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
immediately after finish the experiment.We can observe many oil droplets after the oil mist have been sprayed into the oilmist cup. Try to adjust the electric voltage to dispel the remainder oil. Practice moretocontrol themotion of an oil droplet.3.MeasurementPractice(1) Practice controlling the oil dropletsSet thetimerto"End"state.Switch the“Working State"button,“Equilibriumand Lifting"button to"Working"and“Equilibrium”state. Set the electric voltagelarger than 400v by adjusting the equilibrium voltage knob. Spray oil and thenobserve the motion of the oil droplets. Adjust the focus carefully to make sure the oildroplets become clear and bright. Focus on the oil droplets which move upwards withslow velocity. Then decrease the voltage to make sure the oil droplet achieves thebalance state. (Adjust the voltage carefully to keep the oil droplets on one grid line.Wait for a moment to see whether the oil droplets deviate away from the previousposition. If the oil droplets drift in the same direction, we should readjust the voltage.If the oil droplet almost stays at the previous position or it only slightly drifts up anddownresultingfromBrownianmotion,wecanassumetheoildropletisintheequilibrium state.)(2) Practice selecting the oil dropletsIt is important to choose a suitable oil droplet with moderate size.On one hand,the large oil droplet is bright enough but it carries morecharge.Thus, the large oildroplet falls rapidly and it is difficultto measure the movingtime accurately.Ontheother hand, the small oil droplet is easily influenced by the Brownian motion. Thus,the fluctuation for the small oil droplet is very large and it is also difficult to measurethe moving time accurately. Therefore, it is better to choose the oil droplet withmoderate sizeand less charge.It is recommended tomeasurethe oil droplet with theequilibrium voltage in the interval 150~400V and the dropping time near 20s(3) Practice measuring moving time of the oil dropletsSet the “Equilibrium and Lifting" button to "Lifting" state (The voltage willincrease 20oV to lift the oil droplet). When the oil droplet moves above the “StatingLine" (for instance 0.2mm), set the “Equilibrium and Lifting" button to “Equilibrium"state again (The voltage will be reset to the equilibrium value, or decrease 200V).Then set the “Working State" button to “ov" (both upper and lower electrode plateswill connect to the ground). The oil droplet will fall down due to the loss of the
immediately after finish the experiment. We can observe many oil droplets after the oil mist have been sprayed into the oil mist cup. Try to adjust the electric voltage to dispel the remainder oil. Practice more to control the motion of an oil droplet. 3. Measurement Practice (1) Practice controlling the oil droplets Set the timer to “End” state. Switch the “Working State” button, “Equilibrium and Lifting” button to “Working” and “Equilibrium” state. Set the electric voltage larger than 400V by adjusting the equilibrium voltage knob. Spray oil and then observe the motion of the oil droplets. Adjust the focus carefully to make sure the oil droplets become clear and bright. Focus on the oil droplets which move upwards with slow velocity. Then decrease the voltage to make sure the oil droplet achieves the balance state. (Adjust the voltage carefully to keep the oil droplets on one grid line. Wait for a moment to see whether the oil droplets deviate away from the previous position. If the oil droplets drift in the same direction, we should readjust the voltage. If the oil droplet almost stays at the previous position or it only slightly drifts up and down resulting from Brownian motion, we can assume the oil droplet is in the equilibrium state.) (2) Practice selecting the oil droplets It is important to choose a suitable oil droplet with moderate size. On one hand, the large oil droplet is bright enough but it carries more charge. Thus, the large oil droplet falls rapidly and it is difficult to measure the moving time accurately. On the other hand, the small oil droplet is easily influenced by the Brownian motion. Thus, the fluctuation for the small oil droplet is very large and it is also difficult to measure the moving time accurately. Therefore, it is better to choose the oil droplet with moderate size and less charge. It is recommended to measure the oil droplet with the equilibrium voltage in the interval 150~400V and the dropping time near 20s (3) Practice measuring moving time of the oil droplets Set the “Equilibrium and Lifting” button to “Lifting” state (The voltage will increase 200V to lift the oil droplet). When the oil droplet moves above the “Stating Line” (for instance 0.2mm), set the “Equilibrium and Lifting” button to “Equilibrium” state again (The voltage will be reset to the equilibrium value, or decrease 200V). Then set the “Working State” button to “0V” (both upper and lower electrode plates will connect to the ground). The oil droplet will fall down due to the loss of the
electric field force. Press the timer to“Begin"state immediately,when the oil dropletpasses the scale line marked with “o". Then press the timer to “End" state, when theoil droplet reaches the scale line marked with "1.6 It should be noted that the"Working State" button will be switched to Working" state automatically, when wepress the timer to “End” state. At this time, the oil droplet will stop falling. We canpress the"Confirm"button to record the measured data to the screen.4.Formal measurementStatic method: From equation (21-10), it can be inferred that two physicalquantities need to be measured. One is the equilibrium voltage U. The other one isthe time of uniform falling tg during the distance l. Both U and tg can beobtained from the monitor.Dynamic method: From equation (21-9), it can be inferred that we shouldmeasure the time of uniform rising te during the distance l,when voltage U isadded between two electrode plates and the time of uniform falling tg during thesame distance I without voltageFor the same oil droplet, we can repeatedly measure the data five times to obtainthe quantity of electric charge for the oil droplet. To verify that the electric charge isan integer multiple of the elementary charge,we should select 5~10 oil droplets torepeatedly measure the quantity of electric charge for each oil droplet.Experimental Notices(1) In the process of tracking measurement for one oil droplet, we should adjustthe focus of the microscope in time, when the image of the oil droplet becomesblurred.(2) Do not spray lots of oil. The oil drop hole is easily chocked up, since it isvery small. Remove the oil mist cup and spray oil to the oil drop hole directly are alsoforbidden.(3) Do not open the oil drop box without permission. Please be careful that thenozzle of the sprayer is made of glass and do not make it broken.(4) If the electrode plates are not horizontal, the oil droplets will drift forward orbackward, or even drift out of the sight
electric field force. Press the timer to “Begin” state immediately, when the oil droplet passes the scale line marked with “0”. Then press the timer to “End” state, when the oil droplet reaches the scale line marked with “1.6”. It should be noted that the “Working State” button will be switched to “Working” state automatically, when we press the timer to “End” state. At this time, the oil droplet will stop falling. We can press the “Confirm” button to record the measured data to the screen. 4. Formal measurement Static method: From equation (21-10), it can be inferred that two physical quantities need to be measured. One is the equilibrium voltage U . The other one is the time of uniform falling g t during the distance l . Both U and g t can be obtained from the monitor. Dynamic method: From equation (21-9), it can be inferred that we should measure the time of uniform rising e t during the distance l , when voltage U is added between two electrode plates and the time of uniform falling g t during the same distance l without voltage. For the same oil droplet, we can repeatedly measure the data five times to obtain the quantity of electric charge for the oil droplet. To verify that the electric charge is an integer multiple of the elementary charge, we should select 5~10 oil droplets to repeatedly measure the quantity of electric charge for each oil droplet. Experimental Notices (1) In the process of tracking measurement for one oil droplet, we should adjust the focus of the microscope in time, when the image of the oil droplet becomes blurred. (2) Do not spray lots of oil. The oil drop hole is easily chocked up, since it is very small. Remove the oil mist cup and spray oil to the oil drop hole directly are also forbidden. (3) Do not open the oil drop box without permission. Please be careful that the nozzle of the sprayer is made of glass and do not make it broken. (4) If the electrode plates are not horizontal, the oil droplets will drift forward or backward, or even drift out of the sight
Experimental data recording andprocessing(1) Static method: From the equation (21-10), we can set the density of the oilp=981kg/m(20°C), the gravitational acceleration g=9.794m/s?, the viscouscoefficient of the air n=1.83x10-kg/(m·s), the uniform falling distancel=1.6x10-m，thecorrectionconstantb=6.17x10-m·cmHg，theatmospheric pressure p=76.0cmHg,the distance between two electrode platesd=5.00x10-m.The time Ig should be the averaged value for severalmeasurements(2) To obtain the value of e by using the graphing method. Assume the electriccharge for each oil droplet is qi,q..,qm. We can obtain the approximate integer n.through dividing q by the currently accepted value of the elementary chargee=1.60x10-9c.Then,we can obtain a straight lineby settingn,as an independentvariable and q,as a dependent variable.The slop of the straight line is theelementary charge, i.e. the value of e.(3) Compare the accepted value and the experimental value of the elementarycharge e to obtain the relative error.Questions(1) In the process oftracking measurement for one oil droplet, why some times theimage of the oil droplet may become blurred? How to avoid losing the oil dropletduring the experimental measurement? (How to know whether the electrode plates arehorizontal or not? What is the impact, if the electrode plates are not horizontal?)(2) What is the impact, if the oil droplet is not in the equilibrium state during themeasurement? Why should we adjust the voltage to ensure the oil droplet is in theequilibrium state for each measurement of t,?(3) What is the advantage by using the CCD imaging system compared with theobservationbyusingthemicroscopedirectly?
Experimental data recording and processing (1) Static method: From the equation (21-10), we can set the density of the oil 3 o = 981kg/m (20 C) , the gravitational acceleration 2 g = 9.794m/s , the viscous coefficient of the air 5 1.83 10 kg/(m s) − = , the uniform falling distance 3 l 1.6 10 m− = , the correction constant 6 b 6.17 10 m cmHg − = , the atmospheric pressure p = 76.0cmHg , the distance between two electrode plates 3 d 5.00 10 m− = . The time g t should be the averaged value for several measurements (2) To obtain the value of e by using the graphing method. Assume the electric charge for each oil droplet is 1 2, , ., m q q q . We can obtain the approximate integer i n through dividing i q by the currently accepted value of the elementary charge 19 e 1.60 10 C − = . Then ,we can obtain a straight line by setting i n as an independent variable and i q as a dependent variable. The slop of the straight line is the elementary charge, i.e. the value of e . (3) Compare the accepted value and the experimental value of the elementary charge e to obtain the relative error. Questions (1) In the process of tracking measurement for one oil droplet, why some times the image of the oil droplet may become blurred? How to avoid losing the oil droplet during the experimental measurement? (How to know whether the electrode plates are horizontal or not? What is the impact, if the electrode plates are not horizontal?) (2) What is the impact, if the oil droplet is not in the equilibrium state during the measurement? Why should we adjust the voltage to ensure the oil droplet is in the equilibrium state for each measurement of g t ? (3) What is the advantage by using the CCD imaging system compared with the observation by using the microscope directly?
(4) Why should we make the oil droplet remain at rest or in the uniform motion state?How to make sure the oil droplet moves uniformly in the measurable range?
(4) Why should we make the oil droplet remain at rest or in the uniform motion state? How to make sure the oil droplet moves uniformly in the measurable range?