国际物理林匹克竞赛试题Exp.docx
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国际物理林匹克竞赛试题Exp.docx
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国际物理林匹克竞赛试题Exp
PLANCK’SCONSTANTINTHELIGHTOFANINCANDESCENTLAMP
In1900Planckintroducedthehypothesisthatlightisemittedbymatterintheformofquantaofenergyhν.In1905Einsteinextendedthisideaproposingthatonceemitted,theenergyquantumremainsintactasaquantumoflight(thatlaterreceivedthenamephoton).Ordinarylightiscomposedofanenormousnumberofphotonsoneachwavefront.Theyremainmaskedinthewave,justasindividualatomsareinbulkmatter,buth–thePlanck’sconstant–revealstheirpresence.ThepurposeofthisexperimentistomeasurePlanck'sconstant.
Abodynotonlyemits,itcanalsoabsorbradiationarrivingfromoutside.Blackbodyisthenamegiventoabodythatcanabsorballradiationincidentuponit,foranywavelength.Itisafullradiator.Referringtoelectromagneticradiation,blackbodiesabsorbeverything,reflectnothing,andemiteverything.Realbodiesarenotcompletelyblack;theratiobetweentheenergyemittedbyabodyandtheonethatwouldbeemittedbyablackbodyatthesametemperature,iscalledemissivity,,usuallydependingonthewavelength.
PlanckfoundthatthepowerdensityradiatedbyabodyatabsolutetemperatureTintheformofelectromagneticradiationofwavelengthcanbewrittenas
(1)
wherec1andc2areconstants.Inthisquestionweaskyoutodeterminec2experimentally,whichisproportionaltoh.
Foremissionatsmall,faratleftofthemaximainFigureF-1,itispermissibletodropthe-1fromthedenominatorofEq.
(1),thatreducesto
(2)
ThebasicelementsofthisexperimentalquestionaresketchedinFig.F-2.
∙TheemitterbodyisthetungstenfilamentofanincandescentlampAthatemitsawiderangeof’s,andwhoseluminositycanbevaried.
∙
ThetesttubeBcontainsaliquidfilterthatonlytransmitsathinbandofthevisiblespectrumaroundavalueλ0(seeFig.F-3).Moreinformationonthefilterpropertieswillbefoundinpage5.
∙Finally,thetransmittedradiationfallsuponaphotoresistorC(alsoknownasLDR,theacronymofLightDependentResistor).SomepropertiesoftheLDRwillbedescribedinpage6.
TheLDRresistanceRdependsonitsillumination,E,whichisproportionaltothefilamentpowerenergydensity
wherethedimensionlessparameterγisapropertyoftheLDRthatwillbedeterminedintheexperiment.ForthissetupwefinallyobtainarelationbetweentheLDRresistanceRandthefilamenttemperatureT
(3)
thatwewilluseinpage6.Inthisrelationc3isanunknownproportionalityconstant.BymeasuringRasafunctiononTonecanobtainc2,theobjectiveofthisexperimentalquestion.
DESCRIPTIONOFTHEAPPARATUS
ThecomponentsoftheapparatusareshowninFig.F-4,whichalsoincludessomeindicationsforitssetup.Checknowthatallthecomponentsareavailable,butrefrainformakinganymanipulationonthemuntilreadingtheinstructionsinthenextpage.
EQUIPMENT:
1.Platform.IthasadiskonthetopthatholdsasupportfortheLDR,asupportforthetubeandasupportforanelectriclampof12V,0.1A.
2.Protectingcover.
3.10turnsand1kpotentiometer.
4.12Vbattery.
5.Redandblackwireswithplugsatbothendstoconnectplatformtopotentiometer.
6.Redandblackwireswithplugsatoneendandsocketsforthebatteryattheotherend.
7.Multimetertoworkasohmmeter.
8.Multimetertoworkasvoltmeter.
9.Multimetertoworkasammeter.
10.Testtubewithliquidfilter.
11.Standforthetesttube.
12.Greyfilter.
13.Ruler.
Anabridgedsetofinstructionsfortheuseofmultimeters,alongwithinformationontheleastsquaresmethod,isprovidedinaseparatepage.
SETTINGUPTHEEQUIPMENT
Followtheseinstructions:
∙CarefullymaketheelectricconnectionsasindicatedinFig.F-4,butdonotplugthewires6tothepotentiometer.
∙BylookingatFig.F-5,followthestepsindicatedbelow:
1.Turnthepotentiometerknobanticlockwiseuntilreachingtheend.
2.TurnslowlythesupportforthetesttubesothatoneofthelateralholesisinfrontofthelampandtheotherinfrontoftheLDR.
3.BringtheLDRnearertothetesttubesupportuntilmakingalighttouchwithitslateralhole.ItisadvisabletoorienttheLDRsurfaceasindicatedinFig.F-5.
4.Insertthetesttubeintoitssupport.
5.Putthecoverontotheplatformtoprotectfromtheoutsidelight.BesuretokeeptheLDRintotaldarknessforatleast10minutesbeforestartingthemeasurementsofitsresistance.Thisisacautionarystep,astheresistancevalueatdarknessisnotreachedinstantaneously.
Task1
DrawinAnswerSheet1thecompleteelectriccircuitsintheboxesandbetweentheboxes,whenthecircuitisfullyconnected.Please,takeintoaccounttheindicationscontainedinFig.F-4tomakethedrawings.
Measurementofthefilamenttemperature
TheelectricresistanceRBofaconductingfilamentcanbegivenas
(4)
whereistheresistivityoftheconductor,listhelengthandSthecrosssectionofthefilament.
Thisresistancedependsonthetemperatureduetodifferentcausessuchas:
∙Metalresistivityincreaseswithtemperature.Fortungstenandfortemperaturesintherange300Kto3655K,itcanbegivenbytheempiricalexpression,validinSIunits,
(5)
∙Thermaldilatationmodifiesthefilament’slengthandsection.However,itseffectsonthefilamentresistancewillbenegligiblesmallinthisexperiment.
From(4)and(5)andneglectingdilatationsonegets
(6)
∙Therefore,togetTitisnecessarytodeterminea.ThiscanbeachievedbymeasuringthefilamentresistanceRB,0atambienttemperatureT0.
Task2
a)MeasurewiththemultimetertheambienttemperatureT0.
b)ItisnotagoodideatousetheohmmetertomeasurethefilamentresistanceRB,0atT0becauseitintroducesasmallunknowncurrentthatincreasesthefilamenttemperature.Instead,tofindRB,0connectthebatterytothepotentiometerandmakeasufficientnumberofcurrentreadingsforvoltagesfromthelowestvaluesattainableupto1V.(Itwillproveusefultomakeatleast15readingsbelow100mV.)Attheend,leavethepotentiometerintheinitialpositionanddisconnectoneofthecablesfrombatterytopotentiometer.
FindRBforeachpairofvaluesofVandI,translatethesevaluesintotheTableforTask2,b)intheAnswerSheets.Indicatetherethelowestvoltagethatyoucanexperimentallyattain.DrawagraphandrepresentRBintheverticalaxisagainstI.
c)Afterinspectingthegraphicsobtainedatb),selectanappropriaterangeofvaluestomakealinearfittothedatasuitableforextrapolatingtotheordinateattheorigin,RB,0.WritetheselectedvaluesintheTableforTask2,c)intheAnswerSheets.Finally,obtainRB,0andΔRB,0.
d)ComputethenumericalvaluesofaandaforRB,0inΩandT0inKusing(6).
OPTICALPROPERTIESOFTHEFILTER
Theliquidfilterinthetesttubeisanaqueoussolutionofcoppersulphate(II)andOrange(II)anilinedye.Thepurposeofthesaltistoabsorbtheinfraredradiationemittedbythefilament.
Thefiltertransmittance(transmittedintensity/incidentintensity)isshowninFigureF-6versusthewavelength.
F-6
Task3
Determine0andfromFig.F-6.
Note:
2isthetotalwidthathalfheightand0thewavelengthatthemaximum.
PROPERTIESOFTHELDR
ThematerialwhichcomposestheLDRisnonconductingindarknessconditions.Byilluminatingitsomechargecarriersareactivatedallowingsomeflowofelectriccurrentthroughit.IntermsoftheresistanceoftheLDRonecanwritethefollowingrelation
(7)
wherebisaconstantthatdependsonthecompositionandgeometryoftheLDRandγisadimensionlessparameterthatmeasuresthevariationoftheresistancewiththeilluminationEproducedbytheincidentradiation.Theoretically,anidealLDRwouldhaveγ=1,howevermanyfactorsintervene,sothatintherealcaseγ<1.
Itisnecessarytodetermineγ.ThisisachievedbymeasuringapairRandE(Fig.F-7)andthenintroducingbetweenthelampandthetubethegreyfilterF(Fig.F-8)whosetransmittanceisknowntobe51.2%,andweconsiderfreeoferror.ThisproducesanilluminationE’=0.51E.AftermeasuringtheresistanceR’correspondingtothisillumination,wehave
Fromthis
(8)
Donotcarryoutthisprocedureuntilarrivingatpartb)oftask4below.
Task4
a)CheckthattheLDRremainedincompletedarknessforatleast10minutesbeforestartingthispart.Connectthebatterytothepotentiometerand,rotatingtheknobveryslowly,increasethelampvoltage.ReadthepairsofvaluesofVandIforVintherangebetween9.50Vand11.50V,andobtainthecorrespondingLDRresistancesR.(Itwillbeusefultomakeatleast12readings).TranslateallthesevaluestoatableintheAnswerSheet.TodealwiththedelayintheLDRresponse,werecommendthefollowingprocedure:
OncearrivedatV>9.5V,wait10minapproximatelybeforemakingthefirstreading.Thenwait5minforthesecondone,andsoon.Beforedoinganyfurthercalculationgotonextstep.
b)OnceobtainedthelowestvalueoftheresistanceR,opentheprotectingcover,putthegreyfilterasindicatedinF-9,coveragain-assoonaspossible-theplatformandrecordthenewLDRresistanceR’.Usingthesedatain(8)computeandΔ.
c)ModifyEq.(3)todisplayalineardependenceoflnRon
.Writedownthatequationthereandlabelitas(9).
d)Usingnowthedatafroma),workoutatablethatwillservetoplotEq.(9).
e)Makethegraphicsplotand,knowingthatc2=hc/k,computehandΔhbyanymethod(youareallowedtousestatisticalfuncti
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