AtomicandModernPhysicsforAPPhysicsAlumniWavesandParticles(Hewitt38)Inthesectiononlight,Italkedabouthowtherearetwomodelsforwhatlightis:awaveoraparticle.ThewavetheorywasprovenbyYoung’sdouble-slitinterferenceexperimentinwhichlightdidsomethingthatonlywavesdo:constructiveanddestructiveinterference.TheparticletheorywasprovenbyEinsteinthroughthephotoelectriceffect:heshowedthatthereisaminimumamountoflightnecessarytogetthecurrenttoflowinthiswayandthatamountwasonequantumoflightwhichisalsocalledaphoton.Itturnsoutthatalloftheotherparticles(protons,electrons,etc.)alsohavewaveproperties.Thishasbeendemonstratedmanytimes.Youcanevensaythatyouhavewavepropertieswhenyoumove,butsinceyou’resobigandsoslow,there’snowaytomeasurethem.Electrons.Onewayofexplainingwhyelectronscanonlybeincertainorbitalsaroundthenucleus(likeintheBohrmodel)istolookatthewavelengthandseethatonlycertainorbitshavetherightlengthstofitanintegralnumberofwavelengths.ThisistheDeBrogliemodel.Inphysics,wethinkiftheorbitalsas“electronclouds”wherethereisahighprobabilityoffindinganelectron.Ithinkofitliketheelectronismovingreallyfastsoitblursouttheshapeofitsprobabilitycloud.Theprincipleofcomplementaritysaysthatwecanobservethewavepropertiesandparticlepropertiesofmatteronlyseparately,notatthesametime.BasicAtomStuff(Hewitt39)Youprobablyrememberallthisfromchemistry.Intheatom,there’sanucleusthathasprotonswhicharepositivelychargedandneutronswhicharenegativelycharged.Theyareheldtogetherbythestrongforce.Thestrongforceisreallystrongbutactsonlyatcloserange.Ithastobestrongerthantheelectrostaticforcebecausethenucleusstaystogethereventhoughtheprotonsarerepellingeachother.Protonsandneutronsarehadronsbecausetheyaremadeoutofquarks.Hadronsarerelativelyheavyparticlesandtheyexperiencethestrongforce(alsosometimescalledthehadronicforce).Electronsaremuchlighterandfasterthanprotonsandneutrons.Theyareleptonsanddon’texperiencethestrongforce.Theyarenegativelycharged.Theamountofchargeonanelectronisthesameasthechargeonaproton(butit’stheoppositesign).AtomicMass,AtomicNumber,andIsotopes(Hewitt39.4)Thenumberofprotonsdeterminestheatomicnumberoftheatomandalsoitselement(likeoxygenoriron).Thenumberofneutronscontributestotheatomicmass.Theatomicmassisthenumberofprotonsplusthenumberofneutrons.Twoatomswiththesamenumberofprotonsarethesameelement,butiftheyhavedifferentnumbersofneutrons,theyaredifferentisotopes.Thereisanotationthatshowstheatomicnumberandthe

atomicmasslikethis: .Thebottomnumber,92,isthenumberofprotonswhichisalsotheatomicnumber.Thetopnumberistheatomicmass.Wecanseethatthisuraniumhas146neutronsinit.Thenumberofelectronsisapproximatelythesameasthenumberofprotons.Ifthey’reexactlyequal,thentheatomisuncharged.Ifthere’ssomenumberofelectronsmissingorsomeextraelectrons.thentheatomispositivelyornegativelychargedandit’scalledanion.Whenyouwriteelectronswiththeiratomicmassandatomicnumber,itlookslikethis:

.Theatomicnumberissupposedtobethetotalnumberofprotonsandelectronsaretheoppositechargeasprotons,sothey’re-1.Thetotalmassiszerobecauseelectronsaretiny.Theydon’tdecayandthey’renotexpectedtodecaybecausetheyaren’tmadeoutofsmallerparts.Protonsandneutronsaremadeoutofquarks(threeeach).Sofar,nobodyhasseenaprotondecayeventhoughit’smadeoutofsmallerparts(andphysicistshavebeendoingexperimentsonthisfordecades),butneutronsdodecay.Theybreakuptoformaperfectlygoodproton,anormalelectron,andanantineutrino(tinyantimatterparticlewithnocharge).ElectronsEmittingLightAsyouknow,electronsgoaroundthenucleusinorbitals.Theorbitalsclosertothenucleusarelowerenergy,thehigheronestakemoreenergy.Electrons“prefer”tobeinthelowerorbitalsbutwhenthoseorbitalsarefull,theyhavetobeinhigherorbitals.Whenenergycomestoanatom(forexample,byabsorbingaphotonoflight),thatenergyisabsorbedbyanelectronandtheelectrongoestoahigherenergystate(orbital).Assoonasit’spossible,thatelectronisgoingtowanttogobacktothelowerenergystate,soitwillpackageupthedifferenceinenergybetweenthehighstateit’satandthelowerstateitcangoto(becauseit’sempty)andejectthatenergyasaphoton.Becausetheenergylevelsoftheorbitalsarefixed,therearealimitednumberofenergytransitionswithveryspecificenergydifferences.Sincethephotonsemittedbyelectronshavetohavethesespecificenergiesandenergyisrelatedtofrequency( ),therearealimitednumberofveryspecificfrequencies(colors)thatcanbeemitted.Whenanatomdoesn’thaveverymanyelectrons(anelementwithasmallatomicnumber),thereareonlyafewpossiblefrequenciestoemitandtheemissionisaspecificcolor–likethecharacteristicredofneonlights.Whentherearelotsofelectrons(anelementwithalargeatomicnumber),therearelotsofcolorsandittogetheritlookswhite–likethelightfromtheTungstenfilamentinalightbulb(atomicnumber74).Whenwelookatlightandseparateitoutintoitscolors(likewhitelightmakingarainbow),wecallthisaspectrum.Therearesomedifferenttypesofspectra:

92238U

−10e

E = hν = hf

TypeofSpectrum

whatitlookslike causedby

continuous(rainbow)

emissionfromanelementwithlotsofelectrons,sunlight

emission(mostlyblackwithafewlines)

anelementwithafewelectronsgettingenergyandreleasingitasphotons

absorption(mostlyrainbowwithafewlinesmissing)

Lightshiningthroughanelementthat’sabsorbingspecificenergies

ElectronsinChemistryWhenanatomhasmanyelectrons,theyareindifferent“shells.”Theinner(lower-energy)shellsarefullandstablebuttheoutershellmightnotbefull.Thisoutershellisthevalenceshellandtheelectronsinitarethevalenceelectrons.Theyaretheonesthatinteractwiththerestoftheworld,participatinginchemicalreactions,formingchemicalbonds,etc.Soit’simportantattimestoknowthenumberofvalenceelectrons(justtheoutershell)whichisdifferentfromthenumberoftotalelectrons.NuclearReactions(Hewitt39)Nuclearreactionsaredifferentfromregularchemicalreactions.Remember,chemicalreactionsarewhenthevalenceelectronsareinteractingwitheachother,thenucleusjustgoesalong.Innuclearreactions,somethinghappensinsidethenucleus.Whatusuallyhappensisradioactivedecay,inwhichstufffromthenucleusgetsejected.Sometimes,thenucleuswillsplitapartintotwosmallernuclei(whichwillbe,ofcourse,differentelements).Thisiscallednuclearfission.

Herearethetypesofthingsthatgetejectedfromthenucleusinnuclearreactions:typeofradiation

symbol whatitis whereitcomesfrom

alpha twoprotonsandtwoneutrons(aheliumnucleus)

twoprotonsandtwoneutronsfromtheoldnucleus

beta anelectron aneutronfromtheoldnucleusbecomesaprotonandanelectron(andanantineutrino)

gamma ahigh-energyphoton energyreleasedinthenucleus

Nuclearreactionscanbebalanced,alotlikewhatyoudoinchemistryforchemicalreactions(buteasier).Youjusthavetomaketheatomicnumbersandatomicmassesmakesense.So,forexample,ifyouhaveThorium-234anditemitsanelectronthroughbetaradiation,whatdoyouget?Well,Thorium-234is sothereactionis

Thenumbershavetoadduptothesameonbothsides,sowehave:

Andwelookupwhathasatomicnumber91anditturnsouttobeProtoactinium,sothefinishedreactionis:

Easy,right?NuclearFissionandFusion(Hewitt40)You’veprobablystudiedthismanytimesbefore.Ournuclearpowerplantsusenuclearfissiontoreleaseenergythattheyusetomakeelectricity.Nuclearfissioniswhenyouallow(orencourage!)unstable,energeticatomstobreakapartintosmaller,more-stablestuffandreleasetheenergy.

24α

−10e

γ

90234Th

90234 Th→ −1

0e + ???

90234 Th→ −1

0e + 91234???

90234 Th→ −1

0e + 91234 Pa

Oneofthethingsyoucancalculateinnuclearfissionishowtheenergyreleaseisrelatedtotheamountofmasslostinthereaction.Thiscomesfromthefamousequation:

Nuclearfusionisthereactionthatmakesstarsshine,includingoursun.Inthisreaction,smallernuclei(likeHydrogen)areforcedtogethertomakelargernuclei(likeHelium)andenergyisreleased.BigTheoriesinModernPhysicsSpecialTheoryofRelativity(Hewitt15and16)Ifyouwanttotrytounderstandrelativity,IstronglyrecommendthatyoureadthechaptersintheHewittbook.Ittakesawhiletounderstandbuthedoesagreatjobexplainingit.Thehighlights:FirstPostulate:Allthelawsofphysicsarethesameinanyinertialreferenceframe.Thisessentiallysaysthatthere’snodifferencebetweenbeingstillandmovingatconstantvelocity.Now,thereisadifferencebetweenthatandaccelerating.Whenyou’reacceleratingthere’sanetforceonyouandyoucanfeelit.SecondPostulate:thespeedoflightisalwaysthesame,nomatterwhatreferenceframeyouuse.ThisisimportantandtheyaskquestionsaboutitontheSAT.Basically,norelativemotionaffectsthespeedoflight.Thespeedoflightisalwaysthesame.Exceptwhenit’ssloweddownbychangingmedia(seethereviewofopticsforthat).Nothinggoesfasterthanthespeedoflight:andnothingcangoatthespeedoflightexceptlight.TimeDilation:oneoftheconsequencesofthepostulatesisthattimepassesmoreslowlyinamovingframeofreference.Soifyougoonaspaceshipforwhatyouaresureisathree-hourtour,itcouldbedayslaterherewhenyoureturn.LengthContraction:distancesgetshorterwhenviewedfromamovingreferenceframe.Ifyouaretravellingpastme,Iwilllookskinnytoyouandthedistancebetweenuswilllookshorter.Butalso,youwilllookskinnytome.MassChanges:thefasteryougo,themoremassiveyouget.Thisiswhathelpskeepyoufromgoingatorfasterthanthespeedoflight.CorrespondencePrinciple:whenthingsaregoingslowcomparedtothespeedoflight,youdon’tnoticethesethingsandthereisasmoothtransitionbetweenhavingrelativisticeffectsandnothavingthem.Themathworksoutreallynicely.

E = mc2E = energy (J)m = mass (kg)c = speed of light = 3.0 × 108 m/s

GeneralTheoryofRelativityTheGeneralTheoryhandleswhathappensinmovingframesofreference.Itsays,basically,thatthere’snodifferencebetweenagravitationalfieldandanacceleratedframeofreference.Itexplainsthatspace-timeiswarpedsothatthemovementsoftheplanetsandstarsandstuffcanbeexplainedbythecurvatureofspace-timeinsteadofbygravitationalforces.TheStandardModelThisisthebasictheoryaboutthefundamentalforcesandparticlesintheuniverse.Therearefourfundamentalforces:Force whatitaffects howitactsGravitational massiveparticles attractiveonly,varieswith

distanceaccordingtoinverse-squarelaw

Electromagnetic chargedparticles attractiveandrepulsive,varieswithdistance,comesintwoforms(electricalandmagnetic)

Strong hadrons(particlesmadeofquarkslikeprotonsandneutrons)

onlyforvery,veryshortdistances,it’sattractive

Weak leptons(likeelectrons) mediatesbetadecayTheStandardModelwasabletorelatetheElectromagnetic,Strong,andWeakforcestoeachother,unifyingthemintooneforce.Thisdoesn’tincludethegravitationalforce,butifweadheretowhatEinsteinsaidintheGeneralTheory,thengravityisn’taforce.TheStandardModelalsoclassifiedallofmatterintoasmallnumberofparticles:quarksandleptons.Thisisthefamouspostersummarizingthat: