force qE is in the oppositedirection of gravity. Then, the droplet is accelerated upwards by the effect of electricfield force. By considering the viscous drag from the air, the acceleration goes downas the velocity of the droplet increases. The resistance force, the gravity and theelectric field force are balanced as the velocity become y after it moves up in ashort distance. As in the Fig. 21-2, the oil-drop will rise at a constant speed and thereholds(21-2)6元av=qE-mgFig.21-2:Theforceandmovementofoil droplets in anelectricfield
gravity. Since the viscous drag caused by air on the droplet r f is proportional to the velocity, the viscous resistance and gravity become balanced (buoyant force in the Air is ignored) and the droplet falls at a constant speed after it speeds up to velocity g v . As shown in the Fig. 21-1, by the Stokes law we get 6 g a v mg = (21-1) where is the viscous coefficient of the air, a is the radius of the droplet (The droplet can be treated as a ball approximately because of the surface tension). Fig. 21-1: The force of oil droplets in the gravitational field When the voltage U is added to the parallel plates, the droplet is in the electrostatic field with strength E . Assume the electric force qE is in the opposite direction of gravity. Then, the droplet is accelerated upwards by the effect of electric field force. By considering the viscous drag from the air, the acceleration goes down as the velocity of the droplet increases. The resistance force, the gravity and the electric field force are balanced as the velocity become e v after it moves up in a short distance. As in the Fig. 21-2, the oil-drop will rise at a constant speed and there holds 6 e a v qE mg = − . (21-2) Fig. 21-2: The force and movement of oil droplets in an electric field
SinceUE=(21-3)dcombine the above Eqns. (21-1), (21-2) and (21-3) to solve ford'g+ye(21-4)q=mgUTo measure the charge q of the oil droplet, the mass m is needed besides U, d,'g and ve. Suppose the density ofthe oil droplet is p.The mass is obtained by4(21-5)_元apm=3From (21-1) and (21-5), the radius of the droplet is9v,(21-6)2pgBecause the oil droplet is quite tiny (the radius is 10-6m), the air cannot be treated asa continuous medium.The viscous coefficient n should be corrected tonn=(21-7)1+6,pawhere b is the correction constant, p is the air pressure and a is the radius ofthedroplet without correction given by (21-6) because it is not necessary to calculate theaccuratevaluein the correctionterm.The uniform rising distance and the uniform falling distance of the droplet arechosen equal to I in the experiment. If the time of uniform falling is measured as tgand the time of uniform rising is measured as t., then(21-8)g11Plug the formulae (21-5) to (21-8) into (21-4) to obtain18元nl凯+一g=2pg[1+b/(pa)/
Since U E d = , (21-3) combine the above Eqns. (21-1), (21-2) and (21-3) to solve for ( ) g e g d v v q mg U v + = . (21-4) To measure the charge q of the oil droplet, the mass m is needed besides U , d , g v and e v . Suppose the density of the oil droplet is . The mass is obtained by 4 3 3 m a = . (21-5) From (21-1) and (21-5), the radius of the droplet is 9 2 g v a g = . (21-6) Because the oil droplet is quite tiny (the radius is m), the air cannot be treated as a continuous medium. The viscous coefficient should be corrected to 1 b pa = + , (21-7) where b is the correction constant, p is the air pressure and a is the radius of the droplet without correction given by (21-6) because it is not necessary to calculate the accurate value in the correction term. The uniform rising distance and the uniform falling distance of the droplet are chosen equal to l in the experiment. If the time of uniform falling is measured as g t and the time of uniform rising is measured as e t , then g g l v t = , e e l v t = . (21-8) Plug the formulae (21-5) to (21-8) into (21-4) to obtain ( ) 3/2 1/2 18 1 1 1 2 1 e g g l d q g b pa U t t t = + +
Set18元2K1+b/(pa)V2pgto get-e(+))(21-9)which is the formula to obtain the charge of the oil-drop by the dynamic method.2.StaticmethodRegulate the voltage between two parallel electrode plates to keep the dropletimmovable(qE =mg as in the Fig.21-2), that is y,=0.Letting t.→oo, it is easyto get from (21-9)or18元dnl(21-10)U/2pg(1+b/(pa)which is the formula to obtain the charge of the oil-drop by the static method with[9nVg2pgIn order to get thecharge of the electron e, thegreatest common factor of the chargeq for different droplets is the value of the elementary charge e, i.e. the charge of theelectron e.For one oil droplet, if the variation of the charge of the droplet Aq, ismeasured andapproximatedbyan integermultiple of somesmallestunit whichistheelementary charge e.Experimental content and procedure1. Introduction of the ApparatusThe microscopic Millikan oil-drop apparatus includes an oil-drop box, oil-droplighting device, leveling system, CCD TV measurement microscope, circuit box,sprayer and so on, shown in the Fig. 21-3. The oil-drop box is a parallel plate
Set ( ) 3/2 18 2 1 l K d g b pa = + to get 1/2 1 1 1 e g g K q U t t t = + (21-9) which is the formula to obtain the charge of the oil-drop by the dynamic method. 2. Static method Regulate the voltage between two parallel electrode plates to keep the droplet immovable ( qE mg = as in the Fig. 21-2), that is 0 e v = . Letting e t → , it is easy to get from (21-9) 3/2 1 g K q U t = , or ( ( )) 3/2 18 2 1 g l d q g t b pa U = + (21-10) which is the formula to obtain the charge of the oil-drop by the static method with 9 2 g v a g = . In order to get the charge of the electron e , the greatest common factor of the charge q for different droplets is the value of the elementary charge e , i.e. the charge of the electron e . For one oil droplet, if the variation of the charge of the droplet i q is measured and approximated by an integer multiple of some smallest unit which is the elementary charge e . Experimental content and procedure 1. Introduction of the Apparatus The microscopic Millikan oil-drop apparatus includes an oil-drop box, oil-drop lighting device, leveling system, CCD TV measurement microscope, circuit box, sprayer and so on, shown in the Fig. 21-3. The oil-drop box is a parallel plate
capacitor made of two metal plates with bakelite ring in between. There is a hole inthe center of the upper plate for oil mist falling. Holes are cut into the ring forillumination by abright lightand viewing througha microscope823Fig. 21-3: Oil-drop experimental device: 1. oil mist cup, 2. swith of oil mist hole, 3. windproofcover,4.upper electrode plate, 5.oil drop box,6.lower electrodeplate,7.basis,8.cover ofthemist cup,9. nozzle of the sprayer,10.oil mist hole, 11.pressure spring,12.base ofthe oil dropboxA windproof cover is put outside of the oil-drop box with an oil mist cup. In thecenter of the bottom of the cup, there is an oil drop hole and a block to control the oildrop. On the upper electrode plate, there is a pressure spring which is movable fromthe left to the right. It should be noted that the upper electrode plate can be taken outonly when the pressure spring is switched to the boundary position.The screen of the monitor is divided into 10x3 grids for the standardMillikan's oil-drop experiment instrument. The physical distance for each grid is0.2mm.2.Apparatus AdjustmentThe standard scale of the 10x3 grids, the values of U and t will bedisplayed on the screen of the monitor, when we turn on the monitor and theMillikan's oil-drop experiment instrument.Adjust the leveling handwheel at the bottom of the adjusting instrument to makesurethebuilt-inbubbleindicateshorizontalDo not fill too much oil in the sprayer. Otherwise, a lot of "oil" but not “oil mist"will be sprayed out of the sprayer. Do not put the nozzle of the sprayer inside the oilspray hole to avoid the oil drop hole being choked up with the large oil droplets.Please wipe the surplus oil on the upper electrode plate and clean the oil mist cup
capacitor made of two metal plates with bakelite ring in between. There is a hole in the center of the upper plate for oil mist falling. Holes are cut into the ring for illumination by a bright light and viewing through a microscope. Fig. 21-3: Oil-drop experimental device: 1. oil mist cup, 2. swith of oil mist hole, 3. windproof cover, 4. upper electrode plate, 5. oil drop box, 6. lower electrode plate, 7. basis, 8. cover of the mist cup, 9. nozzle of the sprayer, 10. oil mist hole, 11. pressure spring, 12. base of the oil drop box A windproof cover is put outside of the oil-drop box with an oil mist cup. In the center of the bottom of the cup, there is an oil drop hole and a block to control the oil drop. On the upper electrode plate, there is a pressure spring which is movable from the left to the right. It should be noted that the upper electrode plate can be taken out only when the pressure spring is switched to the boundary position. The screen of the monitor is divided into 10 3 grids for the standard Millikan’s oil-drop experiment instrument. The physical distance for each grid is 0.2mm. 2. Apparatus Adjustment The standard scale of the 10 3 grids, the values of U and t will be displayed on the screen of the monitor, when we turn on the monitor and the Millikan’s oil-drop experiment instrument. Adjust the leveling handwheel at the bottom of the adjusting instrument to make sure the built-in bubble indicates horizontal. Do not fill too much oil in the sprayer. Otherwise, a lot of “oil” but not “oil mist” will be sprayed out of the sprayer. Do not put the nozzle of the sprayer inside the oil spray hole to avoid the oil drop hole being choked up with the large oil droplets. Please wipe the surplus oil on the upper electrode plate and clean the oil mist cup