15.3. THEPERIODICTABLE 251
theeightelementsofLithiumtoNeonintheupperrow,andSodiumtoArgoninthe
lowerrow. Nextcometwolong rowsoftheperiodictable,with 18 elementseach:
PotassiumtoKryptonintheupperrow,andRubidiumtoXenoninthelowerrow.
Thencomesalonggroupof 32 elements,containingtherareearths,whosenamesI
canneverremember. Thelastgroupoftheheaviestelements,containingThorium,
Uranium, and some otherelements that have beencreatedin thelaboratory but
whichdon’tappearinnature,isnotcompletelyfilled. Thelimitationonthesizeof
theperiodictable comesnotfromatomic physics, butfromnuclear physics, since
nucleibeyondsomelimitingZtendtobehighly radioactive, anddecayaninstant
aftertheyareproduced.
- TermNotation TheHartreeapproximationignoresallcorrellationsbetween
electrons,andinparticularitignoresthecorrellationsthatleadtotheatomicground
statebeinganeigenstateoftotalspin,orbital,andspin+orbitalangularmomenta
S% = S% 1 +S% 2 +...+S%Z
%L = %L 1 +L% 2 +...+L%Z
S% = J% 1 +J% 2 +...+J%Z (15.72)Infact,theHamiltoniancommuteswithJ^2 ,L^2 ,S^2 ,andthegroundstateinparticular
hasdefinitevaluesofthequantumnumbersJ,L,S,whereweusecapitalslettersto
emphasizethatthesearequantumnumbersfortheensembleofelectrons.TheTerm
Notationor Spectroscopic Descriptionofamany electronstatewithdefinite
quantumnumbersJ,L,Sisgivenbytheexpression
2 S+1L
J (15.73)where
L= 0 1 2 3 4 5 ...
L= S P D F G H ...
(15.74)
Thereexists somefolkloreknownasHund’s Ruleswhichallow oneto guess,
sometimes,thetermdescriptionforthegroundstateofagivenatom.Intheserules,
the phrase”highest (lowest) possible” means: highest (lowest) possibleconsistent
withtheexclusionprinciple. Therulesareasfollows:
Hund’s Rule’s
1.Otherthingsbeingequal,thelowestenergystateofatomicelectronsisthestate
withthehighestS.