2.8.2Moreonthephotoelectriceffect
Thevacuumphotocell
Thephotoelectriceffectcanbedemonstratedusingapieceofequipmentcalleda
vacuumphotocell.
light(photons)
metal
vacuumtube(glass)
photoelectrons
μA
variablepowersupply
micro-ammeter
Lightisshoneonametalattachedtooneelectrode(calledthephotocathode).
Electronsareemitted,someofwhichtravelthroughthevacuumtotheother
electrode(theanode).Theneteffectisthatthephotocathodeloseselectronsand
theanodegainselectrons.Thissetsupapotentialdifferencebetweenthetwo
electrodes.Ifthetwoelectrodesareconnectedbyanexternalcircuit,electrons
willflowfromtheanodeandbacktothecathode.Thissmallcurrentcanbe
measuredusingasensitivemicro-ammeter.
Avariablepowersupplycanbeusedtoapplyapotentialdifferenceacrossthe
photocell,effectivelyrepellingphotoelectronsfromthe‘anode’ontherighthand
side.Inordertostopthephotoelectronswiththegreatestkineticenergy(Ek(max))
makingittothe‘anode’,apotentialcalledthestoppingpotential,needstobe
applied.Atthispoint,noelectronswillarriveatthe‘anode’andsonocurrent
willflowinthecircuit.
Thestoppingpotential(Vstop)isrelatedtothemaximumkineticenergy(Ek(max))
ofthephotoelectrons.Asanelectrongains1electron-volt(1.6x10-19J)ofkinetic
energywhenitisacceleratedthroughapotentialof1volt,todeceleratethe
fastestphotoelectronweneedtoapplyastoppingpotential:
𝐸((*+,)
𝑉"#$% =
1.6×10345
(1)!Lightwithafrequencyof3x1015Hzisshoneonavacuumphotocell
containingzincmetal(workfunctionϕ=6.93x10-19J).Whatisthemaximumkinetic
energyEk(max)oftheemittedphotoelectrons?WhatstoppingpotentialVstopwould
needtobeappliedtoreducetheexternalcircuitcurrenttozero?(Theplanck
contanth=6.63x10-34Js).
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Ek(max)versusfrequencygraphs
Ifwechangethefrequencyoftheincidentlightandmeasurethemaximum
kineticenergyoftheemittedphotoelectrons(bymeasuringthestopping
potential-discussedabove),wecanconstructagraphofEk(max)versus
frequency.
Ifwerearrangetheformulaℎ𝑓 = 𝜙 + 𝐸((*+,) ,tomake𝐸((*+,) thesubjectwe
get:
𝐸((*+,) = ℎ𝑓 − 𝜙
Thisisintheformy=mx+c
(2)!SketchthegraphofEk(max)versusfrequency:
Ek(max)
frequency
(3)!Whatisthegradientoftheline?Whatisthey-intercept?
Thegoldleafelectroscope
Onemethodofdemonstratingthephotoelectriceffectistouseagoldleaf
electroscope.Whenultravioletlightwithafrequencyabovethethreshold
frequencyisshoneonthezincmetal,thegoldleafisseentorise.
UVlight
zincmetal
goldleaf
(4)!Explaininasmuchdetailasyoucanwhythegoldleafrises.Youmayneedto
researchtheworkingsofthegoldleafelectroscopeforthis.
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