The electron - P3, week 5

7/29/2019 The electron - P3, week 5

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Discoveryoftheelectron

Excuseme..Howcanyoudiscoverapar6clesosmallthatnobodyhaseverseenone?

ThomsonbecameProfessorofExperimentalPhysics(CavendishLabs,Cambridge)in1884

Oneofthephenomenahewasstudyingwastheconduc&onofelectricitythroughgases

Hewasveryinterestedininvesgangalong-standingpuzzlewhichwasknownasCathodeRays

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CathodeRays

Gasesatatmosphericpressurearebadconductorsofelectricity

Topassanelectriccurrentthroughagasaspecialapparatusisneeded:agas-dischargetube

Agas-dischargetubeisusuallyaglasstubewithelectrodesatitsendssothatavoltagecanbeapplied

Whenvoltageisappliedandthepressureofthegasisreduced(byavacuumpump)eventuallyacurrentwillflow

andthegaswillbegintoglow

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CathodeRays

Gas-dischargetubesfirstdevelopedbetween1857-1870 Nooneknewwhatcausedtheglowsoscienststrieddifferentexperimentstoseeiftheycouldfindout

WilliamCrookesnocedtheglowwasmostintenseoppositethenegaveelectrode(cathode):cathoderays

Chargedparclesorelectromagnecwaves?

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Thomsondiscoversthe

electron Thomsonperformsaseriesofexperimentsin1897anddiscoversthatcathoderaysgetdeflectedwhenpassed

throughanelectricfield

Theraysmovetowardstheposivelychargedplatesotheymusthavenega&vecharge

"Whatarethese

parcles?Arethey

atoms,ormolecules,or

maYerinasllfinerstate

ofsubdivision?"

J.J.Thomson

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Thomsondiscoversthe

electron Thomsonperformsaseriesofexperimentsin1897anddiscoversthatcathoderaysgetdeflectedwhenpassed

throughanelectricfield

Theraysmovetowardstheposivelychargedplatesotheymusthavenega&vecharge

Thenheappliedamagne&cfieldandtheraysweredeflectedintheoppositedirecon

Applyingbothfieldstogetherunltheirrespecveforcescancelledoutallowedhimtocalculatethespeedoftheraysandthecharge-to-massra&o(specificcharge)oftheparcle

Thomsonsexperiment

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Thomson talks about Electrical Engineering andshares his thoughts about the discovery of theelectron:

hYp://www.nobelprize.org/mediaplayer/index.php?id=322 hYp://www-outreach.phy.cam.ac.uk/camphy/electron/electron1_1.htm

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Theelectrongun

Thermionicemission:heangupametalcausesitsfreeelectronstogainK.E.andescapefromitssurface

Electrongun:Adevicethatacceleratesfreeelectronsinavacuum

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Theelectrongun

Thermionicemission:heangupametalcausesitsfreeelectronstogainK.E.andescapefromitssurface

Electrongun:Adevicethatacceleratesfreeelectronsinavacuum

WorkdoneoneachelectronisW=eV e=chargeofelectron=1.610-19coulombs V=p.d.betweencathodeandanode

K.E.ofelectronsatanode=mev2

W =K.E. eV=1

2m

ev

2 v =

2eV

me

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Electronbeaminuniform

electric:ield

Electronsgetdeflectedtowardsthe+veplatewhenpassingthroughanelectricfield

Whendeflected,theyfollowaparabolicpath Forceexperiencedbyeachelectron

+

-

d

F= eE=eV

d=ma a =

eV

med

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y =1

2

eVx2

medv

2


electric:ield

Horizontaldistancecoveredint:x=vt Vercaldistancecoveredint:y=at2 Substungweget:

+

-

dv

x

y

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electric:ield

Vercalspeedaermet: Direconofbeamatmet:

+

-

dv

x

y

vy = at=eV

medt=

eVx

medv

v

vy vxy

v

vy vxy

tan()=vy

v

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Example

Anelectrongunoperangat3000Visusedtoaccelerate

electronsbetweentwooppositelychargedparallelplates.The

distancebetweentheplatesis50mmandthelengthofthe

platesis100mm.Calculatethedefleconoftheelectronsatthe

pointwheretheyexitthefieldwhenthevoltageacrosstheplateis1000V.Assumethespecificchargeoftheelectrone/

me=1.76x1011Coulombperkilogram.

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Example

Abeamofelectronsmovingwithavelocityof107m/senters

midwaybetweentwohorizontalplatesPandQinadirecon

paralleltotheplatesasshown.PandQare5cmlongandhavea

p.d.Vappliedbetweenthem.CalculateVifthebeamis

deflectedsothatitjustgrazestheedgeofthelowerplateQ.(Assumee/me=1.8x10

11C/kg)

2cm

v

1cm

P

Q

V

5cm

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magnetic:ield Thepathelectronstakegetsalteredbythepresenceofamagnecfield

Amagnecfielddeflectstheelectronsbutdoesnotchangetheirspeedortheirkinecenergy

Magne&cforcegivenbyF=Bev e=chargeofelectron B=magnecfieldstrength v=speedoftheelectron

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magnetic:ield Themagnecforceactsasthecentripetalforceandelectronsmoveinacircleofradiusr

F= Bve =m

ev2

r r =

mev

Be

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magnetic:ield IftheanglebetweenthevelocityofthebeamvandthemagnecfieldBisnot90thenthebeampathisaspiral

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Speci:icchargeoftheelectron

Thespecificchargeoftheelectronisthechargeperunitmass(e/me)

Abeamofelectronsenteringauniformmagnecfieldat90tracesacircleofradiusr

TheelectronbeamdeliverselectronswithK.E.

WhereVistheappliedvoltage(orp.d.betweenanodeandcathode)

1

2

me

v2= eV

r =mev

Be v =

Ber

me

e

me

=

2V

B2

r2

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Example

Posivelychargedparcleswithspecificcharge108C/kgare

rotanginacircularorbitofradiusrinsideauniformmagnec

fieldofstrength0.5T.Showthattheperiodoftheirmoonis

independentofrandcalculatethisperiod.

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Thevelocityselector

dvV

+

-

E

B

Bev =eV

d v =

V

Bd

Fornodefleconmagnecforce=electricforce Speedvfornodeflecon:

Thisarrangementcanbeusedasavelocityselectorifthebeamconsistsofparcleswithdifferentspeeds

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Example

Abeamofelectronsisfiredintoauniformelectricfieldasinthe

previousfigure.Thelengthoftheplatesgenerangthefieldis

100mmandtheirdistanceapartis50mm.Aconstantvoltageof

720Visappliedacrosstheplatesandthebeamisdeflected

vercallybyadistanceof25mm.Thebeamisthenstraightenedoutbyapplyingauniformmagnecfieldofstrength0.65mT

perpendiculartothebeam.Calculate

a) Thespeedofthebeamwhenenteringthefieldsb) Thespecificchargeoftheelectron

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Measurementofchargeof

electron

+

-

Where

Q=thechargeofthedroplet

V=voltageapplied

d=distancebetweentheplates

m=massofthedroplet

Electricforce

Weight

QV

d=mg

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Measuringthemassofatiny

oildroplet Viscosityisameasureofthethicknessofasubstance Viscousforcesactonanybodymovingthroughaviscoussubstance

Becauseoildropletsaresony,whentheyfallthroughair,theyexperienceaviscousforceF

StokesLaw:F=6Rv =viscosityoffluid R=radiusofsphere v=speedofsphere

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Measuringthemassofatiny

oildroplet Terminalspeed=thespeedofabodywhennonetforceisacngonit

Theterminalspeedcanbedeterminedbymingthefallofthedropletoveraknowndistance

Fortheoildropletmovingatterminalspeed:6Rv=mg Dropletisasphereofuniformdensity Volumeofsphereis mass=volumexdensity

4

3R

3

6Rv = 4

3R

3gR =

9v

2g23


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Example

Calculatetheradiusofadropofoil,density900kg/m3,which

fallswithaterminalvelocityof2.9x10-4m/sthroughairof

viscocity1.8x10-5Ns/m2.Ignorethedensityoftheair.Ifthe

chargeonthedropis-3e,whatp.d.mustbeappliedbetween

twoplates5mmapart(e=1.6x10-19

C)tokeepitstaonary?(assumeg=9.8m/s)

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Motionofchargeddropletsin

anelectric:ield Whathappenswhentheelectricforceduetothevoltageapplieddoesnotbalancethegravitaonalforce?

A)Voltageholdingvoltage qV/d=mg+6Rv

Direcon

ofmoon

Fviscous

Weight

Direcon

ofmoonFviscous

Weight25


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Photoelectricity

Aheatedcathode(metalconductor)canbeusedtoproduceasupplyofelectronsbythermionicemission

EnergycanbesuppliedtotheconductoralsointheformofUVlight

H.Hertz1857-1894

Observaons: Emissiononlyoccursifthefrequencyof

incidentlightexceedsaminimum'threshold

frequency

nr.electronsemiYed/sec.proporonaltolightintensity

ElectronsemiYedhavearangeofK.E.uptoamaximumvaluethatdependsonthemetal

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Einsteinandphotoelectricity

In1905Einsteinpublishedapaperexplainingtheeffect Assumedthatlighttravelsinshortpacketscalledwavepackets

Photon=wavepacketoflight=quantumoflight

TheamountofenergyeachphotonhasisgivenbyE=hf=hc/where

f=frequencyofphoton h=Planckconstant=6.63x10-34Js c=speedoflight=3x108m/s =wavelengthofphoton

Reminder:EnergymeasuredinJoules (somemesalsogiveninelectronvolteV) 1eV=1.6x10-19Joules

A.Einsteinin1905

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Einsteinandphotoelectricity

Workfunc&onW theworkneededtoremoveanelectronfromthesurfaceofthemetal

EinsteinsequaonforthephotoelectriceffectMaximumK.E.=hf-W

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Thresholdfrequency

ElectronscanonlyescapeifthemaximumK.E.>0 Thismeansthatthephotonfrequencyf>f0(thresholdfrequency)

Thresholdfrequencyf0=W/h

V

P Q

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Thresholdfrequency

Ifweapplyavoltagebetweenthetwoplateswecanhelporhindertheemissionofelectrons

MaximumK.E.=hfWeV StoppingpotenalVs=(hfW)/e

V

P Q

+ -

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Example

Sodiumhasaworkfunconof2eV.Calculatethemaximum

energyandspeedoftheemiYedelectronswhensodiumis

illuminatedbyradiaonofwavelength150nm.Whatistheleast

frequencyofradiaon(thresholdfrequency)forwhichelectrons

areemiYed?(Assumeh=6.6x10-34

Js,e=-1.6x10-19

C,me=9.1x10-31kg,c=3x108m/s)

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ToDo

Readchapter27[p.552-571Properesoftheelectron] HomeworkAssignmentwk5:quesons27.1,27.2,27.3,27.4,27.9,27.13

Handitinnolaterthan4:00pmnextWednesday-LATEWORKWILLNOTBEACCEPTED

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The electron - P3, week 5