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哈里德 物理学基础 学习指导 40 All About Atoms

Chapter40
AllAboutAtoms
soon.
ThePauliexclusionprinciplesaysthatnotwoelectronsinanatomcanhavethesamequantumnumbers.Theideaisthatonceoneelectronisinthen7.state,thenextelectronmustgointothen-2state,and
-
Buttherearemorequantumnumbersthanjustn.Anelectroninanatomisspecifiedbythequantumnumbers{rL,l,mtms}Iistheorbitalangularmomentumoftheelectrorl,trllisthezcomponentofthisangularmomentum,andm"isthezcomponentoftheelectron'sspin.
Thepreferredwaytodistinguishbetweenstatesofthesamenisbytheangularmomentum.Astheelectronorbitsthenucleusithasorbitalangularmomentum.ThequantumnumberIhastobeanintegerbetween0andn-1,soforn-3/canbe0or1or2.Weattachnamestothevaluesofl,andcallthembythefirst
letterrsol-0iss,l:Ii.p,l:2isd,l-3is/,andcontinueswithgandh.Sothestaterr-2,,I-0iscalled2s,andthestaten-4,I-2iscalled4d.
Thenextquantumnumber,TTL1,isthezcomponentofl.(Itrquantummechanics,w€usezasthefirstaxischosen,ratherthanr.Thezcomponentcouldbealloftheangularmomentum,ornoneofit,oreveninthe-zdirection.Som;hastobeanintegerbetween-landl.Forthe3pstate,m1couldbe-1or0or+1.Astheelectronorbitsthenucleus,italsospinsonitsownaxis.Theangularmomentumofthespinningisalwayss*,rowedon'tbotherwritingit.Butthe
-
zcomponentcanbe+|ot-+(fromtheminimumtothemaximuminstepsof1.
.
5nft4dThePauliexclusionprinciplestillsaysthatnotwoelectronsinanatomcanhave
thesamequantumnumbers.Thefirstelectronisinthestate{1,0,0,++},theEsecondir{1,0,0,-+},andthethirdir{2,0,0,++},becausethen-flevelisfsfilled.Previously,theenergiesofthestatesdependedonlyonnsothat2sand2phavethesameenergy.Thisisnotentirelytrue.Asthenumberofelectronsinandaatomincreases,theyhavemoreeffectoneachother,andtheenergyof2pisslightly'J-greaterthan2s,so2sisfilledfirst.Theenergyof3disgreaterthantheenergyof
3p3pisgreaterthantheenergyof3s,somuchsothattheenergyof3disgreaterthan
theenergyof4s(insomeatoms.Byfillingupthelevelsfromthelowestenergy,
-fawecreatetheperiodictable(locatedattheendofthebook.
Onewaytowritetheelectronconfigurationofanelectronisnl#.The#isthe
numberofelectronsinthenllevel.Soaftertwoelectrons,wecouldwritels2.The2selectronconfigurationofaluminum(Z:13is!s22s22pu3s23p'.Aconfigurationof1s22sz2p63s24srwouldbealuminuminanexcitedstate.
299

300
CHAPTER40.ALLABOUTATOMS
EXAMPLE
Whatistheelectronconfigurationofarsenic(Ar,Z-33inthefirstexcitedstate?
Student:Sotherecanbeonlytwoelectronsinthelsstate,right?T\rtor:Correct,{1,0,0,+L,}and{1,0,0,-+}.
Student:Andtherecan'tbeoneinthelpstate,becausepmeansI-1and/hastobelessthann,right?
Ttrtor:Correct.
Student:Sohowcantherebesixelectronsinthe2pstate?
T\rtor:BecauseI-I,som7canbe-1or0or1.Therearethreepossibilitiesform7,andforeachofthem
therearetwopossibilitiesform",and3x2-6.
Student:Doesthatmeanthattherecanbe6electronsinanyplevel?T\rtor:Yes,and10inanydlevel.
Student:Therecanbe2electronsin1,and2+6-8inn-2,and2+6+10:18inn-3.Istheresomeeasywaytodeterminehowmanycanfitinannlevel?T\rtorz2,8,18istwiceI,4.,9,so2n2.
Student:2(42-32,soAsisoneelectronpast32.
T\rtor:Therecanbe32electronsinthen-4level,butyouneedtofillthen--1,2,and3levelsfirst.Student:Oops.2inn-IandSinn-2and18inn-3is28.Arsenicis5electronspastn-3.Tntor:Careful.4shaslowerenergythan3d,soyoustartn-4beforefinishingn-3.
Student:Oky.
rs22s22puJszJpu
Yes.Sometimesyou'llseealevelcalleda"shell."
Student:Andthelastthreegointo4p.
T\rtor:That'sthelowestenergyplaceforthemtogo.Forthefirstexcitedstate,moveoneofthemuptothenexthighestlevel.
Student:5sislowerthan4d.
Student:That's18,andIneed15more.Thencomes4s2,andthen3dr0,soIfillthe3dlevel.
I\rtor:
rs22s22p63s2Bpu4s2Jdro4p'5s1
Weuseanx-rayspectrumtoidentifythenucleusofanatom.Wetakeanatomandbombarditwithhigh-energyelectrons.Sometimestheincomingelectronknocksoutoneoftheelectrons.Anelectronfromahigherlevelcomesdowntofillthelowerenergylevel,givingofftheextraenergyasanemittedphoton.Thisphotontypicallyhasahighenergyandisinthex-rayspectrum.
Whenanelectrondropsfromahigherleveltoalowerone,itemitsaphotonwithacharacteristicenergy.Theenergyofthephotonmustequalthedifferenceinenergyofthetwolevels.Whenanelectrondropsfromn-2ton-1wecallitaKophoton.Whenanelectrondropsfromn-3ton-1wecallitaKpphoton.Wealsogetphotonsofotherenergies,uptoamaximumequaltotheenergyoftheincomingelectron.
Previouslyweused-13.6eVxZ'lr'fortheenergyoftheelectron.Thiswasappliedtoasingleelectroninanatoma"oneelectronatom."Withmorethanoneelectrontheenergybecomesverydifficultto
-calculate,butwecangetanestimate.Becausethereisoneelectroninthen-1level(theotherhasbeen
knockedout,w€usethecombinedchargeofthenucleusplusthelselectron.

301
EXAMPLE
WhataretheminimumwavelengthandKpwavelengthforcesium(Ct,Z-55whenbombardedwith42keVphotons?
energiesistheenergyoftheKpphoton.T\rtor:Verygood.
Student:ButIuseZ-Itofindtheenergiesofthestates.
L/n'
Student:Kpmeansfromrr--3torr-1.Ifindtheenergyofthetwostates,thenthedifferenceinthe
D
-
(13.6eV(Z-D'
n2
12
E1:-
Es:-
(13'6evX55-12
:-39.66kev-
-4.41keV
(13'6eVx55-12
32
Student:Whatiftheincomingelectrondoesn'thave39.66keVofenergy.Tntor:Thenitwouldn'tbeabletoknocktheelectronoutofthen-Ilevel.Student:SothewavelengthoftheKBphotonis
Et:A,E-l(-39.66keV-(-4.4IkeVl:35.25keV
\p:y_Ery:35,251eV
Tutor:Good.
Student:HowdoIgettheminimumwavelength?Student:42keY.
o.o3b2nm:3b.2pm
T\rtor:What'sthemostenergythatyoucouldpossiblygetfroma42keVphoton?Thtor:Andthelargestenergyistheshortestwavelength.
min
t?10,
:Y-ll':Y-E42,000eV
Student:Sotheminimumwavelengthphotonistheonewithanenergyof42keV.
o.o2sbnm
-2e.bpm

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