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36thInternationalPhysicsOlympiad.Salamanca(España)2005PLANCK’SCONSTANTINTHELIGHTOFANINCANDESCENTLAMPIn1900Planckintroducedthehypothesisthatlightisemittedbymatterintheformofquantaofenergyhν.In1905Einsteinextendedthisideaproposingthatonceemitted,theenergyquantumremainsintactasaquantumoflight(thatlaterreceivedthenamephoton).Ordinarylightiscomposedofanenormousnumberofphotonsoneachwavefront.Theyremainmaskedinthewave,justasindividualatomsareinbulkmatter,buth–thePlanck’sconstant–revealstheirpresence.ThepurposeofthisexperimentistomeasurePlanck'sconstant.Abodynotonlyemits,itcanalsoabsorbradiationarrivingfromoutside.Blackbodyisthenamegiventoabodythatcanabsorballradiationincidentuponit,foranywavelength.Itisafullradiator.Referringtoelectromagneticradiation,blackbodiesabsorbeverything,reflectnothing,andemiteverything.Realbodiesarenotcompletelyblack;theratiobetweentheenergyemittedbyabodyandtheonethatwouldbeemittedbyablackbodyatthesametemperature,iscalledemissivity,ε,usuallydependingonthewavelength.PlanckfoundthatthepowerdensityradiatedbyabodyatabsolutetemperatureTintheformofelectromagneticradiationofwavelengthλcanbewrittenas()1/512−=Tcecuλλλε(1)wherec1andc2areconstants.Inthisquestionweaskyoutodeterminec2experimentally,whichisproportionaltoh.Foremissionatsmallλ,faratleftofthemaximainFigureF-1,itispermissibletodropthe-1fromthedenominatorofEq.(1),thatreducesto/512Tcecuλλλε=(2)ThebasicelementsofthisexperimentalquestionaresketchedinFig.F-2.•TheemitterbodyisthetungstenfilamentofanincandescentlampAthatemitsawiderangeofλ’s,andwhoseluminositycanbevaried.•ThetesttubeBcontainsaliquidfilterthatonlytransmitsathinbandofthevisiblespectrumaroundavalueλ0(seeFig.F-3).Moreinformationonthefilterpropertieswillbefoundinpage5.•Finally,thetransmittedradiationfallsuponaphotoresistorC(alsoknownasLDR,theacronymofLightDependentResistor).SomepropertiesoftheLDRwillbedescribedinpage6.TheLDRresistanceRdependsonitsillumination,E,whichisproportionaltothefilamentpowerenergydensity00EuRuREλγλγ−−∝⎫⎪⇒∝⎬∝⎪⎭wherethedimensionlessparameterγisapropertyoftheLDRthatwillbedeterminedintheexperiment.ForthissetupwefinallyobtainarelationbetweentheLDRresistanceRandthefilamenttemperatureTTcecR02/3λγ=(3)thatwewilluseinpage6.Inthisrelationc3isanunknownproportionalityconstant.BymeasuringRasafunctiononTonecanobtainc2,theobjectiveofthisexperimentalquestion.F-2ABCF-3uλλλ0F-1uλλT3T2T136thInternationalPhysicsOlympiad.Salamanca(España)2005DESCRIPTIONOFTHEAPPARATUSThecomponentsoftheapparatusareshowninFig.F-4,whichalsoincludessomeindicationsforitssetup.Checknowthatallthecomponentsareavailable,butrefrainformakinganymanipulationonthemuntilreadingtheinstructionsinthenextpage.EQUIPMENT:1.Platform.IthasadiskonthetopthatholdsasupportfortheLDR,asupportforthetubeandasupportforanelectriclampof12V,0.1A.2.Protectingcover.3.10turnsand1kΩpotentiometer.4.12Vbattery.5.Redandblackwireswithplugsatbothendstoconnectplatformtopotentiometer.6.Redandblackwireswithplugsatoneendandsocketsforthebatteryattheotherend.7.Multimetertoworkasohmmeter.8.Multimetertoworkasvoltmeter.9.Multimetertoworkasammeter.10.Testtubewithliquidfilter.11.Standforthetesttube.12.Greyfilter.13.Ruler.Anabridgedsetofinstructionsfortheuseofmultimeters,alongwithinformationontheleastsquaresmethod,isprovidedinaseparatepage.F-412367101145891312AVΩ36thInternationalPhysicsOlympiad.Salamanca(España)2005SETTINGUPTHEEQUIPMENTFollowtheseinstructions:•CarefullymaketheelectricconnectionsasindicatedinFig.F-4,butdonotplugthewires6tothepotentiometer.•BylookingatFig.F-5,followthestepsindicatedbelow:1.Turnthepotentiometerknobanticlockwiseuntilreachingtheend.2.TurnslowlythesupportforthetesttubesothatoneofthelateralholesisinfrontofthelampandtheotherinfrontoftheLDR.3.BringtheLDRnearertothetesttubesupportuntilmakingalighttouchwithitslateralhole.ItisadvisabletoorienttheLDRsurfaceasindicatedinFig.F-5.4.Insertthetesttubeintoitssupport.5.Putthecoverontotheplatformtoprotectfromtheoutsidelight.BesuretokeeptheLDRintotaldarknessforatleast10minutesbeforestartingthemeasurementsofitsresistance.Thisisacautionarystep,astheresistancevalueatdarknessisnotreachedinstantaneously.F-52351436thInternationalPhysicsOlympiad.Salamanca(España)2005Task1DrawinAnswerSheet1thecompleteelectriccircuitsintheboxesandbetweentheboxes,whenthecircuitisfullyconnected.Please,takeintoaccounttheindicationscontainedinFig.F-4tomakethedrawings.MeasurementofthefilamenttemperatureTheelectricresistanceRBofaconductingfilamentcanbegivenasSlRBρ=(4)whereρistheresistivityoftheconductor,listhelengthandSthecrosssectionofthefilament.Thisresistancedependsonthetemperatureduetodifferentcausessuchas:•Metalresistivityincreaseswithtemperature.Fortungstenandfortemperaturesintherange300Kto3655K,itcanbegivenbytheempiricalexpression,validinSIunits,83.081005.3ρ⋅=T(5)•Thermaldilatationmodifiesthefilament’slengthandsection.However,itseffectsonthefilamentresistancewillbenegligiblesmallinthisexperiment.From(4)and(5)andneglectingdilatationsonegets83.0BRaT=(6)•Therefore,togetTitisnecessarytodeterminea.Thiscanbeachievedbymeasuri