hsc physics summary pages

7/31/2019 HSC Physics Summary Pages

1/69

WilliamKimHSCPhysicsSummary|page1

Phy

sicsSummary

Con

tents

Page

CoreTopicOne:Space

1.Gravity

2

2.SpaceLaunchandReturn

3

3.FutureSpaceTravel

13

4.SpecialRelativity

14

CoreTopicTwo:MotorsandGene

rators

1.TheMotorEffect

19

2.ElectromagneticInduction

24

3.ElectricGenerators

27

4.Transformers

29

5.ElectricMotors

31

CoreTopicThree:FromIdeastoImplementation

1.CathodeRays

32

2.QuantumTheory

37

3.SolidStateDevices

43

4.Superconductivity

48

OptionTopic:QuantatoQuarks

1.ModelsoftheAtom

53

2.QuantumPhysics

57

3.TheElectronMicroscope

59

4.ApplicationsofRadioactivity

61

5.NuclearApplications

66

6.TheStructureofMatter

67


2/69


Cor

eTopicOne:Space

1.T

heEarthhasagravitationalfieldthatexertsaforceonobjects

bothonitandaroundit

Defineweightastheforceon

anobjectduetoa

gravitationalfield

Definegravitationalpotential

energyastheworkdoneto

moveanobjectfromavery

largedistanceawaytoapoint

inagravitationalfield.

Theweightofanobjectistheforceofgravityactingonit.

WhereWistheweig

htinnewtons(N),misthemassinkilograms(kg)andgcanbeeither:

1.Theaccelerationduetogravity(=9.8m/s/s

attheEarthssurface);or

2.Thegravitationalfieldstrength(=9.8N/kg

attheEarthssurface).

Asweliftanobjectfromthegroundtoaheightabo

vethegroundwedoworkonit.Thisworkis

storedintheobjecta

sgravitationalpotentialenergy

.Foranobjectofmassmataheighthabove

theEarthssurfacethegravitationalpotentialenergyEisgivenby:

Howeve

rthisequationisvalidonlywh

entheobjectisneartheEarthssurface.

Thegravitationalpotentialenergyisameasureof

theworkdoneinmovinganobjectfrom

infinitytoapointinthefield.Thegeneralexpressio

nforthegravitationalpotentialenergyofan

objectofmassmata

distancerfromthecentreofth

eEarth(orotherplanet)isgiv

enby:

W

hereMisthemassoftheEarth

(orotherplanet).

ChangeinGravitationalPotentialEnergy

Thechangeinpotentialenergyofamassm1asitmovesfrominfinitytoadistance

rfromasource

ofagravitationalfield(duetoamassm2)isgivenby:

rmmG

Ep

2

1

=

ChangeinGravitationalPotentialEnergyNeart

heEarth(whenradiusincreasesfromAtoB)

NewtonsLaw

ofUniversal

Gravitation

whereGistheuniversal

gravitationalconstant.

TheGravitationalField

Surroundinganyobjectwith

massisagravitationalfield.

22

1 rmmG

F=

2rGm

g=

gm

W

r

=

mgh

Ep=

rmM

G

E

E

p

=

=

B

A

E

p

r

r

GmM

E

1

1


3/69


2.M

anyfactorshavetobetakenin

toaccounttoachieveasuccessfulrocketlaunch,maintainastableorbitandreturntoEarth

Describethetrajectoryofan

objectundergoingprojectile

motionwithintheEarths

gravitationalfieldintermsof

horizontalandvertical

components

Anymovingobjectthatmovesonlyundertheforce

ofgravityisaprojectile.Theh

orizontalmotion

ofaprojectileisinde

pendenttotheverticalmotion.

Thereasonforthisresultisthatgravityisthe

onlyforceactingontheobjectsandthisalwaysacts

towardsthecentreoftheEarth.

Projectilemotionca

nbeanalysedbyrealisingthat:

1.Thehorizontalmotionisconstantvelocity.

2.Theverticalm

otionofconstantacceleration(withaccelerationofg).

EquationsofUnifor

mlyAcceleratedMotion

ThePathofaProjectile

Thevelocityatanyp

ointofthepathofaprojectileissimplythevectorsumofthe

horizontaland

verticalvelocitycom

ponentsatthatpoint.

Thehorizontalco

mponentisconstant.

Theverticalcomponentchangesatg,theaccelerationduetogravity.

Trajectories

Thepathfollowedbyaprojectileitstrajectory

isaparabola(orlinear)

xu

x

y

as

u

v

ta

tu

s

ta

u

v

2212

2

2

+

=

+

=

+

=

r

r

r

(1)Horizontalmotion:

tu

x

x

=

(2)Verticalmotion:

2

21

ta

y

g

=

From(1):

xu

x

t

=

Combining(2)&(3):

(

)2

2

2

21

21

x

ua

ux

a

y

xg

x

g

=

=

=

=

2

2

2

)

(xg ua

k

x

k

y


4/69


0

21

2

=

EE

e

Rm

MG

mv

DescribeGalileosanalysis

of

projectilemotion

Explaintheconceptofesca

pe

velocityintermsofthe:

ogravitationalconstant

omassandradiusofthe

planet

Galileowasresponsiblefordeducingtheparabolicshapeofthetrajectoryofaprojectile.Galileos

analysisofprojectile

motionledhimtoconsiderreferenceframes.Thesearewhat

allmeasurements

arecomparedto.

TheconceptofGalileanrelativityrefersthatthelawsofmechanicsarethesameinaframe

ofreferencethatisatrestoronethatmoveswithco

nstantvelocity.

Ifanobjectisprojectedupwardwithalargeenough

velocityitcanescapethegrav

itationalpullof

theEarth(orotherplanet)andgointospace.Thene

cessaryvelocitytoleavetheEarth(orother

planet)iscalledthee

scapevelocity.

Escapevelocitydependsonthegravitationalconstant,themassandradiusoftheplanet.

Supposeanobjectof

massmisprojectedvertically

upwardfromtheEarthssurfac

e(massofMand

radiusR)withaninitialvelocityu.Theinitialmechanicalenergy,thatis,kineticandpotential

energyisgivenby:

Letusassumethatth

einitialspeedisjustenoughso

thattheobjectreachesinfinity

withzero

velocity.Thevalueo

ftheinitialvelocityforwhichthisoccursistheescapevelocity

ev.

Whentheobjectisatinfinitythemechanicalenergy

iszero(thekineticenergyisz

erosincethe

velocityiszeroandt

hepotentialenergyiszerobecausethisiswhereweselectedthezeroof

potentialenergy).

Hence

whichleadsto:

E

E

e

RGM

v

2

=

EE

p

k

Rm

MG

mu

E

E

i

i

=

+

2

21


5/69


Rv

g

2

=

rv

ac

2

=

DiscussNewtonsanalysis

of

escapevelocity

CircularMotion

Themotionofanobjectinacircularpathwithconstantspeediscalleduniformcircularmotion.

Althoughthespeedr

emainsthesameinuniformcir

cularmotion,itfollowsthatan

objecttravelling

inacircularpathmustbeaccelerating,sincethevelocity(thatis,thespeedinagivendirection)is

continuallychanging

.

CentripetalAcceleration

Ascanbesee

n,whenthechangeinvelocity

isplacedintheaveragepositio

nbetweenv1and

v2,itisdirectedtowa

rdsthecentreofthecircle.Wh

enanobjectismovingwithun

iformcircular

motion,theaccelerat

ion(thecentripetalacceleration)isdirectedtowardsthecentreofthecircle.

Foranobjectmoving

inacircleofradiusrwithanorbitalvelocityofv,thecentrip

etalacceleration

aisgivenby:

EarthOrbits

AsatellitecanbeputintoEarthorbitbyliftingitto

asufficientheightandthengiv

ingitthe

requiredhorizontalv

elocitysothatitdoesnotfallb

acktoEarth.Forthesatelliteto

circletheEarth,

thecentripetalforcerequiredisprovidedbythegravitationalattractionbetweenthesatelliteandthe

Earth.Hencethecentripetalaccelerationisgivenby

:

IsaacNewtonproposedtheid

ea

ofartificialsatellitesofthe

Earth.Heconsideredhowa

projectilecouldbelaunched

horizontallyfromthetopofa

highmountainsothatitwould

notfalltoEarth.

Asthelaunchvelocity

wasincreased,thedistanceth

at

theobjectwouldtravelbefore

hittingtheEarthwouldincrea

se

untilsuchatimethatthe

velocitywouldbesufficientto

puttheobjectintoorbitaroun

d

theEarth.(Ahighervelocity

wouldleadtotheobject

escapingfromtheEarth.)

2

1

v

v=

2

1

v

v

2v

1v

v

2v

1

vv

Thechangeinvelocityisgivenby:

andsince:

itfollowsthattheobjectisaccelerating.

1

2

v

v

v

=

tv

a

=

r


6/69


gRv

mg

Rmv

mg

mgN

2

2

1+=

+

=

=

Usethetermgforcesto

explaintheforcesactingon

anastronautduringlaunch

Comparetheforcesactingon

anastronautduringlaunch

withwhathappensduringa

rollercoasterride

Thehumanbodyisrelativelyunaffectedbyhighspeeds.Changesinspeed,however,thatis,

accelerations,cananddoaffectthehumanbodycre

atingaccelerationstress.

g-forces

Accelerationforces

g-forcesaremeasuredinunitsofgravitationalacceleration

g.Forexample,

aforceof5gisequiv

alenttoaccelerationfivetimes

theaccelerationduetogravity.

Iftheaccelerationsarealongthebodyslongaxisth

entwodistincteffectsareposs

ible:

1.Iftheaccelerationisinthedirectionofthep

ersonsheadtheymayexperienceablackout

asthebloodrushestotheirfeet;or

2.Iftheaccelerationistowardstheirfeet,they

mayexperiencearedoutwheretheblood

rushestotheirheadandretina.

Asyoufallfromaheight,youexperiencenegative

g-forces(youfeellighter).Whenyoupullout

ofadipafterahillorfollowaninsideloop,youexperiencepositiveg-forces(youfeelheavier).

Thepositiveg-forcesarelikethoseastronautsexperienceatlift-off.

Considerariderina

caratthebottomofaninsideloop.Theriderhastwoforcesactingonthem:

1.Theirnormal

weight(mg)actingdown;and

2.Thenormalreactionforce(N)actingup.T

hisisthepushoftheseatupwa

rdsontheir

bottom.

Assumethattheloop

ispartofacircleofradiusR.Acentripetalforceisrequiredfortheriderto

travelinacircle.Thisisthedifferencebetweenthe

normalforceandtheweightforce,thatis:

Rmv

mg

N

Rmv

mg

N

2

2:

+

=

=

Theg-forcesarefoundfromthe'normalforcedividedbytheweight.Thatis:

gsfeltbyrid

er

N mg

g-forcesonAstronauts

Humanscanwithstand4g

withoutundueconcern.

Accelerationsupto~10gare

tolerableforshorttimeswhen

theaccelerationisdirected

paralleltoalinedrawnbetwe

en

thepersonsfrontandback.


7/69


Discusstheimpactofthe

Earthsorbitalmotionandits

rotationalmotiononthe

launchofarocket

Analysethechanging

accelerationofarocket

duringlaunchintermsofth

e:

LawofConservationof

Momentum

Forcesexperiencedby

astronauts

Amovingplatformo

ffersaboosttothevelocityof

aprojectilelaunchedfromit,if

launchedinthe

directionofmotiono

ftheplatform.Thisprincipleisusedinthelaunchofarocket

byconsidering

thattheEarthrevolvesaroundtheSunat107,000km

/hrelativetotheSunandrotatesonceonits

axisperdaysothata

pointontheEquatorhasarotationalvelocityofapproximately1,700km/h

relativetotheSun.H

ence,theEarthisitselfamovingplatformwithtwodifferentmotionswhich

canbeexploitedina

rocketlaunchtogainaboostinvelocity.

EarthOrbit

Arocketheadingintoorbitislaunchedtotheeastto

receiveavelocityboostfrom

theEarths

rotationalmotion.

AnInterplanetaryT

rip

Theflightofarocketheadingintospaceistimedso

thatitcanheadoutinthedirectionofthe

Earthsmotionandtherebyreceiveanextraboost.

LawofConservatio

nofMomentum

Rocketenginesgeneratethrustbyburningfuelandexpellingtheresultinggases.C

onservationof

momentummeansth

atasthegasesmoveoneway,therocketmovestheother.(Momentumbefore

theburningiszero;h

encethemomentumafterisalsozero.Thegasescarrymomentuminone

directiondown,andsotherocketcarriesanequalm

omentumintheoppositedirectionup.)

Asfueliscon

sumedandthegasesexpelled,

themassofthesystemdecreas

es.Since

accelerationispropo

rtionaltothethrustandinverse

lyproportionaltothemass,as

themass

decreases,theaccelerationincreases.Hencetheforcesontheastronautsincrease.

ForcesExperienced

byAstronauts

gforcesvariedduringthelaunchofSaturnV,alarg

ethree-stagerocketusedtolau

nchtheApollo

spacecraft.Thisisattributedtothesequentialshutdownofthemultiplerocketenginesofeachstage

atechniquedesignedspecificallytoavoidextremegforces.


8/69


Analysetheforcesinvolved

inuniformcircularmotion

forarangeofobjects,

includingsatellitesorbiting

theEarth

Comparequalitativelyand

quantitativelylowEarthand

geostationaryorbits

LowEarthOrbit

AlowEarthorbitisgenerallyanorbithigherthanapproximately250km,inorder

toavoid

atmosphericdrag,an

dlowerthanapproximately1000km,whichisthealtitudeatwhichtheVan

Allenradiationbelts

starttoappear.ThespaceshuttleutilisesalowEarthorbitsom

ewherebetween

250kmand400kmdependinguponthemission.At250km,anorbitingspacecraf

thasavelocity

of27,900km/handtakesjust90minutestocompleteanorbitoftheEarth.

GeostationaryOrbit

Ageostationaryorbitisatanaltitudeatwhichthep

eriodoftheorbitpreciselymatchesthatofthe

Earth.IfovertheEquator,suchanorbitwouldallow

asatellitetoremainparked

overafixed

pointonthesurfaceoftheEarththroughouttheday

andnight.FromtheEarthsuch

asatellite

appearstobestationaryinthesky,alwayslocatedinthesamedirectionregardless

ofthetimeof

day.Thisisparticula

rlyusefulforcommunications

satellitesbecauseareceivingdishneedonly

pointtoafixedspotIntheskyinordertoremainin

contactwiththesatellite.

Thealtitudeo

fsuchanorbitisapproximately38,800km.Ifasatelliteatthisheightisnot

positionedovertheE

quatorbutatsomeotherlatitude,itwillnotremainfixedatonepointinthe

sky.Instead,fromtheEarththesatellitewillappear

totraceoutafigureofeightpatheach24

hours.ItstillhasaperiodequaltotheEarths,howe

ver,andsothisorbitisreferredtoas

geosynchronous.

Motion

FcProvidedBy

Whirlingrockonastring

Thestring

Electronorbitingatomicnucleus

Electron-n

ucleuselectricalattraction

Carcornering

Frictionbe

tweentyresandroad

Moonrevolving

aroundEarth

Moon-Earthgravitationalattraction

SatelliterevolvingaroundEarth

Satellite-E

arthgravitationalattraction


9/69


Discusstheimportantof

NewtonsLawofUniversal

Gravitationinunderstandin

g

andcalculatingthemotionof

satellites

Oncealaunchedrockethasachievedasufficientalt

itudeabovethesurfaceoftheE

arth,itcanbe

acceleratedintoanorbit.Itmustattainaspecificspeedthatisdependentonlyupon

themassand

radiusoftheEarthandthealtitudeaboveit.Ifthats

peedisnotreached,thespacec

raftwillspiral

backinuntilitre-enterstheatmosphere;ifthespeedisexceeded,itwillspiralout.

Thiscanbe

consideredbyapprec

iatingthatthesimplestorbitalmotionisauniformspeedalongacircularpath

aroundtheEarth.

Uniformcirc

ularmotion,asalreadymentioned,isacircularmotionwithauniformorbital

velocity.AccordingtoNewtonsFirstLawofMotion,aspacecraftinorbitaround

theEarth,orany

objectincircularmotion,requiressomeforcetokeepitthere,otherwiseitwouldflyoffatatangent

tothecircle.Thisforceisdirectedbacktowardsthe

centreofthecircle.Inthecase

ofspacecraft,it

isthegravitationalattractionbetweentheEarthand

thespacecraftthatactstomain

tainthecircular

motionthatistheorbit.Theforcerequiredtomaintaincircularmotion,knownasc

entripetalforce,

canbedeterminedus

ingthefollowingequation:

TheapplicationofNewtonsLawofUniver

salGravitationtotheorbitalmotionofa

satellitewillproduce

anexpressionforthecriticalo

rbitalvelocitymentionedearlie

r.Recallthatthis

lawstatesthatthegravitationalattractionbetweena

satelliteandtheEarthwouldb

egivenbythe

followingexpression

:

Thisgravitationalforceofattractionalsoservesast

hecentripetalforceforthecircularorbital

motion,hence:

Therefore,wecaneq

uatetheformulaforFGwithth

atforFC:

2rmmG

F

S

E

G

=

C

G

F

F

=

rmv

FC

2

=

rvm

rmmG

S

S

E

2

2

=

where

v=orbitalvelocity(ms-

1)

rGm

v

E

=

where

r=rE+altitude(m)

UsingNewtonsLawof

UniversalGravitationcombin

ed

withtheexpressionfor

centripetalforce,wecansee

thattheorbitalvelocity

requiredforaparticularorbit

dependsonlyonthemassofthe

Earth,theradiusoftheEarth

andthealtitudeoftheorbit

(distancefromthesurfaceofthe

Earth).Giventhatthemassand

radiusoftheEarthhavefixed

values,thismeansthataltitud

e

istheonlyvariablethat

determinesthespecificvelocity

required.Inaddition,the

greatertheradiusoftheorbit,

thelowertheorbitalvelocity

required.


10/69

WilliamKimHSCPhysic

sSummary|page10

Further,wecanusetheexpressionfororbitalvelocitytoproveKeplersThirdLa

wtheLawof

Periods.Theperiodorthetimetakentocompleteo

nefullorbitcanbefoundbydividingthelength

oftheorbit(thecircu

mferenceofthecircle)bytheorbitalvelocity,v.

Changingthesubjectofthisexpressiontovandthensubstitutingintotheformulaforvgiven

above:

Thismeansthatfora

nysatelliteoftheEarthatanyaltitude,theratior3:T

2a

lwaysequalsthesame

fixedvalue.

2

23

4

2

EE

Gm

Tr

rGm

Tr

=

=v

r

T

2=

KeplersThirdLaw:

TheLawofPeriods


11/69

WilliamKimHSCPhysic

sSummary|page11

Describehowaslingshot

effectisprovidedbyplanet

s

forspaceprobes

Accountfortheorbitaldecay

ofsatellitesinlowEarthorbit

ManyoftodaysspaceprobestodistantplanetssuchasJupiteruseagravitationalslingshoteffect

(alsoknownasagravity-assisttrajectory)thatbringstheprobeclosetootherplanetstoincreasethe

probesvelocity.In1

974,Mariner10wasdirectedpastVenusonitswaytoMercu

ry.ThePioneer

andVoyagerprobesalsousedthismethod.

ConsideratriptoJupitersuchastheGalileo

probethatinvolvedasinglefly-byofVenus

andtwooftheEarth.AstheprobeapproachesVenu

s,itisacceleratedbyVenusg

ravitational

attraction,causingit

tospeeduprelativetoVenus.(ByNewtonsThirdLaw,Venu

swillalso

experienceaforceslowingitdown.Itsmass,howe

ver,issomuchgreaterthantha

toftheprobe

thatthevelocitydecr

easeisimperceptible.)

Astheprobe

passesVenus,itsspeedisreduced(relativetoVenus).Relativ

etotheSun,

however,itsspeedhasincreased.Theprobepicksu

pangularmomentumfromthe

planet(which

losesanequalamountofanangularmomentum).G

ravityallowsthecouplingbetweentheprobe

andplanettofacilitatethetransfer.Forthisreason,gravity-assisttrajectoriesshouldmorecorrectly

becalledangularmo

mentum-assisttrajectories.

AllsatellitesinlowE

arthorbitaresubjecttosomedegreeofatmosphericdragthatwilleventually

decaytheirorbitand

limittheirlifetimes.Asasatelliteslows,itlosesaltitudeandbeginsaslow

spiraldownwards.Asitdescends,itencountershigherdensityairandhigherdrag,

speedingupthe

process.Bythetime

thesatelliteisbelowanaltitudeof200kmithasonlyafewhoursleftbefore

collidingwiththeEa

rth.There-entryprocessgeneratesmuchheatandmostsatellitesburnup

(vaporise)beforeimpacting.

viSacecra

ft

Vi

Planet

Vf

vf=vi+2Vi


12/69

WilliamKimHSCPhysic

sSummary|page12

Discussissuesassociated

withsafere-entryintothe

Earthsatmosphereand

landingontheEarthssurfa

ce

Identifythatthereisan

optimumangleforre-entry

intotheEarthsatmosphere

andtheconsequencesof

failingtoachievethisangle

.

Therearesignificant

technicaldifficultiesinvolved

insafere-entry,themostimportantbeing:

1.TheheatgeneratedasthespacecraftcontactstheEarthsatmosphere;and

2.Keepingtheretarding-forces(g-forces)with

insafelimitsforhumans.

HeatingEffects

TheEarthsatmosphereprovidesaerodynamicdrag

onthespacecraftandasaresu

lthigh

temperaturesaregeneratedbyfrictionwithairmole

cules.

g-Forces

Theangleofre-entry

iscritical:tooshallowandthe

spacecraftwillbounceoffthe

atmosphereback

intospace;toosteep

andtheg-forceswillbetoogre

atforthecrewtosurvive(and

thetemperatures

generatedwiththeatmospherewillbetoohigheven

fortherefractingmaterialsused).

Theallowedangleofre-entryis6.21relativetotheEarthshorizon.


13/69

WilliamKimHSCPhysic

sSummary|page13

3.F

uturespacetravelandexplorationwillentailacombinationofnewtechnologiesbasedoncurrentandemergingknowledge

Discussthelimitationof

currentmaximumvelocities

beingtooslowforextended

spacetraveltobeviable

Describedifficulties

associatedwitheffectivean

d

reliablecommunications

betweensatellitesandearth

causedby:

-distance

-vanAllenradiationbe

lts

-sunspotactivity

Scientistshavenotyetbeenabletoproducespeedsofspacecraftmorethanafewtensofthousands

ofkilometresperhour.Whentravellingtodistantplanetaryobjects,theenginesof

spacecraftare

notonasspacecraftrelyoninertiatomovealong.T

oincreasethespeedsignificantlywouldrequire

theenginestobeope

rating,whichwouldrequiremorefuel.Morefuelwouldrequiremorethrust

puttingthespacecraftintoorbit,whichwouldrequiremorefuelandsoon.

Toincreasethespeedofspacecrafttovalues

thatwouldmakeinterplanetarytravelfeasible

requiresawholenew

technology(onenotbasedon

theemissionofgasesproduced

bycombustion).

Clearly,whilecurren

tmaximumvelocitiesarejustadequateforinterplanetarytrav

el,theyare

entirelyinadequateforinterstellartravel.

Distance

Microwavesandradiowaves,likeallEMwaves,travelthroughspaceatthespeed

oflight.Thisis

thefastestspeedpossibleinouruniverseandthereforeplacesalimitonthespeedandresponsetime

ofspacecommunications.Theimmensedistanceinvolvedinspacecommunication

screatesa

distance-relatedtime

lag.Also,asEMradiationobe

ysaninversesquarelaw,there

isalossof

signalstrengthasdis

tanceincreases.Thisisreferredtoasspaceloss.

VanAllenradiation

belts

Therearetwobeltso

fenergeticchargedparticles,m

ainlyelectronsandprotons,ly

ingatright

anglestotheequator

oftheEarth.Someofthesolarwindparticlesbecometrapped

intheVanAllen

radiationbelts.Intensesolaractivitycandisruptthe

VanAllenBelts.Thisinturnisassociatedwith

aurorasandmagneticstorms.Thechargedparticles

driftingaroundtheEarthintheouterbelt

correspondstoanele

ctriccurrentandhencehasanassociatedmagneticfield.Onceortwicea

monththiscurrentin

creasesandasaresultitsmagn

eticfieldincreases.Thiscanle

adtointerference

ofshortwaveradioc

ommunication,errorsincomm

unicationsatellitesandevenfa

ilureofelectrical

transmissionlines.

Sunspotactivity

Sunspotsareassociatedwiththesolarwind(consistingofastreamofchargedparticles).Thesolar

windaffectstheEarthsmagneticfieldandthisinturnaffectsradiocommunication.


14/69

WilliamKimHSCPhysic

sSummary|page14

4.C

urrentandemergingunderstandingabouttimeandspacehasbeendependentuponearliermodelsofthetransmissionoflight

Outlinethefeaturesofthe

ethermodelforthe

transmissionoflight

Describeandevaluatethe

Michelson-Morleyattempt

to

measuretherelativevelocity

oftheEarththroughtheeth

er

Discusstheroleofcritical

experimentsinscience,suc

h

asMichelson-Morleys,in

makingdeterminationsabout

competingtheories

Itwasbelievedthatlightwavesrequireamediumtopropagate.Althoughnobodycouldfindsucha

medium,beliefinits

existencewassostrongthatit

wasgivenanametheether.

Theether:-

Filled

allofspace,hadlowdensityandwasperfectlytransparent

-

Permeatedallmatterandyetwascompletelypermeabletomaterial

objects

-

Hadg

reatelasticitytosupportandpropagatethelightwaves

TheEtherWind

BecausetheEarthwasmovingaroundtheSun,itwasreasonedthatanetherwindshouldbe

blowingpasttheEarth.However,ifawindblows,thespeedofsoundrelativetoth

estationary

observerwouldvary.Thusitwasbelievedthatthes

peedoflightshouldvaryduetothepresenceof

theetherwind.Itw

asinanattempttodetectthisdifferencethatMichelsonandM

orleydidtheir

famousexperiment.

TheMichelson-MorleyExperiment

LightsentfromSissplitintotwoperpendicularbea

msbythehalf-silveredmirror

atA.Thesetwo

beamsarethenreflec

tedbackbythemirrorsM1andM2andarerecombinedinthe

observerseye.

Aninterferencepatte

rnresultsfromthesetwobeam

s.

ThebeamAM

1travelledacrosstheether,whilstAM2travelledwithandag

ainsttheether.

Thetimestodothiscanbeshowntobedifferentan

dsointroduceaphasedifferencebetweenthe

beams.Whentheentireapparatuswasrotatedthrou

gh90,achangeintheinterfer

encepatternwas

expected.Nonewasobserved.

Theresultof

theMichelson-Morleyexperimentwasthatnomotionofthe

Earthrelativeto

theetherwasdetecta

ble.

Fromahypothesis,p

redictionsaremadeofwhatshouldhappenifaparticularexperimentis

performed.Iftheresultsarenotinagreementwiththeprediction,thehypothesisis

incorrect.Aswe

haveseen,thefactth

atanullresultwasfoundfrom

thisexperimentshowedtheetherhypothesisto

beinvalid.Thisopen

edupacompletelyrevolutiona

ryviewofspaceandtimewith

theworkof

Einstein.

EtherWindM

2

M1

S

A


15/69

WilliamKimHSCPhysic

sSummary|page15

Outlinethenatureofinertia

l

framesofreference

Discusstheprincipleof

relativity

FramesofReferenc

e

Framesofreferenceareobjectsorcoordinatesystem

swithrespecttowhichwetak

emeasurements.

Position

Inmaths,theCartesiancoordinatesystemisusedan

dpositionisreferredtotheaxesx,yandz.In

experimentsinclass,thelaboratoryistheframeofreference.

Velocity

AnobjectPtravelsw

ithvelocityvwithrespecttoa

referenceframeS.AnotherframeSmoves

withvelocityurelativetoS.ThevelocityofPrelativetoSisv=vu.Velocitythusdepends

uponthereferenceframe.

InertialFramesofR

eference

Aninertialframeofreferenceisonethatismovin

gwithconstantvelocityorisatrest(thetwo

conditionsbeingindistinguishable).Insuchreferenceframes,NewtonsLawofInertiaholds.

Anon-inertialfram

eofreferenceisonethatisaccelerating.

Threehundredyears

beforeEinstein,Galileoposed

asimpleidea,nowcalledthep

rincipleof

relativity,whichstatesthatallsteadymotionisrela

tiveandcannotbedetectedwithoutreferenceto

anoutsidepoint.ThisideacanbefoundbuiltintoN

ewtonsFirstLawofMotiona

swell.

Twopointstoberein

forced:

Theprinciple

ofrelativityappliesonlyfornon-acceleratedsteadymotion

Thisprinciplestatesthatwithinaninertialfr

ameofreferenceyoucannotperformany

mechanicalexperimentorobservationthatw

ouldrevealtoyouwhetheryouweremoving

withuniform

velocityorstandingstill.

S

'S

u

vP


16/69

WilliamKimHSCPhysic

sSummary|page16

Identifythesignificanceof

Einsteinsassumptionofthe

constancyofthespeedof

light

Recognisethatifcisconstant

thenspaceandtimebecome

relative

Discusstheconceptthat

lengthstandardsaredefined

intermsoftimewith

referencetotheoriginal

meter

Identifytheusefulnessof

discussingspace/time,rather

thansimplespace

Accountfortheneed,when

consideringspace/time,to

defineeventsusingfour

dimensions

In1905,AlbertEinsteinproposedthatthespeedof

lightisconstantandisindepe

ndentofthe

speedofthesourceo

rtheobserver.Thispremiseex

plainedthenegativeresultof

theMichelson-

Morleyexperimenta

ndshowedthattheetherconceptwasnotneeded.

Asaconsequenceofthislawoflightitcan

beshownthatthereisnosuch

thingasan

absoluteframeofref

erence.Allinertialreferencefr

amesareequivalent.Thatis,allmotionis

relative.Thelawsof

physicsarethesameinallfram

esofreference;thatis,theprincipleof

relativityalwaysholds.

InNewtonianphysics,distanceandvelocitycanbe

relativeterms,buttimeisanab

soluteand

fundamentalquantity

.Einsteinradicallyalteredthe

assumptionsofNewtonianphy

sicssothatnow

thespeedoflightisabsolute,andspaceandtimearebothrelativequantitiesthatdependuponthe

motionoftheobserver.(Ourrealityiswhatwemeasureittobe.Realityandobservationcannotbe

separated.Rememberthisasweproceed).

Inotherwords,themeasuredlengthofanobjectandthetimetakenbyaneventdependentirely

uponthevelocityoftheobserver.(Thisiswhyourc

urrentstandardoflengthisdefinedintermsof

timethemetreisth

edistancetravelledbylightin

avacuuminthefraction1/299792458ofa

second).

Furthertothis,sinceneitherspacenortimeisabs

olute,thetheoryofrelativityhasreplacedthem

withtheconceptofa

space-timecontinuum.(Space

andtime,notjustspace,arere

lative

quantities).

Anyeventthenhasfourdimensions(threespace

coordinatesplusatimecoordin

ate)thatfully

defineitspositionwithinitsframeofreference.


17/69

WilliamKimHSCPhysic

sSummary|page17

Explainqualitativelyand

quantitativelythe

consequenceofspecial

relativityinrelationto:

Therelativityof

simultaneity

Theequivalencebetween

massandenergy

Lengthcontraction

Timedilation

TheRelativityofSimultaneity(simultaneityandthevelocityoflight)

Observersinrelative

motionwilldisagreeonthesim

ultaneityofeventsseparated

inspace.

TheEquivalenceBe

tweenMassandEnergy

Themassofamovin

gobjectisgreaterthanwhen

itisstationaryitexperiencesmassdilation

(coveredlater).

Sincecisthe

maximumspeedintheunivers

eitfollowsthatasteadyforce

appliedtoan

objectcannotcontinuetoaccelerate.Itfollowsthattheinertia,thatistheresistance

toacceleration,

mustincrease.Butin

ertiaisameasureofmassandsothemasshasincreased.

Itisthisincre

aseinmassthatpreventsanyo

bjectfromexceedingthespeed

oflight,because

asitacceleratestohighervelocitiesitsmassincreases,whichmeansthatfurtherac

celerationswill

requireevengreaterforce.Thisisfurthercomplicatedbytimedilationbecause,as

speedsincrease

tonearlightspeed,anyappliedforcehaslessandle

sstimeinwhichtoact.Thecombinedeffectis

thatasmassbecomesinfiniteandtimedilates,anin

finiteforcewouldberequiredtoachieveany

accelerationatall.Su

fficientforcecanneverbesuppliedtoacceleratebeyondthespeedoflight.

Ifforceisapp

liedtoanobject,thenworkisdoneonitenergyisgiventotheobject.This

energywouldtaketh

eformofincreasedkineticene

rgyastheobjectspeedsup.Bu

tatnearlight

speedtheobjectdoesnotspeedup.Theappliedforceisgivingenergytotheobjectandtheobject

doesnotacquirethekineticenergywewouldexpect.Instead,itacquiresextramas

s.Einsteinmade

aninferencehereand

statedthatthemass(orinertia

)oftheobjectcontainedtheex

traenergy.

Relativityres

ultsinanewdefinitionofenergyasfollows:

whereE=totalenergy,Ek=

kineticenergy,m=mass,c=speedoflight

Whenanobjectisstationary,ithasnokineticenergy,butstillhassomeenergyduetoits

mass.Thisis

calleditsmassenergyorreste

nergyandisgivenby:

whereE=restenergy(J),m=mass(kg),c=speedoflight(3x

108ms-

1)

2

mc

E

E

k+

=

2

mc

E=


18/69

WilliamKimHSCPhysic

sSummary|page18

Discusstheimplicationsof

timedilationandlength

contractionforspacetravel

Tomeasurespeedweneedtomeasuredistanceand

time.Ifcremainsconstant,the

nitfollowsthat

distance(length)and

timemustchange.Spaceandtimearerelativeconcepts.

LengthContraction

(theLorentz-FitzGeraldContr

action)

Thelengthofamov

ingrodappearstocontractinthedirectionofmotionrelative

toastationary

observer.

wherelisthemovinglength,l0istherestlength(thatis,theleng

thasmeasured

byanobserveratrestwithrespecttotherod)andvisthespeedof

therod.

TimeDilation

Timeinamovingf

rameappearstogoslowerrelativetoastationaryobserver

whe

retistheobservedtimefora

stationaryobserverandt0isth

etimeforan

observertravellingintheframe.t0iscalledthepropertime(thisisthetime

mea

suredbyanobserverpresentatthesamelocationastheeventsthatindicate

thestartandendofanevent).

MassDilation

Themassofamovingobjectisgreaterthanwhen

itisstationary.

whe

remisthemassforamovingobjectandm0isthemassforthatobjectwhen

itis

stationary.

Therelativityoftime

allowsforspacetravelintothefuturebutnotintothepast.W

hentravellingat

relativisticspeeds(0.1corfaster),relativityinfluencesthetimethatpassesonthes

pacecraft.

Astronautsonarelativisticinterstellarjourneywouldfindtheirtriphastakenfeweryearsthan

observedonEarth.

ImplicationsofSpecial

Relativity:

22

0

1

cv

l

l

=

22

0

1

cvt

t

=

22

0

1

cvm

m

=


19/69

WilliamKimHSCPhysic

sSummary|page19

Cor

eTopicTwo:MotorsandGe

nerators

1.M

otorsusetheeffectofforceso

ncurrent-carryingconductorsinmagneticfields

Identifythatmovingcharged

particlesinamagneticfield

experienceaforce

Chargedparticlesmo

vinginanexternalmagneticfieldwillexperienceaforce.Ift

hemoving

chargedparticlesare

flowingthrough,andconfined

within,aconductorthatisinanexternal

magneticfield,theconductorwillalsoexperiencea

force.Thiseffectisknownasthemotoreffect.

F=qvB

UselefthandFBIgun

Anexample:VanAllenRadiationBelts

TheEarthsmagneticfieldcaptureschargedparticlesfromthesolarwind(lowene

rgy)andcosmic

rays(highenergy).T

hechargesareforcetospiralalongthefieldlinesaccumulatin

gintotwo

doughnut-shapedbeltsofradiationcalledtheupperandlowerVanAllenradiatio

nbelts.


20/69

WilliamKimHSCPhysic

sSummary|page20

Discusstheeffect,onthe

magnitudeoftheforceona

current-carryingconductor,

ofvariationsin:

Thestrengthofthe

magneticfieldinwhich

it

islocated

Themagnitudeofthe

currentintheconductor

Thelengthofthe

conductorintheexternal

magneticfield

Theanglebetweenthe

directionoftheexternal

magneticfieldandthe

directionofthelengtho

f

theconductor

Theforceispropo

rtionaltothemagneticfieldstr

ength,B

Theforceispropo

rtionaltothecurrent,I

Theforceispropo

rtionaltothelength,L

Theforceisatam

aximumwhentheconductoris

atrightanglestothefield,and

iszerowhenthe

conductorisparallel

tothefield.Themagnitudeoftheforceisproportionaltothecomponentofthe

fieldthatisatrightanglestotheconductor.

sinBIl

F=


21/69

WilliamKimHSCPhysic

sSummary|page21

Describequalitativelyand

quantitativelytheforceon

longparallelcurrent-carrying

conductors:

(Ampereslaw)

AmperesLaw

Twoparallelwires,e

achcarryingacurrent,willexe

rtaforceontheother.Thishappensbecause

eachcurrentproduce

samagneticfield(asinOerste

dsexperiment).Thereforeeac

hwirefindsitself

carryingacurrentacrossthemagneticfieldproduce

dbytheotherwireandhenceexperiencesa

force.

Determiningthema

gnitudeoftheforcebetween

twoparallelconductors

Themagneticfieldstrengthatadistance,d,fromalongstraightconductorcarryingacurrent,I,can

befoundusingthefo

rmula:

wherek=2.0x10-7 NA-2

Themagnitudeoftheforceexperiencedbyalength,l,ofaconductorduetotoanexternalmagnetic

fieldis:

Ifcurrentsareinthe

samedirection,thenthecondu

ctorswillattract.

Ifcurrentsareinopp

ositedirections,thentheconductorswillrepel.

dIIk

lF

2

1

=

dkI

B=

dIIk

lFrearrangeddkI

lI

For

lBI

F

2

1

1

22

=

==

d

I1

I2


22/69

WilliamKimHSCPhysic

sSummary|page22

Fd

=

b

Definetorqueastheturning

momentofaforceusing:

Identifytheforces

experiencedbyacurrent-

carryingloopinamagnetic

fieldanddescribethenet

resultoftheforces

Generally,=nBIAcos!

Torqueisturningforce.ItsunitsareNewton-met

res(Nm).

where

=torque,inNm

F=force,inN

D=distancefromrotationalaxis,inm

CurrentLoops

Fd

=

d

l

F=BIl

=BIld

F=BIl

=BIld

Rotationalaxis

I

N

S

BIA

d

l

BIB

Ild

BIld

BIld

=

==

+

=

+

=

)2

(2

2

1

(Forea

chturnoftheloop)

b b

max=nBIA

zero

=nBIAcos!


23/69

WilliamKimHSCPhysic

sSummary|page23

Accountforthemotoreffect

duetotheforceactingona

current-carryingconductor

in

amagneticfield

Describethemainfeatures

of

aDCelectricmotor

Discusstheimportanceoft

he

inventionofthecommutato

r

fordevelopingelectric

motors

Describetheroleofthemetal

splitringandthebrushesin

theoperationofthe

commutator

Describehowtherequired

magneticfieldscanbe

producedeitherbycurrent-

carryingcoilsorpermanent

magnets

Themotoreffect

Recallthatchargedp

articlesmovinginanexternalmagneticfieldwillexperienceaforce.Ifthe

movingchargedparticlesareflowingthrough,andconfinedwithin,aconductorthatisinan

externalmagneticfie

ld,theconductorwillalsoexperienceaforce.

Anelectricmotorisadevicethattransformselectricalpotentialenergyintorotatio

nalkinetic

energy.

AnatomyofaDCm

otor

-

Permanentma

gnets:provideanexternalmagneticfieldinwhichthecoilro

tates.Asthe

magnetsarefix

ed,theyareknownasthestato

r.

-

Rotatingcoil:

carriesadirectcurrentthatinte

ractswiththemagneticfield,p

roducingtorque.

-

Armature:ism

adeofferromagneticmaterial

andallowsthecoiltorotatefreelyonanaxle.

Thearmatureandcoiltogetherareknownastherotor.Thearmatureprotrud

esfromthe

motorcasing,e

nablingthemovementofthecoiltobeusedtodowork.

-

Commutators:reversethecurrentofthecoil

everyhalfturntomaintaincon

sistentdirection

andtorque.Itisamechanicalswitchthatautomaticallychangesthedirection

ofthecurrent

flowingthroughthecoilwhenthetorquefalls

tozero.

-

Brushes:maintainelectricalcontactofcoilsw

iththerestofthecircuit.

ThedevelopmentofDCmotorsoutstrippedthatofACmotorsandgeneratorsfortworeasons:

-Voltaicbatteriesco

uldsupplypower

-Theycouldusepow

erfulelectromagnetsthatwere

farstrongerthanpermanentm

agnets

Thedevelopmentofthecommutatorwasimportant

becauseitledtothedevelopmentofmodern

electricmotorsandg

enerators.Itenabledmotorsto

providesteadycircularmotion

ofadriveshaft.

ThemagneticfieldofaDCmotorcanbeprovidedeitherbypermanentmagnetsor

by

electromagnets.


24/69

WilliamKimHSCPhysic

sSummary|page24

2.T

herelativemotionbetweenaconductorandmagneticfieldisusedtogenerateanelectricalvoltage

OutlineMichaelFaradays

discoveryofthegeneration

of

anelectriccurrentbya

movingmagnet

Faradayhadfoundth

at3thingsarenecessarytogenerate(orinduce)anEMF(voltagesupply):

-

Amagneticfield(fromsomemagne

tsorelectromagnet)

-

Acon

ductor(eg.wireorcoilofwire)

-

Relativemotion/changebetweenthefieldandtheconductor

Iftheconductorform

edaclosedloopthenaninducedcurrentwouldalsoflow.

Ifthiswireisdroppe

dsothatitcutsfluxlines,then

avoltageappearsbetweenthe

endsbecause

electronsareforcedtotheright.Theyeventuallysto

pmovingbecausetheycreateanelectricfield

pushingthemback.

Aslongasthemagnetismoving,anemfandcurren

tisinduced.

FaradaysLaw

wire

v

B

occur

to

for

taken

time

min

coil

of

area

A

Tin

strength),

(field

de

nsity

flux

magnetic

BBA

in

Wb

flux,

magnetic

in

change

coil

on

turns

of

number

Vin

EMF,

induced

where

2

===

=

=

=

=

=

=

n

n

Theinducedvoltagecanbeincreasedby:

Increasingn:moreturnsonthecoil

IncreasingB:usestrongmag

nets

IncreasingA:useabiggerco

il

Decreasingt:gofaster!


25/69

WilliamKimHSCPhysic

sSummary|page25

Definemagneticfield

strengthBasmagneticflux

density

Explaintheconceptof

magneticfluxintermsof

magneticfluxdensityand

surfacearea

Explaingeneratedpotential

differenceastherateof

changeofmagneticflux

throughacircuit

AccountforLenzsLawin

termsofconservationof

energyandrelateittothe

productionofbackemfin

motors

Magneticfluxdensityisthemagneticfluxperunit

areaandisameasureofthemagneticfield

strength.

Theinducedemfisp

roportionaltotherateofchang

eoffluxthroughthecircuit.SeeFaradaysLaw

(above).

LenzsLaw

ThisisasupplementarylawtoFaradaysLaw.Itsaysthatanyinducedemforcurr

entwillhavea

directionthatoppose

sthechangethatcausedit.Thisisreallyjustarestatementof

thelawof

conservationofenergybecausetheinducedelectricalenergyhascomefromthethingthatcauses

theoriginalmotion.Eg.Inahydroelectricpowerstation,thekineticenergyofflow

ingwateris

convertedintoelectricalenergy.

N

in

Wb

flux,

magnetic

min

area,

Tin

density,

flux

magnetic

where

sin

2

=

=

=

=

A

BBA


26/69

WilliamKimHSCPhysic

sSummary|page26

Explainthat,inelectric

motors,backemfopposesthe

supplyemf

ApplyLenzsLawtothe

productionofeddycurrents

Backemf

Backemfisgenerate

dinanycoilthatexperiencesc

hangingBfields,eventhoughitisproducing

them.

Notethatbackemfisfrequencydependentthehig

herthefrequencyofthechangingfield,the

greaterthebackemf

produced.

Backemfisalsoproducedintherotatingcoilofam

otor:

-Whenthemotorisspinningatitsoperatingspeed,

backemfwillhaveitsmaxvalue,but

-Whenthemotorisjustturnedonitisntspinningyetsothereisnobackemf.

-Thiscanleadtoexcessivecurrentsothemotorma

ybeprotectedbyusingastartingresistance

thatlimitscurrent.W

henuptospeedtheresistoristakenoutofthecircuit.

EddyCurrents-areinducedcurrents(usuallyunw

antedorunintended)intwo-dimensional

conductors(eg.sheetmetal)orthree-dimensionalconductors(eg.ablockofsteel).Sometimesitis

necessarytodesigna

gainstthem.Eg.thecoreofam

otorismadeofsoftiron,andismadeofthin

layers(laminated)to

preventeddycurrents.

Somedevicesrelyoneddycurrentstowork:

Electromagneticbrak

ingamovingconductornearmagnetswillslowdownbecausetheeddy

currentsopposeitsm

otion.

ElectromagneticswitchingsecuritygatesthatarereallycoilswithACgenerate

ahighfrequency

Bfield.Metalinthis

fielddevelopseddycurrentsth

atworkagainstthefield,slowingitdown.A

detectorcircuitpicks

uponthisandsetsoffanalarm

.

InductionCooktops-

areanapplicationofFaradaysLaw.Insteadofaheatingelem

ent,thiscooktop

containsasetofcoilswithalternatingcurrentpassingthroughthem.ThisproducesachangingB

fieldabovethecooktop.Ametalsaucepanplacedonthecooktopisaconductorin

thechangingB

fieldandthereforeanelectriccurrentisinducedinthebaseofthepan.Thecurrent

heatsthepan,

andthisheatcooksthefood.Inductioncooktopsare

approximatelytwiceasefficie

ntasagas

cooktop,butareexpensivetopurchase.

Thecoilbecomesan

electromagnetandgenerate

san

alternatingBfieldBUTitalso

experiencesthechangingB

fieldandgeneratesitsownemf

thatopposestheappliedemf.

Movement

ofmetal

Eddycurrentloop


27/69

WilliamKimHSCPhysic

sSummary|page27

3.G

eneratorsareusedtoprovidelargescalepowerproductionin

isolatedareasandasabackupinemergencysituations

Identifythemaincomponents

ofagenerator

Comparethestructureand

functionofageneratortoan

electricmotor

Describetheoperationofan

ACandaDCgenerator

Anelectricgenerato

r(dynamo)isadevicethatinc

ludesalloftheelementsnecessarytotransform

mechanicalkineticenergytoelectricityaccordingtoFaradaysLaw:

-

Amagneticfield(providedbyasetofperman

entmagnets);

-

Aconductor(a

coilmountedonanaxle,soitcanspin);

-

Relativemotion(thecoilismadetospinbyso

meotherformofenergy).

Infact,mostgeneratorsareconstructedjustlikeam

otor,howevertheflowofenergythroughthem

isdifferent.

Motor:electricalenergyk

ineticenergy

Generator:kineticen

ergye

lectricalenergy

EMFisgeneratedin

thecoilandacircuitiscompletedtotheoutsideworldthroughringconnectors,

justlikemotors.Ifstandardslipringsareusedthen

adynamonaturallyproducesalternatingcurrent

AC.

Ifasplitringcommu

tatorisusedinstead,thenthed

irectionofthecurrentflowing

fromthecoilis

reversedeverycyc

le.Thisproducesapulsingtyp

eofdirectcurrentDC.

t

+ -I

t

+ -I

t

EDoublingthefrequencyof

rotationdoublesthe

maximuminducedemf


28/69

WilliamKimHSCPhysic

sSummary|page28

Discusstheenergylossesthat

occurasenergyisfed

throughtransmissionlines

fromthegeneratortothe

consumer

Analysetheeffectsofthe

developmentofACandDC

generatorsonsocietyandthe

environment

Assessevidenceaboutthe

physiologicaleffectson

humanslivingnearhigh

voltagepowerlines

Evengoodelectrical

conductorslikecopperusedto

supplyelectricity,sometimesthrough

considerablecablele

ngthstotownsandcities,generatesubstantialresistances.Itfollowsthatto

minimiseenergylossinthewires,thecurrentneeds

tobekeptlow(heatinglosses

varyasthe

squareofthecurrent).Thisisachievedbytransmittingtheenergyathighvoltages.

Positive

Negative

Impacton

society

-Improvedlifestyle

-S

treetlighting

-E

lectrictrains

-C

ommunication

-C

omputerisationofmanysystem

s

e

g.banking,stockmarket

-Industrialdevelopmentmore

jobs

-

Possibleriskofcancerlivingnear

distributioncables

-

Longerworkinghours

-

Relianceonelectricityleavesus

vulnerabletosystemslossdueto

electricalfailure

Impacton

environment

-L

otsofelectrictrainshavereduced

p

ollutionfromsteamtrainsand

m

adepublictransportmore

a

vailable

-E

lectricityhasreplacedolder,

m

ore-pollutingtechnologieseg.

e

lectricalheatinginsteadofcoal

b

urninginfireplaces

-

Burningcoalinpowerstations

producessmokeand

CO2(a

greenhousegas)

-

Nuclearpowerstatio

nsproduce

radioactivewater&haveariskof

nuclearaccident

-

Hydroelectricschemesredirect

waterawayfromriverhabitats

-

Miningimpactsnega

tivelyon

environment

-

Visualpollutionofcables

1979studyfoundchildrenlivingnearhighvoltagepowerlinesappearedtodevelopaparticular

formofcancer.1997

studyshowednoevidenceofanincreaseriskofchildhoodca

ncerat

residentialmagnetic

fieldlevels.1998panelstatedthatEMfieldsshouldbeconsid

eredpossible

humancarcinogens

andthatthereisnoconclusiveandconsistentevidencethatE

Mfieldscause

anyhumandisease.


29/69

WilliamKimHSCPhysic

sSummary|page29

4.T

ransformersallowgeneratedvoltagetobeeitherincreasedor

decreasedbeforeitisused

Explainthepurposeand

principlesoftransformersin

electricalcircuits

Comparestep-upandstep-

downtransformers

Determinetherelationship

betweentheratioofthe

numberofturnsinthe

primaryandsecondarycoils

andtheratioofprimaryto

secondaryvoltage

Atransformerisad

evicethataltersthevoltageandcurrentofanelectricitysupply.

TheACvoltagesour

ceproducesanalternatingcurrentintheprimarycoil.Thisproducesan

alternatingBfieldthatthreadsthroughthesecondarycoil.Thesecondarycoilnow

has:

-

Conductor

-

Bfield

-

Change

andthereforegeneratesitsownvoltage.Ifthereisa

closedloopthenanalternating

currentwill

flowaswell.

Step-uptransformers

:increasevoltageanddecrease

current

Step-downtransformers:decreasevoltageandincre

asecurrent

Vp=primaryvoltage

(voltagein)

Ip=primarycurrent

np=numberofturns

onprimarycoil

Vs=secondaryvolta

ge(voltageout)

Is=secondarycurren

t

ns=numberofturns

onsecondarycoil

If100%efficient(thisneedsperfectfluxlinkage,

usuallyusinganironcore)then:

Powerinprimary=P

owerinsecondary

sp

sp

nn

VV

=

ps

sp

sp

ps

sp

s

s

p

p

II

nn

VV

II

VV

IV

IV

=

=

=

=


30/69

WilliamKimHSCPhysic

sSummary|page30

Explainwhyvoltage

transformationsarerelated

to

theconservationofenergy

Explaintheroleof

transformersinelectricity

sub-stations

Discusswhysomeelectrica

l

appliancesinthehomethat

areconnectedtothemains

domesticpowersupplyuse

a

transformer

Analysetheimpactofthe

developmentoftransformers

onsociety

ThePrincipleofCon

servationofEnergystatesthat

energycannotbecreatedordestroyedbutthatit

canbetransformedfromoneformtoanother.Thismeansthatifastep-uptransformergivesa

greatervoltageatthe

output,itscurrentmustbedec

reased:i.e.powerin=powero

ut.

NSWpowerstations

produceelectricitywithavoltageofabout23,000Vandacurrentofabout

30,000A.Unfortunately,thisamountistoohighto

besentthroughacable.Thisis

becauseitheats

thecablecausingene

rgyloss.Thisiscalledjouleheatingandhappensbecause:

P=I2R

Sotoreducejoulehe

ating,thecurrentmustbereducedasmuchaspossiblewitha

step-up

transformer.

Additionaltransform

ersbetweenthepowerstationandconsumer(insub-stations)

graduallystep-

downthevoltage,to

240Vbythetimeitgetstohouseholdusers.Thisisbecausea

thighvoltages,

electricitycanconductthroughair,makingitdangerousforuseinthehome.

Mostelectroniccircu

itsaredesignedtooperateatlo

wDCvoltagesofbetween3V

and12V.

Therefore,household

appliancesthathaveelectroniccircuitsinthemwillhaveeith

eraplug-in

transformeroraninb

uilttransformertostepdownthedomestic240Vsupply.Thesetransformers

alsohavearectifiercircuitbuiltintothemthatconv

ertsACtoDC.

TVsalsocontainastep-uptransformerforproducin

gthehighvoltagesneededfor

theCRT.

Thedevelopmentofthegeneratorandtransformerh

asallowedforthesettingupofnationalpower

gridsinalmostevery

country,makingthatmostcon

venientandflexibleformofen

ergy,electricity,

accessiblefrommanymilesaway.Thetransformersroleistostepvoltageupand

downtomake

efficienttransportationanddistributionpossible.


31/69

WilliamKimHSCPhysic

sSummary|page31

5.M

otorsareusedinindustriesandthehomeusuallytoconverte

lectricalenergyintomoreusefulformsofenergy

Describethemainfeatures

of

anACelectricmotor

ExplainthatACmotors

usuallyproducelowpower

andrelatethistotheirusein

powertools

Explaintheadvantagesof

inductionmotors

ACinductionmotor:

-

Therotorend

ringsshortcircuitnon-ferrous

rotorbars,thatissealedi.e.n

oexternal

connectionsatall(usuallyasquirrelcage).Encasedinalaminatedironarm

ature.

-

Thestatorsurroundingelectromagnet.

-

ConnectiontostatorthesurroundingelectromagnetreceivestheAC.

InanACinductionmotor,theprincipleofoperationis:

1.ACtosurroundingelectromagnet,which

2.Producesanoscillating(rotating)Bfield,which

3.Inducesacurrentintherotor,which

4.Turnstherotorintoanelectromagnetthat

5.Triestooppo

sethefieldbeinggeneratedby

thestator.

6.Thestatorandtherotorpushagainsteachot

her(usingtheirBfields),which

7.Causesthero

tortoturn!Brilliant!

Poweristherateofwork.Workisdonewhenenergyistransformedfromonetypetoanother.

Inductionmotorsare

consideredtoproducelowpow

erbecausetheamountofmechanicalwork

theyachieveislowc

omparedwiththeelectricalenergyconsumed.Thelostpowerofinduction

motorsisconsumedinmagnetisingtheworkingpar

tsofthemotorandincreatinginduction

currentsintherotor.

ACinductionmotorsareconsideredtobeunsuitableforuseinheavyindustry

becausetheirlowpowerratingwouldmakethemto

oexpensivetorunwhenperformingaspecific

task.However,theyareusedextensivelyinpowertoolsandelectricdomesticapplianceswherethe

lossofpowerisnoteconomicallysignificant.

AdvantagesofACinductionmotors:

1.Simplicityof

design;

2.Highefficiency(hencelowmaintenancetherearenobrushesorcommutatorstowearout);

3.Relativelylowcost

AC(synchronous)motor:

-

Arotatingcoil

-

Surroundingmagnets

-

Connectiontocoilviaslip

rings(commutatorforD

C

motor)


32/69

WilliamKimHSCPhysic

sSummary|page32

Cor

eTopicThree:FromIdeastoImplementation

1.Increasedunderstandingsofcath

oderaysledtothedevelopmentoftelevision

Explainthatcathoderay

tubesallowedthe

manipulationofastreamof

chargedparticles

Explainwhytheapparent

inconsistentbehaviourof

cathoderayscauseddebate

as

towhethertheywerecharged

particlesorelectromagnetic

waves

DischargeTubes

-

Investigationofvacuumtubescouldnotoccuruntilgoodvacuumpumpshad

beeninvented.

Avacuumtube

isaglasstubefittedwithanelectrodeateitherend,andalmostalloftheair

suckedout.

-

Thepositiveelectrodeistheanode;Theneg

ativeelectrodeisthecathode.Whenahigh

voltageisconnectedbetweentheelectrodes,a

ninvisibleraytravelsfromthe

cathodetothe

anode.Theywerecalledcathoderays.Cathoderayscauseglasstoglowgreen.

-

Adischargetubeisacathoderaytubewithavacuumpumpfitted,sothatthe

airpressure

insidethetube

canbevaried.Atdifferentairp

ressures,differentbrighteffectsappearinthe

tubese.g.bands,striationsanddarkspaces.Thesearecausedbycathoderays

strikingatoms

intheairinside

thetube.Theatomsbecomeexcitedthenreleasephotonsofv

isiblelight

-

Abeamofelectronstravelsfromthecathodetotheanodeandcanbedeflectedbyelectrical

and/ormagneticfields.

In1892Hertzdemon

stratedthatcathoderayscould

penetratethinmetalfoils.This

hebelieved

supportedawavenature.

In1895Jean-Baptise

Perrinshowedthatcathoderaysdepositednegativechargeso

nimpactwithan

object,suggestingaparticlenature.

Therewascontroversyoverthenatureofcathodera

yswavesorparticles.

Cathode

Anode

Glassglowshere


33/69

WilliamKimHSCPhysic

sSummary|page33

Identifythatchargedplates

produceanelectricfield

Describequantitativelythe

forceactingonacharge

movingthroughamagnetic

field

Discussqualitativelythe

electricfieldstrengthduetoa

pointcharge,positiveand

negativechargesand

oppositelychargedparallel

plates.

Describequantitativelythe

electricfielddueto

oppositelychargedparallel

plates

Ifmetalplatesareseparatedbyadistanceandareattachedtoapowersource,anelectricfieldwill

beproducedbetween

them.E=V/d

Recallthattheforce

(F)actingonacharge(q)movingwithavelocity(v)atanang

letoamagnetic

field(B),isgivenby:

WhereFB=magneticforce(N)

q=charge(C)

v=velocityofcharge(ms-

1)

B=magneticfieldst

rength(T)

Ifapositivechargeisplacednearanotherpositivec

harge,itwillexperienceaforceofrepulsion.

Apositivechargepla

cedinafieldwillexperiencea

forceinthedirectionofthearrow.

Anegativechargeplacedinafieldwillexperienceaforceoppositetothedirection

ofthearrow.

WhereFE=electricforce(N)

q=charge(C)

E=electricfieldstre

ngth(NC-1)

qvB

FB=

++++++++

-----------

qE

FE

=


34/69

WilliamKimHSCPhysic

sSummary|page34

BE

v

qE

qvB

F

F

E

M =

==

OutlineThomsons

experimenttomeasurethe

charge/massratioofan

electron

J.J.ThomsonsExperiment

-

ByfittingplatestohisCRT,hecouldsubjectthecathoderaystoanelectricfield.Therays

deflected,provingthattheywerechargedparticles,notelectromagneticwav

es.

-

Henoticedthattheraysdeflectedtowardthepositiveplate,provingthattheyw

erenegatively

chargedparticle

s.

-

Bycrossingelectricandmagneticfields,Thoms

onwasabletodeducethevelocityofthe

cathoderays.

-

ByturningofftheEfield,theparticlesfollowed

acirculararccausedbytheB

field.The

magneticforcew

asactinglikeacentripetalfor

ce.

-

ThomsonhadalreadymeasuredBandworkedo

utv.Bymeasuringtheradiusofcurvaturer,he

couldthencalculateq/m,i.e.thecharge/massr

atioofanelectron.

-

q/mfortheseparticleswas1800timesgreaterthanforahydrogenion,thesimplestknown

atomicion.

-

Thomsonquickly

comparedthechargesandfou

ndthemtobeaboutthesame(thoughopposite

insign)

-

Thereforemassforcathoderayparticleswas1800timessmallerthanhydroge

n

-

Thereforecathod

erayparticlesweresubatomic

particles!

-

Thisw

asthefirstdiscoveryofsubatomicparticles

-

Theywerelatercalledelectrons.

Brv

mq

rmv

qvB

=

=

2

Cathoderayparticles

B

E

MF

EF

Thomsonadjustedthestrength

ofthefieldssothattheparticles

werenotdeflected.

Bycarefullymeasuringthe

strengthofthefields,Thomson

couldcalculatev.


35/69

WilliamKimHSCPhysic

sSummary|page35

Outlinetheroleinacathode

raytubeof:

Electrodesinthe

electrodegun

Theelectricfield

Thefluorescent

screen

TheCathodeRayT

ube

EachCRThasavacuumtube/chamber,acathode,a

nanode,andatarget.

Electrodesintheelectrongun

Theelectrongunpro

ducesanarrowbeamofelectro

ns.Itconsistsofafilament,ac

athodeandtwo

open-cylinderanodes.Theanodeshelptoaccelerateandfocustheelectrons.

Aringshapedelectrodethegridbetweenthecathodeandanodescontrolstheb

rightnessofthe

spotbycontrollingthenumberofelectronsemitted

bythegun.Bymakingthegrid

negativewith

respecttothecathodethenumberofelectrons,andhencethebrightnessisreduced.

Theelectricfield

Actsasadeflectionsystem.Itconsistsoftwosetsofparallelplatesconnectedtoa

parallelplates

connectedtoapotentialdifference.Thisproducesanelectricfieldbetweentheplates.TheY-plates

controltheverticaldeflectionandtheX-platestheh

orizontaldeflection.

Thefluorescentscreen

Theinsideglassofth

eendofthetubeiscoatedwithafluorescentmaterialforexample,zinc

sulphide.Whenanelectronbeamhitsthescreen,thecoatingfluorescesandaspot

oflightisseen

onthescreen.Thesc

reenactsasadetectorofcatho

derays.

Anode

Cath

ode

Electrons

Toplatesandscreen


36/69

WilliamKimHSCPhysic

sSummary|page36

Outlineapplicationsof

cathoderaysinoscilloscopes,

electronmicroscopesand

televisionsets

Discusstheimpactof

increasedunderstandingsof

cathoderaysandthe

developmentofthe

oscilloscopeonexperiment

al

physics

TheCathodeRayO

scilloscope(CRO)

Isanelectronicsdiag

nosticsdevicebecauseitcanshowagraphofhowvoltagesvaryovertime.

Deflectionoftheelectronbeamisachievedbytwosetsofplates.

Horizontalplatescau

severticaldeflectionwhileverticalplatescausehorizontalde

flection.

TVTube

Anelectrongunagainproducestheelectronbeam.Coilsareusedinsteadofplates,however.

Electriccurrentthrou

ghthecoilsproducemagnetic

fieldsthatcandeflectthebeam

squicklyfrom

sidetoside,andmoreslowlyfrombottomtotop.In

thiswaythebeamscanstheentirescreen.By

varyingtheintensity

ofthebeam,apictureisbuiltu

p.Thepictureisrefreshed50times/second,

whichistoofasttob

enoticedbythehumaneye.

TheElectronMicro

scope

Useselectronsinstea

doflight.Theirwavelengthis

100,000timessmallerthanvisiblelight,

thereforetheirresolv

ingpoweris100,000timesgre

ater.

-

Asampleisplacedinsidethechamber(which

isreallytheCRT)

-

Theairisthensu

ckedout

-

Anelectrongunproducestheelectronbeam

-

Coilsproducemagneticfieldstofocusthebeam

(magneticlenses)

-

Thebeamscansoverthesurfaceofthesample

-

Detectorspickup

thereflectedandscatteredelectronbeam,andfromthisinfor

mationa3

dimensionalimageisconstructed

Theintroductionofe

lectroniccontrolsystemsinto

allformsofscienceandindustryhasseenthe

cathoderayoscillosc

ope(CRO)becomeoneofthemostwidelyutilisedtestinstruments.Because

ofitsabilitytomake

voltagesvisible,thecathode

rayoscilloscopeisapowerfuldiagnosticand

developmenttool.


37/69

WilliamKimHSCPhysic

sSummary|page37

2.T

hereconceptualisationofthem

odeloflightledtoanundersta

ndingofthephotoelectriceffectandblackbodyradiation

ExplainqualitativelyHertzs

experimentsinmeasuringthe

speedofradiowavesand

howtheyrelatetolightwaves

Recall:Maxwellsth

eoryofelectromagneticwaves

In1864Maxwell,throughasetoffourbrilliantequations,predictedarangeofinvisiblewaves

madeupofanelectricandmagneticwavethatregenerateeachother.Thespeedof

thesewaveswas

calculatedtobe3x1

08ms-

1andprobablyincluded

light.

HeinrichHertzsExperiment:(provingMaxwellstheory)

Performedin1886,H

ertzbuiltequipmenttogenerateandtransmitEMwaveswith

!

"

1m.Healso

hadaseparatereceiv

er(aloopofwire)locatedabout20maway.Sparkgapswereincludedtoshow

whenhighvoltageA

Cwaspresentinthetransmitte

rorreceiver.Thereceiversparkonlyappeared

whenthetransmitter

sparkwaspresent.Hertzhypothesisedthatthesparkssetupchangingelectric

andmagneticfieldsthatpropagatedasanelectromagneticwave,aspostulatedbyMaxwell.He

showedthatthesewerewavesbeingtransmittedbecausehecouldreflect,refractandpolarisethem.

Bymeasuringthefre

quency,hecalculatedv(v=f!

)anditcameoutas3x108ms

-1.These

propertiesprovedMaxwellstheoryandastheyare

alsoexhibitedbylight,Hertzw

asableto

provideexperimentalevidencethatlightisaformoftransverseelectromagneticwave.

v

B

E

toinduction

coil

tra

nsmitter

charged

plates

receiver

0K)thenitvibra

tes,whichcontributestotheco

llisionsandthe

resistanceofthelattice.Ifitstemperatureisreduced

,thenthevibrationsalsoreduc

e,loweringthe

resistance.Theresist

anceofapuremetaldropstozeroat0K.

nAe

I

v=

)

(

nvAe

I=


50/69

WilliamKimHSCPhysic

sSummary|page50

Identifythatsuperconducto

rs,

whilestillhavinglattices,

allowtheelectronstopass

throughunimpededwithno

energylossatparticular

temperatures

Explaincurrenttheorythat

suggeststhatsuperconductors

areconductingmaterialsthat,

atspecifictemperatures,

forceelectronstopairand,

throughinteractionswithth

e

crystallattice,areultimately

abletoformanunimpeded

orderlystream

Superconductors

Somematerials,calledsuperconductors,achievezeroresistancesuddenlyatsom

enon-zero

temperature,calledthecriticaltemperatureortransitiontemperature(Tc).

TheBCSTheoryof

Superconductivity

ThisistheNobelPrizewinningtheorytoexplain(type1)superconductivityfromBardeen,Cooper

andShrieffer.

Thetheorystatesthatsuperconductivityistheresultoftheinteractionbetweenelectronpairs(called

Cooperpairs)andvibrationsofthecrystallattice:

-

Afirstelectrontravellingthroughthelatticeattr

actsthepositiveionsandthisd

istortsthelattice.

-

Thedistortioncreatesaconcentrationofpositivechargethatattractsaseconde

lectron.

-

Thesecondelectronridesthewavebehindthe

firstelectron.

-

Thesonicfrequencyvibrationofthelatticeform

senergyunitscalledphonons

.Theexchange

ofphononenergy

fromthefirsttothesecondelectronkeepsthecooperpairtogetherforsome

time.

Temperature(K)

Resistance()

Normalconductivity

Superconductivity

Criticaltemperature,Tc

Limitingconditions:

-

tccriticaltemperature

-

Iccriticalcurrent

-

Bccriticalmagneticfield


51/69

WilliamKimHSCPhysic

sSummary|page51

Discusstheadvantagesof

usingsuperconductorsand

identifycurrentlimitations

to

theiruse

ApplicationofSupe

rconductors

PowerTransmission

Oneofthebiggestproblemswithcurrentpowertransmissionsystemsisjouleheating.The

resistanceofthecablecausesthecabletobeheated.Thisrepresentsalossofenerg

y.SinceP=I2R,

thejouleheatingisproportionaltoI2.Hencetransfo

rmersareusedtolowercurrentasmuchas

possiblepriortotransmission,andthisnecessitatestheuseofACelectricity.

Ifsuperconductorscouldbeusedfortransmissioncablesthentheirzeroresistance

meansthatno

energywouldbelost

(i.e.nojouleheating).

-

Cableofsamesizecouldcarry3to5timesasm

uchcurrent

-

DCisthemorelogicalchoicebecause

-

Dontneed

tolowercurrent

-

Dontneed

transformers;and

-

ACinvolve

saslightenergyloss

Advantages

-

Nojouleheating,henceenergysavings

-

Thiswouldlowerdemandfornewpowerstations

-

Greaterefficiencymeanslesswastageandlessdemandforfuel,andthereforeless

environmentalim

pact

Disadvantages

-

Thecableswould

needtobekeptverycold

-

Installationcosts

wouldbehigh

-

Allapplianceswouldneedtoberedesignedtow

orkonDC

-

Currenthightemperaturesuperconductorsareceramicandthereforetoobrittle

tobemadeinto

wires


52/69

WilliamKimHSCPhysic

sSummary|page52

ApplicationofSuperconductors

PowerGeneration

Thehugedynamosinapowerstationcanalsobemademoreefficientwithsuperconductors

becausetheseuseele

ctromagnetstoproducethenecessarymagneticfield.Ifsuperconductorswere

usedtomaketheelectromagnetsthentheywouldbemoreefficient,makingthewh

oledevicemore

efficient.

PowerStorage

Thisissomethingthatisverydifficulttodowithcu

rrenttechnology,andmeansth

atpowerstations

mustadjusttheiroutputtothedemandatthetime.W

ithsuperconductors,alonglo

opcanfunction

asastoragedevice.C

urrentintroducedintotheloop

willcontinuetoflowaroundtheloop

indefinitely,andcanberetrievedwhenrequired.Apowerstoragedeviceconnected

toapower

stationwouldallowthestationtoruncontinuouslyatpeakefficiency,regardlessoffluctuationsin

demand.

Electronics

Mostelectronicswouldalsobecomemoreefficient

ifbuiltusingsuperconductors.

Considera

computerCPU.This

isa70Wdevice,whichmeans

thatheatgenerationisaproblemanda

limitationtohowfastitcanberun.Ifbuiltusingsuperconductors,thisheatproblemwouldbe

eliminated,allowing

theCPUtoberunatfasterspe

eds.Buthowcouldwereplace

the

semiconductortransistor?In1962,BrianJosephson

inventedasuperconductorswitchthatperforms

thesametaskasatra

nsistorswitchbutismuchfaster.ThisdeviceiscalledaJose

phsonJunction.

CPUsbuiltofthosewouldbeverymuchfasterthan

currentCPUs.

MedicalDiagnostics

AnMRImachinema

psthewatermoleculesinsideapersonsbodytobuildupa3Dcomputer

imageofthepersonsorgans.Itdoesthisbyhaving

alargesuperconductingcoilth

atproducesan

intensemagneticfield(4T).Thepersonliesinsidethecoil.Radiofrequencyradiationisdirectedto

thepatientsbodyan

dtheseconditionscausetheH

atomstovibrate.Thedevicepi

cksupthe

signalsproducedbytheHatoms,worksouttheirlocationsandmapsthem.

Th

eMeissnerEffect:

-

Superconductorsresistthe

penetrationofmagnetic

fieldsintothem

-

Theydevelopelectric

currentstomaketheirown

Bfieldtopushback

-

Thiscanbeusedtofloata

magnetovera

superconductor

-

Thismagneticlevitation

ideahasbeenusedin

Japantobuildan

experimentalmaglevtrain


53/69

WilliamKimHSCPhysic

sSummary|page53

OptionTopic:QuantatoQuarks

1.P

roblemswiththeRutherfordmodeloftheatomledtothesearchforamodelthatwouldbette

rexplaintheobservedphenom

ena

Discussthestructureofthe

Rutherfordmodelofthe

atom,theexistenceofthe

nucleusandtheelectron

orbits

J.J.ThomsonsMo

del

ThediscoveryofelectronsbyThomsonhadchangedtheviewonindivisibilityofa

toms.Thomson

wasabletodeterminethechargeandmassofelectronsandthemassoftheelectronwasfoundtobe

1800timeslighterthanthelightestatom,Hydrogen.Heconcludedthatelectronsaresub-atomic.

Heproposed

acrudemodeloftheatom,kno

wnastheplum-puddingmodel.Negative

electronsarelikeplu

msinthepositivepudding.

ErnestRutherfordsAlphaParticleScatteringExperiment

-

In1911GeigerandMarsden,attheinstigationo

fRutherford,performedanexperimentin

whichthenewly

discoveredpositivelychargedalphaparticleswerefiredatathingoldfoil.

-

Itwasobservedthatmostofthealphaparticlespassedthroughwithonlysmall

deflections(as

expectedwiththeThomsonmodeloftheatomo

fthetime).

-

Howeveritwasf

oundthatabout1in8000alphaparticlesdeflectedbackatanglesgreaterthan

90!Fromthisre

sult,Rutherfordproposedthattheonlywaythatthealphaparticlescouldbe

deflectedthrough

largeanglesisifalltheatomspositivechargeandnearlyallitsmasswas

concentratedina

smalldensenucleuswiththee

lectronssomedistanceaway.

-

Fromtheresultsofthealphaparticlescatteringexperiment,Rutherfordwasabletoshowthat

theatomismostlyemptyspaceandwasabletoestimatethesizeoftheatoman

ditsnucleus.

-

Heproposedamodelwhereorbitingelectronsw

ereheldtothepositivenucleusbyelectrostatic

attraction.Thism

odelwascriticisedasthephys

icsknowledgeofthetimesugg

estedanorbiting

electronwouldemitelectromagneticradiationandspiralintothenucleus.

InadequaciesofRutherfordsAtom

AlthoughRutherford

smodelsuccessfullyexplainedalphaparticlescattering,itleftmanyquestions

unanswered:

-

Whatisthenucle

usmadeof?

-

Whatkeepsthen

egativeelectronsfrombeingattractedintothepositivenucleu

s?

-

Howaretheelectronsarrangedaroundthenucle

us?

Deflectionofalpha

particlesbythenucleus

Rutherfordmodelofthe

hydrogenatom

Electron

(in

orbit)

Proton(nucleus)


54/69

WilliamKimHSCPhysic

sSummary|page54

2nh

Analysethesignificanceof

thehydrogenspectruminthe

developmentofBohrsmodel

oftheatom

DiscussPlanckscontribution

totheconceptofquantised

energy

DefineBohrspostulates

NielsBohrsModel

oftheAtom

BohrusesQuantumTheorytoExplaintheSpectrum

ofHydrogen:

Bohrknewthat,somehow,atomsmustproduceradiationthatformedacharacteristicspectrumfor

eachelement.Bohrr

ealisedthattheatomicoscillatorsofPlanckwereprobably

electronsinthe

atom.TheRutherfordmodelfailedtoprovideanyinformationabouttheradiusoftheatomorthe

orbitalfrequenciesoftheelectrons.

BohrwasintroducedtoBalmersequationforthewavelengthsofthespectrallinesof

hydrogen(moreonthislater),apurelyempiricalformulaatthetime.Afterseeing

thisequation,

Bohrrealisedhowelectronswerearrangedinthehy

drogenatomandalsohowqua

ntumideascould

beintroducedtotheatom.

Recall:Planck,EinsteinandQuantisedEnergy

Planckinterpretedhisblackbodyresultasmeaning

thattheatomicoscillatorsthatproducedthe

radiationcouldvibrateonlywithcertaindiscreteam

ountsofenergy,quanta.Einsteinlaterextended

thisideatotheradiationitselfbeingquantised,photons.

BohrsPostulates

In1913,Bohrpublishedthreepapersthataddressed

theproblemofelectronsinthe

Rutherford

modelandpointedoutthattheacceleratingelectron

smustloseenergybyradiation

andcollapse

intothenucleus.Hethenappliedquantumtheoryto

theatom.Toaccountforthediscrepancies

betweentheRutherfordmodeloftheatomandavailableexperimentalevidenceinparticular,the

emissionspectrumofhydrogen,Bohrproposedthre

epostulates:

1.Electronsinanatomexistinstationarystatesinwhichtheypossessanunexplainable

stability.Thesestatescorrespondtocertainallowedorbitsthatallowelectronstorevolve

withoutradiating

energy.

2.Whenanelectronfallsfromahigherenergyleveltoalowerenergylevel,item

itsenergythatis

quantisedbythe

PlanckrelationshipE2E1=

E=hf

3.Angularmomen

tum(mvr)isquantisedandcanonlytakevaluesof

wherenisthe

principlequantum

number.

SpectralLinesofHydrogen

Explained:

The2nd postulateexplainsthe

lineemissionspectra.Emissio

n

ofenergyisdiscontinuousand

correspondstoatransition

betweentwostationarystates.

Sincetheenergyisquantised,

thefrequencyoftheemitted

radiationispredetermined.A

transitionbetweendifferent

stateswillleadtodifferent

frequenciesi.e.colours.


55/69

WilliamKimHSCPhysic

sSummary|page55

DescribehowBohrs

postulatesledtothe

developmentofa

mathematicalmodelto

accountfortheexistenceof

thehydrogenspectrum:

TheBohrModelan

dtheBalmerSeries

OneofthegreatestsuccessesoftheBohrmodelwasthatitwasabletoprovideaphysicalbasisfor

theBalmerseriesfor

mula(whichupuntilthatpointwaspurelyanempiricalformu

la).Bohrs

reasoningwasasfollows:

FromBohrs2nd postulatewehave:

Bohrwasabletoderiveanexpressionfortheenergyoftheorbitsbycombiningtheexpressionfor

potentialenergyoftheelectron-nucleussystemtoitskineticenergy,writtenas:

wheren

=1,2,3;E1=theenergyoftheelectroninthefirstenergy

level=-13.6eV

Fromthisexpression

forenergywehave:

and

hence:

and

since:theexpressionreducesto:

whichistheBa

lmerformula!

(whereRHisRydbergsconstant=1.097*107 m-1)

TheHydrogenAtom

Explained

Wearenowabletoc

alculatethewavelengthsofthe

manyspectrallinesofthehyd

rogenatom.The

originalseriesofthe

spectrallineswasknownastheBalmerseriesandcontained

thefourspectral

linesinthevisibleregionofthespectrum.Theselin

escorrespondtoelectronjumpstothesecond

lowestenergystate,orfirstexcitedstate,(n=2)ofthehydrogenatom.

Balmersformulaallowedforspeculationoftheexistenceofotherlineseriesforhydrogen.These

werelaterdetectedusingspectroscopes.

=

2

2

1

1

1

i

f

n

nR

i

f

E

E

hf

=

1

21En

En=

1

21En

E

f

f=

1

21En

E

i

i=

1

2

2

1

2

1

2

1

1

1

1

E

n

n

En

E

n

hf

i

f

i

f

=

=

c

f

fc

=

=

=

=

2

2

2

2

1

1

1

1

1

1

i

f

H

i

f

n

n

R

n

n

hcE

OtherSeriesofLinesofthe

HydrogenSpectrum:

LymanseriesUVlines

withtransitionstothe

groundstate(n=1)

PaschenseriesIRlines

withtransitionstothe

secondexcitedstate(n=3)

Brackettseries-IRlines

withtransitionstothethird

excitedstate(n=4)

PfundseriesIRlineswith

transitionstothefourth

excitedstate(n=5)


56/69

WilliamKimHSCPhysic

sSummary|page56

Discussthelimitationsofthe

Bohrmodelofthehydrogen

atom

LimitationsoftheB

ohrModel

TheBohrmodeltake

sthefirststeptointroducequa

ntumtheorytothehydrogenatom,buthasthe

followinglimitations

:

-

Multi-ElectronAtoms:TheBohrmodelworks

reasonablywellforatomswithoneelectronin

theiroutershellb

utdoesnotworkforanyothers.Itisnotpossibletocalculate

thewavelengths

ofthespectrallin

esofallotheratoms.

-

RelativeIntensitiesofSpectralLines:Examin

ationofspectrashowsthatthe

spectrallinesare

notofequalinten

sitybuttheBohrmodeldoesn

otexplainwhysomeelectront

ransitionswould

befavouredover

others.

-

HyperfineLines

:Carefulobservationswithbetterinstrumentsshowedthattherewereother

linesknownasth

ehyperfinelines.Theremustb

esomesplittingoftheenergylevelsoftheBohr

atombuttheBoh

rmodelcannotaccountforthis.

-

ZeemanEffect:

Whenagasisexcitedwhilein

amagneticfield,theemissionspectrum

producedshowsasplittingofthespectrallines(calledtheZeemaneffect).Again,theBohr

modelcannotacc

ountforthis

-

AdhocMixture

ofClassicalandQuantumPhysics:Finally,theBohrmodelisamixtureof

classicalphysics

andquantumphysicsandthis,

initself,isaproblem.


57/69

WilliamKimHSCPhysic

sSummary|page57

phhchf

p===

2.T

helimitationsofclassicalphys

icsgavebirthtoquantumphysics

DescribetheimpactofDe

Brogliesproposalthatany

kindofparticlehasboth

waveandparticleproperties

LouisDeBrogliesProposal

In1923,deBrogliea

rguedthatthefactthatnobody

hadmanagedtoperformanex

perimentthat

settledonceandforallwhetherlightwasawaveor

aparticlewasbecausethetwo

kindsof

behaviourareinextricablylinked-hemadethebold

proposalthatallparticlesmus

thaveawave

natureaswellasaparticlenature.

Theexpressionsfortheenergyandmomentumoflightquantahavequantitiesthat

arepropertiesof

particlesontheleft-h

andsideandquantitiesthatare

propertiesofwavesontheright-handside:

Electronshadbeenthoughtofaswell-behavedparticlesexceptforthefactthattheyoccupied

distinctenergystates

inthehydrogenatom.Thesee

nergystateswereassociatedwithintegers.De

Brogliewasawareofotherphenomenainphysicsthatwereassociatedwithintegers.These

includedtheinterferenceofwavesandthevibration

ofstandingwaves.Hestated:Thisfact

suggestedtometheideathatelectrons,too,couldnotberegardedsimplyascorpuscles,butthat

periodicitymustbea

ssignedtothem.

DeBrogliedescribed

howmatterwavesoughttobehaveandsuggestedwaysthat

theycouldbe

observed.ThewavelengthofaphotonwasPlancks

constantdividedbyitsmomentumandde

Broglieproposedtha

t,similarly,thewavelengthofamovingparticlewouldbePla

ncksconstant

dividedbyitsmomentum.Therefore,photonmome

ntumwouldbe:

ThedeBrogliewave

lengthofaparticle:

chf

pchf

mc

hf

mc

mc

hf

E

=

==

=

=2

2

chf

p

hf

E==

mvh

=

DeBrogliesideainitiatedthe

developmentofquantum

mechanicsacomplete

theory,notamixtureof

classicalandquantumideas

asusedbyBohr.

Quantummechanicsisthe

namegiventoasetof

physicallawsthatapplyto

objectsthesizeofatomsor

smaller.Theconceptsof

wave-particledualityand

uncertaintylieattheheartof

quantummechanics.


58/69

WilliamKimHSCPhysic

sSummary|page58

Describetheconfirmationof

DeBrogliesproposalby

DavissonandGermer

Explainthestabilityofthe

electronorbitsintheBohr

atomusingDeBroglies

hypothesis

Confirmationofde

BrogliesProposalbyClintonDavissonandLesterGerme

r

In1923,Davissonan

dGermerprovedthewavenatureofmatterbyobservingsom

echaracteristics

ofwavepropertiessu

chasdiffraction.DavissonandGermerscatteredelectronsfromthesurfaceof

anickelcrystalando

btainedanintensitypatternofthereflectedelectronsthatshoweddiffraction

effects.Thisprovesthatelectronsofparticlenaturealsohavewavecharacteristics.

BohrsStableElectronOrbitsExplained

WhendeBrogliedev

elopedtheideaofmatterwave

s,hehadbelievedthattheorbitsoftheelectron

inthehydrogenatom

weresomethinglikestanding

waves.

Theconditionforastandingwavetoformonastringfixedateachendisthatthelengthof

thestringmustbean

integralnumberofhalf-lengths.Ifweconsideranelectronas

settingupa

standingwavepatternasitorbitsaroundanucleus,theremustbeanintegralnumb

erof

wavelengthsinthatp

attern.Ifthecircumferenceistakenas2rthentherearenwavelengthsinthe

circumference,n=

2r.Fromthis,andthedeBrogliewavelength:

B

utthisisBohrsthirdpostulate

hisquantisationconditionthatangular

m

omentumcanexistonlyintege

rmultiplesof

If

anintegernumberofelectronwavelengthsfitintothecircum

ferenceofthe

electronorbit,standingwavesco

uldbepossibleandhencenoe

nergywouldbe

lo

st.

NickelCrystal

V

Cathode

Anode

Detector

e

22

2

nh

mvr

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