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Millikan'sOilDropExperimentAtthestartofthe20thcentury,scientistsdiscoveredtheexistenceoftheelectron.Theyknewitpossessedamassandanelectricalcharge,andtheyhaddeterminedthecharge-to-massratio,e/m.In1909,RobertMillikanandHarveyFletcherdevelopedanexperimenttodeterminethefundamentalchargeoftheelectron.Thiswasachievedbymeasuringthechargeofoildropsinaknownelectricfield.Ifallelectronshavethesamecharge,thenthemeasuredchargeontheoildropsmustbemultiplesofthesamefundamentalconstant.Safety Voltage:Allthesignalvoltagesaresmallandharmless.Themains
voltagesarefullycontainedintheapparatusduringnormaluse.
Setupinstructionsforstaff.
InstructionalvideosonhowtosetupthisexperimentareavailableontheLancasterPhysics/Outreach/LabinaBoxwebpage.Unboxing:Theapparatuswillbeprovidedinalargewoodenbox,whichmustbeopenedfromthetoplidfirst.Removetheitemswithin,apartfromtheplatform,thenproceedtolifttherestofthewoodensidesofthebox.Figure1:PhotographofthecablesetupoftheMillikan’sexperimentwithinstructionsonhowtoconnecteachcable.
Millikan'sOilDropExperiment
Figure2:PhotographoftheMillikan’sexperimentsetupwithinstructionsonhowtoconnecttheplatestotheplatform.
Background InMillikan’sexperiment,oildropsaresprayedfromanozzleintoavolumebetweentwoclosely-spacedhorizontalmetalplatesthatareinsulatedfromeachother.Thedropscanbekeptfromfallingbyapplyingapotentialdifferencebetweentheplates.
1. Whentheoildropsaresprayedintothevolumetheyarealreadyelectricallycharged.Whatprocessgivesthemtheircharge?
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...........................................................................................................2.Whatforcesactontheoildropswhilsttheyareinthevolume?LabeltheforcesinFigure2below.
Figure2:Representationofastationaryoildropwithinthevolume,onceavoltageisappliedacrosstheplates.
Millikan'sOilDropExperiment
Thedownwardforceactingontheoildropisduetothegravitationalpullonthedrop:
𝐹! = 𝑚𝑔.Theupwardforceistheelectrostaticforce:
𝐹! = 𝐸𝑞.Theelectricfieldcanbeexpressedasafunctionofthevoltage𝑉acrosstheplatesandthespacing𝑑betweenthem:
𝐸 =𝑉𝑑 .
Writedownthevalueof𝑑 forthisapparatus:............................................................................................................................Inthecorrectconditions,theelectrostaticforceandtheforceofgravitycanbebalanced,suchthattheoildropisbroughttorest.Inthiscase,wecanexpressthechargeontheoildropasfollows:
𝐹! = 𝐹! ,
𝑞 =𝑚𝑔𝑉𝑑 .
Asitisverychallengingtomeasurethemassofindividualoildrops,itishelpfultore-expressthemassoftheoildropintermsofthedensityoftheoilasfollows:
𝜌!"# = 𝑚/𝑉!"!!"! Assumingthattheoildropisapproximatelyspherical,itsvolumeisgivenbythefollowingformula:
𝑉!"!!"! =43𝜋𝑟
! ,whereristheradiusoftheoildrop.Thus,thegravitationalpullontheoildropcanbeexpressedas:
𝐹! =43𝑔𝜋𝑟
!𝜌!"#
Millikan'sOilDropExperiment
Thereisathirdforceactingontheoildrops.Thebuoyancyduetothesurroundingairbetweentheplatesintroducesanupwardthrust:
𝐹! =43𝑔𝜋𝑟
!𝜌!"# .Thereforetheequationforthechargeoftheoildropcanbere-expressedas
𝑞 =𝑑𝑉
43 𝜋𝑟!(𝜌!"# − 𝜌!"#) .
Oftheparametersinthisequation,theradius𝑟isdifficulttomeasure.Thefollowingsectionfocusesonhowitcanbedetermined.
Background(continued)
Theradiusofanoildropisverysmallanddifficulttomeasure.However,Millikanfoundthat𝑟couldbemeasuredindirectlybyswitchingoffthevoltageandlettingthedropfall.
Asthedropfallsdownthroughtheviscousair,itexperiencesanupwarddragforcegivenbyStokes’slawasfollows:
𝐹!"#$ = 6𝜋𝜂𝑟𝑣
Inthisequation,𝜂istheviscosityofairand𝑣 isthespeedoftheoildrop.Whentheupwardbuoyantandviscousforcesbalancethedownwardgravitationalforce,thenthedropnolongeraccelerates,andmovesatitsterminalvelocity𝑣!.Thedropsreachterminalvelocityveryquickly,andthiscanbemeasuredbytiminghowlongittakesadroplettofallameasureddistance.
Byequatingtheforcesactingonanoildroptravellingatitsterminalvelocity,wecanderiveanexpressionfortheradiusoftheoildrop.Labeltheforcesonthediagrambelow:
Millikan'sOilDropExperiment
Equatingtheseforces:
𝐹! = 𝐹! + 𝐹!"#$
Theforcesactingonthedropare:
𝐹!"#$ = 6𝜋𝜂𝑟𝑣,
𝐹! =!!𝑔𝜋𝑟!𝜌!"# ,
𝐹! =!!𝑔𝜋𝑟!𝜌!"# .
Therefore,
6𝜋𝜂𝑟𝑣! =!!𝜋𝑟!(𝜌!"# − 𝜌!"#),
𝑟 = 3𝜂𝑣!
2𝑔(𝜌!"# − 𝜌!"#) .
Substitutingthisbackintotheexpressionfor𝑞weget:
𝑞 =9𝜋𝑑𝑉
2𝜂!𝑣!!
𝑔(𝜌!"# − 𝜌!"#).
Therefore,theelectricchargeontheoildropcanbefoundintermsofitsterminalvelocityandtheappliedvoltageacrosstheplates.
Task1
Useadesklampangledtowardstheoildropchamber,ifpossible,togiveanevenandbrightilluminationonthemicroscope.
Canyoureadthegraticulescaleonthemicroscope?Ifnot,askamemberofstaffforassistance.Notethateachlargescaledivisioncorrespondsto1[mm].
Makesurethattheoilexitpipeisinlinewiththesmallholesonthechamberandgiveoneortwosharpsquirtsofthebulbtosprayoilintothegapbetweenthemetalplates.
1. Usethecontrolonthemicroscopetofocusontheoildropsandwaitforthesidewaysmotiontocease.Youmayneedtoplaceanobjectnexttothesmallholestominimiseaircurrents.Adjusttheintensityofthelightonthemicroscopeifnecessary,toincreasethecontrast.
Millikan'sOilDropExperiment
2. Switchonthevoltagesupplytothemetalplates,andwatchthe
chargeddropsmoveupanddownasyouvarythepotentialdifference.Chooseabright,easy-to-seeoildropwhichisneartothegraticule,andusethevoltagecontroltomoveitdownnearthetopofthescreen.Holdittherebyfine-tuningthevoltage.
3. Recordthisvalueof𝑉.
4. Next,turnoffthevoltageandstartthestopclock.Watchthe
dropasitfalls.
5. Youwillneedtokeepfocusingasitdriftsdownwards.Itisbesttoletitfallasfaraspossibletominimisetheuncertaintiesintiminganddistance.
6. Onceithasfallenthrough6largegraduationsonthescreen,
stoptheclockandrecordthetimeanddistanceithasfallen.
7. Theterminalvelocity𝑣!isgivenbytheequation𝑆 = 𝑣! 𝑡,whereSisthedistancetravelledandtisthetimetaken.
Notethatthedistanceyoumeasurehastobedividedby2totakeaccountofthemagnificationofthemicroscope.
Question1
Carryoutmeasurementsonanumberofoildrops.Foreachoildrop,usethemeasurementstocalculateavalueofitselectriccharge,q,usingthefollowingequationfromtheabovederivation:
𝑞 =9𝜋𝑑𝑉
2𝜂!𝑣!!
𝑔(𝜌!"# − 𝜌!"#).
Atableisprovidedbelowforyoutorecordyourmeasurements.Don’tforgettoincludetheuncertainitiesinyourmeasurements.
Someusefulconstantsforthisexperimentarealsogivenbelow:
Airviscosity 𝜂 = 1.83 ± 0.04× 10!! 𝑁𝑠 𝑚!!
Oildensity 𝜌!"# = 874 ± 2 𝑘𝑔 𝑚!!,at20°C
Airdensity 𝜌!"# = 1.30 ± 0.05 𝑘𝑔 𝑚!!,at20°C
PlateSpacing 𝑑 = 6.00 ± 0.05× 10!! 𝑚
Electroniccharge:𝑒 = 1.60 × 10!!"C
Millikan'sOilDropExperiment
VolatgeV
[V]Distances
[m]
Timet
[s]Term
inalVelocity𝑣
! [m/s]
Chargeq[C]
№ofelectrons(q/e)
Millikan'sOilDropExperiment
1. Wereyourresultsonthenumberofelectronsalwaysintegers?
Ifnot,canyouexplainwhy?
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2. Wastheexperimentsuccessful?Whatwasthelargestsourceofuncertainty?Howcouldyouimproveyourresults?
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