物理实验报告(英文)

Diffractionandthephotoelectriceffect

Introduction

ThePlanckconstantisaconstantofphysicswhichreflectsthemagnitudeof

energyquantuminthefieldofquantummechanics.ThesignofPlanck

constantisanditisnamedbyMaxPlanckin1990.Theproportionality

h

constantbetweenaphoton’senergyandthefrequencyofitselectromagnetic

wavewasthefirstdefinitionofthePlanckconstant.Thistheorywas

generalizedbyLouisdeBrogliein1923andconfirmedbyexperiments.There

isadifferencebetween

and(-bar).

iscalledtheDiracconstantor

h

h

reducedPlanckconstantwhichisequaltothePlanckconstantdividedby2π.

(1)Thephotoelectriceffectistheeffectthatwhenamatterwhichcanbemetals,

non-metallicsolids,liquidsorgasesisbombardedbyphotons(light),electrons

inthesubstancewillabsorbtheenergyofphotonsandtheywillbeemitted,

oneelectroncouldonlyabsorbtheenergyofonephoton.Itisusuallyawayto

findthePlanckconstant.Asthelimitingofthefacilities,themainresultswhich

includethewavelengthoflightsandtheplanckconstantarenoteasytobe

gotteninaccuratevalues.ThislabwasdesignedtofindthePlanckconstant

basedonthelightdiffractionandthephotoelectriceffect,therearefouraimsof

thisexperimentwhicharebuildingaspectrometer,findingwavelengthsfor

lasersandLEDSandfindingthePlanckconstant.

1

EnglishName:Vince

Class:Eng1-1B

ChineseName:WenZhengYang

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

Theorem

Whenabeamofmonochromaticlightpassingthroughadiffractiongrating,the

wavelengthandthedistancefromthegratingtothecenterfringefollowthetwo

relationships:

&y.Fortherelationships,

tan()

1

isthe

n

n

dsin

L

orderoffringesanditisequalto

,

isthewavelengthofthis

o,1,2,3

light,,,arethedistancefromthegratingtothecenterfringe,the

d

L

y

fringestothecenterfringeandthedistancebetweentwoslitsinthegrating

respectively,istheanglebetweenthecenterlineandthelineconnectedby

thefringecenterandtheslit.Theformulaofthephotoelectriceffectis

istheenergyoftheelectroescapingfromtheobject,isthe

isthePlanck

,

Ehfw

E

f

frequencyofthelightwhichshotsatthesurfaceoftheobject,

h

constantandistheworkfunction.Foracertainobject,theworkfunctionisa

w

constant.ForLED,Thisformulaalsocanberewrittenas

where

eVhfw

isthequantityofelectricchargeanditis

19and

isthevoltageof

e

1.610

c

V

C

theLED.ForEMwave,

frequency.

(Cisthespeedoflightandisits

CT

f

f

y

C

Formula:

,

,

,

.

n

dsin

,

tan()

CT

1

E

hf

w

eV

hf

w

L

f

2

EnglishName:Vince

ChineseName:WenZhengYang

Class:Eng1-1B

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

Aims

AimI

:buildingaspectrometer

Apparatus:

carton,circulardiffractiongrating,apieceofpaper,ruler,

whitelightLED,scissors.

Diagram1isthesimplemodelthespectrometer

Diagram1:simplemodelofthespectrometer

Methods

Theprocessofmakingasimplespectrometerwasmainly5stepsand

operatedbytwopeople.Firstofall,aholewithpropersizesinthefrontofthe

cartonwasremovedbythescissors.Secondly,acirculardiffractiongrating

wassettotheholetocoverit,whichwasusedtoproducethediffraction

pattern.Thirdly,apieceofpaperwasfixedattheinternalbacksurfaceofthe

carton,whichwasservedasascreentobringoutthediffractionpattern.Then,

ataproperpositiononthetopsurface,anellipticholewhichwaslongand

3

EnglishName:Vince

Class:Eng1-1B

ChineseName:WenZhengYang

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

narrow(thisistohelptoviewbecausethelightfromTHELEDisnotbevery

strong)wasremovedtoviewthediffractionpatternwhichwasinsidethecarton.

Next,arulerwasputatthebottomneartothebacksurfaceandthepurposeof

thisstepwasmeasuringthedistancebetweendifferentfringes.

Theexperimentstartedafterthespectrometerwasfinished.Atthefirst,the

lightofthetorchwasshottothecenterofthediffractiongratingverticallyand

thediffractionpatternappearedonthescreen.Then,observingthediffraction

patternthroughtheviewingholeintopandrecordthepositionofeachfringe.

Next,thedistancesfromthecentertoeachfringewerereadfromtherulerand

theyarerecordedonthedrafterpaper.Later,thelength(L)betweenthefront

surfaceandthebacksurfacewasmeasuredandrecorded.Atlast,theresult

wasrecognizedintothetablewhichwasonthetutorial.

Result

i.Problemswithbuildingandusingthespectrometer

Duringtheprocessofbuildingandusingthespectrometer,therearesome

problemsexistingandwhichwillleadtoerrorsoftheexperimentresult.When

thespectrometerwasmade,thecartonwasnotperfectcube,sothelength(L)

betweenthefrontsurfaceandthebacksurfaceisnotaccurate.Withthe

changeoffringes,Lisnotacertainvalueanditwillchange,thisisbecause

sidesofthenonstandardcubearenotparalleltoeachotherrespectively.The

holewithdiffractionwashardtobeputatthecenterofthefrontsurfaceasthe

4

EnglishName:Vince

Class:Eng1-1B

ChineseName:WenZhengYang

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

positionwasestimatedbyeyes.Thepositionsofeachfringewererecorded

whilethebrightestfringeatthecenterofthebacksurface,sothebrightest

fringeisnotverticaltothescreenandwhichwillleadtothedistancesbetween

thefringesandthecenterfringewerenotcorrect.Whileoperatingthis

experiment,theviewingholeinthetopisnarrow,sothepositionofeachfringe

cannotbelabeledcorrectly.Duetotheweaknessofthelightandseven

differentmonochromaticlightsgatheringtogether,itisnoteasytotellwhereis

thefringecenterofeachmonochromaticlightandwhichalsowillcausethe

errorsonmarkingthepositions.

ii.Resultstable

Table1showstheexperimentdataofaim1andthewavelengthsofdifferent

monochromaticlightscalculatedfromtheit.

Table1:resultsofaim1.

Colors

red

Order(n)

y(cm)

9

L(m)

0.215

0.215

0.215

0.215

Wavelength(nm)

643.6

1

1

1

1

yellow

green

blue

7.5

6.5

5

548.9

482.3

377.5

Asshownintable1,thewavelengthsoftheredlight,yellowlight,greenlight

andthebluelightare643.6nm,548.9nm,482.3nmand377.5nm

respectively.Sofromtheredlighttothebluelight,theirwavelengthsare

deduced.Afterthewhitelightshotsatthediffractinggrating,therearelightand

darksectionsalternatingwitheachother.Threefringefieldswhichareinlight

sectionsappearonthescreenandtheyaresymmetrywiththecenterfringe.In

5

EnglishName:Vince

Class:Eng1-1B

ChineseName:WenZhengYang

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

eachfringefield,therearered,orange,yellowgreen,blue,indigoandviolet

fromtherightsidetotheleftsiderespectively.

Analysis

Thewavelengthofthered,yellow,greenandbluelightis643.6nm,548.9nm,

482.3nm,377.5nmrespectively.Theformulasare

and

n

dsin

y

tan1()

,thereisjust1order,so

.Thedistance(L)fromthecenter

n1

L

fringetotheslitsis

.Thetotallengthofthediffractiongratingis

0.215m

1mm

1103

with600slits,sothedistance()betweentoslitsis

6.So

1.6710m

d

600

y

1.6710

sin(tan1

6

(

,substitutingdifferentvalueofy,the

))

0.125

wavelengthofeachmonochromaticlightwasgottenandtheyareshownin

table1.Table2belowisthecomparisonofthestandardwavelengthforthefor

lights.

Table2isthecomparisonbetweenthestandardwavelengthandthe

wavelengthgottenfromthisexperimentofthefourmonochromaticlights.

Table2:comparison

Color

Standardwavelength(nm)

Wavelengthgottenfromaim1

622-770

577-597

492-577

492-555

643.6

548.9

482.3

377.5

yellow

green

blue

Accordingtothistable,onlythewavelengthofredlightisintherangeofthe

standardwavelength.Thewavelengthsoftheyellow,green,bluelightgotten

fromaim1aresmallerthantherealvalue,whicharecausedbytheerrors

6

EnglishName:Vince

Class:Eng1-1B

ChineseName:WenZhengYang

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

discussedbefore.Therefore,theresultsarenotveryaccurate.Monochromatic

lightisthekindoflightthathasasinglewavelength(2).Thelightcomesfrom

thetorchisWhitelight.Whitelightiscomposedofsevenlightswhicharered,

orange,yellow……andithassevewnavelengths(3).Therefore,whitelightis

polychromaticlightandthisisthereasonwhythediffractingpatternhas

differentcolors.LightisakindofEMwave.EMwavehasvisiblespectrumand

theinvisiblespectrum.Whenthefrequencyoflightisbetween

4.310HZ

14

and

,itisvisiblelightwhichincludesred,orange,yellow,green,

7.510HZ

14

blue,indigo,violetlight.Whenthefrequencyoflightisoutofthisrange,itis

invisiblelight(4).

:

Aim2

Findwavelengthsforlasers

Apparatus:

spectrometer,apieceofpaper,ruler,redlaserpen,blue

laserpen,redandbluegoggles.

Methods

Goggleisakindoflightfilteranditcanavoidthelightdamagingtotheeyesby

changingtheintensityandspectrumofthethroughlights.Thewaysofthisaim

issimilartotheaim1.Firstofall,onepersonusedtheredlaserpentoshotat

thediffractiongratingandtheotherpersonobservedthediffractionpatternby

wearingabluegoggle.Thereasonwhybluegogglewasusedtoobservethe

redlaseristhatitcanabsorbtheredlightwhichwillprotecttheeyes,inthe

sameway,theredgogglewasputontoprotecttheeyeswhenthebluelaser

7

EnglishName:Vince

Class:Eng1-1B

ChineseName:WenZhengYang

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

penwasused(5).Then,thepositionofeachfringewasrecorded.Next,the

distancefromthedifferentfringestothecenterfringewasreadfromtheruler

anditwasrecordedatanothersheetofpaper.Later,usingthebluelaserpen

andwearingtheredgoggletorepeatthelaststeps.

Results

Table3showstheexperimentdataofaim2andthewavelengthoftheredand

bluelasergottenfromit.

:

Table3resultsofaim2

Order(n)

y(cm)

8.6

L(m)

0.215

0.215

0.215

0.215

1

2

1

2

22.9

5.4

11.5

607.5

405.9

393.0

blue

Thewavelengthcalculatedfromthesecondorderissmallerthanthefirstorder,

whichcanbeseenfromtable3.Bothdiffractionpatternsoftheredlaserand

bluelaserhavefivebrightsectionsandtheysymmetryaboutthecenterfringe.

Thebrightsectionandthedarksectionarealternatingwitheachother.When

thebrightsectiongotfarfromthecenterfringe,itbecamedarkeranddarker.

Sothebrightnessofsecondorderisdarkerthanthefirstorder.

Analysis

Table4showsthewavelengthoftheredlightandthebluelightfromaim1and

aim2

Table4:Comparisonoftheresultsforaim1andaim2

8

EnglishName:Vince

Class:Eng1-1B

ChineseName:WenZhengYang

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

Wavelength(nm)from

Color

red

blue

643.6

377.5

607.5

393.0

405.9

Twofringeordersofdiffractioncouldbeseeninaim2andthereisafringeon

thesidesaswellastheback(6).ThewavelengthsoftheredandblueLED

calculatedfromthefirstorderare618.9nmand405.9nm.Fromthesecond

order,thewavelengthsare607.5nmand393.0nmrespectively.Theresults

ofthetwoaimsarenotthesame:wavelengthsoftheredlightinaim2forthe

firstandsecondorderaresmallerthanaim1whilewhichofthebluelightof

aim2arebiggerthanaim1(8).Thevaluesofwavelengthsofdifferentorders

inaim2aredifferent.Asthepatternofthefirstorderisbrighterthanthe

secondorder,whenmarkedthepositionoffringes,itwillbemoreaccurate.

Thus,theresultgottenfromthefirstfringewillbemoreaccuratethanthe

secondorderandtheyaredifferent.Thedifferentseparationsalsowillleadto

thedifferentresults.Iftheslitseparationbecomesnarrower,thediffraction

patternwillbecomeclearer.Ontheoppositeside,thepatternwillbecome

unclearwhentheslitsseparationiswider(7).

Aim3

:FindwavelengthsforLED

Apparatus:

Spectrometer,LEDs,powersupply,blackplasticbag,leads.

Methods

9

EnglishName:Vince

ChineseName:WenZhengYang

Class:Eng1-1B

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

i.Connectthepowerssupplyandthesocketandletthevoltageisthe

minimumvalue

ii.ConnecttheRedLEDtothepowersupplyandregulatethevoltageata

propervaluetomaketheLEDshinenormally.

iii.LetthelightoftheredLEDpassthroughtheemptypenandshotatthe

spectrometerthroughthediffractiongrating.Thediffractionpatternwillbe

moreclearwhentheLEDpassedthroughtheemptypenasthelightwas

gatheredanditsintensitywasstrengthened(9).

iv.Observethediffractionpatternfromtheviewingholewiththeblackplastic

bagcoveredtheheadandtheviewinghole(theLEDwasnotbrightand

noteasytobeseen,toreducethelightlossandhelpview,theblack

plasticbagwasused).

v.Takedonethepositionofthecenterofeachfringe.

vi.Readthedistancefromeachfringetothecenterfringe

vii.Recognizetheresultandmoveittothetableintutorial

viii.Usingtheyellow,blueandgreenLEDsrespectivelytorepeattheabove

process

Results

Table5showstheexperimentdataofaim3andthewavelength,frequencyof

thefourLEDsgottenfromtheresult.

:

Table5

resultsofaim3

Color

Order(n)

y(cm)

L(m)

Wavelength(nm)

Frequency(Hz)

10

EnglishName:Vince

ChineseName:WenZhengYang

Class:Eng1-1B

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

1

1

1

1

9.3

8.2

7.6

6.5

0.215

0.215

0.215

0.215

662

594

555

482

4.5E+14

5.05E+14

5.40E+14

6.22E+14

yellow

green

blue

Thephenomenonofthisaimisnotverycleartosee,therearethreebright

circularsections.Ineachsection,thebrightnessbecamesmallerandsmaller

fromthecentertothesides.OfthefourcolorLEDs,theblueLEDisbrightest,

thenarethegreen,yellow,redLEDrespectively.Thiswasseenfromthe

experiment.

Analysis

Thewavelengthwasgottenfromthesamewayofcalculationasaim1.

C

f

C

(C

,sothefrequencyofeachLEDcanbe

f

310m/s)

8

CT

calculated.ThewavelengthoftheredLED,yellowLED,greenLED,blueLED

fromthisaimare

,

,

and

respectively.The

and

662nm

594nm

555nm

482nm

frequenciesofthemare

,

,

4.510Hz

5.0510Hz

5.4010Hz

14

14

14

6.2210Hz

14

.

Table6showsthecomparisonbetweenthewavelengths,frequenciesofthe

fourLEDSgottenofaim3andthestandardvalue

Table6:comparison

Wavelength(nm)

Color

red

fromaim3

standard

fromaim3

662

594

555

622-770

14

14

14

yellow

green

577-597

492-577

5.0210

5.1910

14

14

5.4010

-6.110

14

14

11

EnglishName:Vince

ChineseName:WenZhengYang

Class:Eng1-1B

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

blue

482

492-255

6.2210

6.110

-11.710

14

14

14

Asshownintable6,boththewavelengthsandthefrequenciesoftheredLED,

yellowLEDandgreenLEDareintherangeofthestandardvalue.However,

theresultoftheblueLEDwasoutoftherange.Thisaimworkswellandthe

resultsaremoreaccuratethanthepreviousaims.

:FindthePlanckconstant

Aim4

Apparatus

Spectrometer,LEDs,powersupply,blackplasticbag,leads.

Methods

i.Connectthepowerssupplyandthesocketandletthevoltageisthe

minimumvalue.

ii.ConnecttheredLEDtothepowersupply.

iii.Regulatethevalueofvoltagethroughthepowersupplyandmakeit

increaseslowly.

iv.WhentheLEDjuststartedtoshine,writingdonethevoltageV,stopping

toregulatethevoltageandusingtheLEDtoshotthediffractiongrating.

v.Viewingthediffractionpatternonthescreenthroughtheviewingholewith

theblackplasticbagcoveredtheheadandthehole.

vi.Markthepositionofthecenterofeachfringeonthescreenpaper.

vii.Readthedistancesfromeachfringetothecenterfringeandwritethe

dataontoanothersheetofpaper.

viii.ReplacetheredLEDintoyellowLED,blueLEDandgreenLED

12

EnglishName:Vince

Class:Eng1-1B

ChineseName:WenZhengYang

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

respectivelyandrepeattheaboveprocessforeachofthem.

ix.Usingthedatatodrawagraphof

onYagainstfonx.

eV

Result

Table7showstheexperimentdataofaim3andthewavelength,frequencyof

thefourLEDsgottenfromtheresult.

:

Table7

resultsofaim3

Order(n)

1

1.4

1.9

2.1

2.3

4.5310

5.0510

5.4010

6.2110

2.241019

3.041019

3.361019

3.681019

4.9421034

6.0181034

6.2211034

5.9161034

yellow

green

blue

1

1

1

Thefrequencieswerecalculatedfromthesamemethodasaim3.Onthe

screen,thediffractionpatternoftheredLEDwasnotclearandthepatternof

theblueLEDisbrightest.ThepatternofthegreenLEDwasmoreclearthan

thetallowLEDandtheredLED.ForeachLED,thepatternsweresimilarto

eachotherandtheyhadthreebrightsections,thebrightnesswasreduced

fromthecenterofthebrightfringetoitsedgeineverybightsection.Inthis

table,

isenergyofthephotoelectronescapingfromtheLED,

V

eV

0

IsthevalueofvoltagewhentheLEDstartedtoshineand

constant.

isthePlanck

h

Graph1istherelationshipbetween

andthefrequencyofthelight.

eV

13

EnglishName:Vince

Class:Eng1-1B

ChineseName:WenZhengYang

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

Graph1:therelationshipbetween

andfrequency.

eV

Forthisgraph,x-axisisthefrequenciesofdifferentkindsoflight,y-axisis

energy

of

the

photoelectron.

4

3

2

1

f(10^14Hz)

0

0

1

2

3

4

5

6

7

-1

-2

Analysis

Theequationof

againstfrequencyis

,wisworkfunction.For

eVhfw

eV

theequation,thegradientisthePlanckconstant,andtheinterceptisthework

function.Accordingtograph1,theequationoftherelationshipbetween

eV

andfrequencyis

,astheunitmagnitudeofthex-axisis

y0.819x1.259

1019

anditofthey-axisis

19.So

.The

Js

10Hz

14

10

J

h

0.819

8.1910

34

10

14

realvalueofthePlanckconstantis

34

,sotheresultisnotvery

Js

6.6310

accurate.Thereexistsomeerrors.Firstofall,astheweaknessoftheLEDs

andeyescannottellthefringescenteraccurately,thedistance(y)fromfringes

tothecenterfringeisnotaccurateanditwillleadtotheinaccuracyof

14

EnglishName:Vince

Class:Eng1-1B

ChineseName:WenZhengYang

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

frequency.Secondly,thevoltageusedshouldbetheinstantvoltagewhilethe

LEDwasjuststartingtoshine.However,thisisimpossibletoachieve.The

abovetwoerrorsarethelargestcausesoferrors.Thedistance(L)between

thegratingtothecenterfringeisalsonotaccurateasitreadbyeyes,whichis

thethirderror.Therefore,errorsonreadingthedistanceandthevoltageare

twoapproximatemeasurementerrors(10).Inaddition,theuncertainerrors

alsoexist.TheLEDmayshineabnormallyasitwasusedbeforeorsomeother

internalproblemsareintheLED,thismayisanerroranditis

uncertain..Operatingthisexperimentinthedark,usingthenewLEDsand

usingothermaterialswhicharemorestableinsteadofcartonarethree

measurementscanbedonetoimprovetheaccuracyofthisexperiment(10).

TheanswersfromtheLEDwithtwocolorscannotbeusedtofindasitisnot

h

monochromaticlightandithastwofrequencies(11).Theerrorinthemethod

forfindinghcanbecalculatedbythismethodwhichis

34

,

Js

h(hs)10

1

n1

where

isthecorrectedstandarddeviation.

.The

s

s

n(hh)

2

i

i

Planckconstant

34

,

Js

Fourcolorsoflightweremeasured,so

h6.6310

Fromtable7,,

,,

are

34

,

34Js

,

.

n4

10

6.01810

h

h

h

h

4.942

Js

1

2

3

4

and

34Js

respectively.So

6.2211034Js

5.91610

hhhh

h

s

5.6617510

34

1

2

3

4

4

1

n1

1

n

i

4

(hi5.66175

10)

(h

h)

2

2

i

3

1

15

EnglishName:Vince

ChineseName:WenZhengYang

Class:Eng1-1B

Studentnumber:SBC-11-1025

Diffractionandthephotoelectriceffect

1

3

.Substitutingthemand

s

hh

2

(h

h)

(h

h)

(h

h)

s

2

2

2

1

2

3

4

can

be

worked

out

which

is

.

Therefore,

1.061034

(12).accordingtothewebsitewhichis

34Js

h(5.6617510

1.0610

)

10

34

34

calledInvestopedia(2012),thestandarddeviationstandsfortherateof

deviationbetweenthestochasticvariableandthemathematicexpectation,so

alowmeansthattheresultswereclosetogether.Thestandarddeviation