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term_symbols - gig egg QghitalAngulag Mgmentum in Atoms...

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Unformatted text preview: § gig egg QghitalAngulag Mgmentum in Atoms Electron spin angular momentum of s=‘/z has a projection on the z—axis of ms=+1l2 or —1l2 (can align with or against a field), electron spin has a magnetic moment, but when paired the moments cancel Electron orbital angular momentum for l=1 (p orbital) has projections on the z- axis of m=-1,0,+1, when m¢0 there is a magnetic moment, but when there is an electron in each of the three p orbitals, the moments cancel. Filled subshells have zero net orbital angular momentum. Paired electrons have no net spin angular momentum. Only partially filled subshells can have magnetic moments. Magnetic materials must have unpaired electrons. Terms mbols-La llin " ' i States 23+1 L\J S is the total spin angular momentum L is the total orbital angular momentum J is the total angular momentum ‘go read “singlet ess zero" 2?” read “doublet pee three-halves” 392 read “triplet dee two” in general capital letters indicate quantities for the whole atom. whereas lower case symbols are used for the individual electrons in the system. The total orbital angular momentum is L i i i LMAxal-MAX—v-"LLEAST vector sum of the orbital angular momenta of each electron where the result must be quantized, Le. a whole number. Use only open shell electrons because closed shells have zero angular momentum. LMAX = i‘ and LLEAST = IMAX " i! iatMAX L 0 1 2 3 Letter Code 8 P D F 4 G In a manner analogous to the hydrogen atom M2 2 L(L + 1M2 The spin angular momentum is S :2 i = SMAX,SMAX_1u-"SLEAST This is a vector sum of the spins of the electrons, use only open shell electrons. SW»X = 21/2 and SLEAST 21/2 — 21/2 or zero (the larger) i ' l—"I The total angular momentum, Russell-Saunders Coupling J = (L+ S),(L + 8—1),...|L — s| for example if L21, 8:1, then J=2,1,0 8:1 3:1 J=0 J=2 L=1 L=1 Q L=‘l s=1 J=1 3P2 3P1 3P0 Boron example: electronic configuration is 1322322}:1 the two electrons in the K shell have L=0, 8:0, J=O, so we need only consider the valence electrons 2522p1 electrons. The 232 electrons have no orbital angular momentum, |1=|2=0, and the spins are paired cancelling their contribution to the spin angular momentum; so we need only consider the 2p1 electron l3=1 so trivially L = Z I i = LMM,LW,O(_1,...LLEIE,‘ST = 53=1l2 so trivially 8 == 2—8.. = 1/2 J: (1+1/2),...l1—1/2I= 3/2,1/2 boron has 2PM and 2PW states These are called sgin-orbit states. They have energies which are slightly different and small compared to the electronic energies of the orbitals. The spin- orbit splittings are smaller for the light atoms and get bigger and more important as the atoms get heavier. You need relativistic quantum theory to calculate spin- orbit splittings. The spin-orbit energy level splittings are described as E — lAn'LS[J(J + 1) r L(L +1) — 3(3 + 1)] spin—orbit _ 2 and can be measured from the observed splittings in high resolution spectra of atoms arising from the same 8 and L levels. Which spin-orbit levels are the lowest in energy? You use Hunds Rules The determination and energy ordering of the Terms for the carbon atom are illustrated in the example following Hunds Rules. Hund's Rules (work best for ground states) 1. For states from the same " J electronic configuration (same n1), the one with the highest S is lowest in energy. 2. Of the states above with the same S, the one with the highest L is lowest in energy. 3. For multiplet J states: When a shell or subshell is less than half— full, states of low J are lower in energy; when a shell or subshell is more than half-full, states of higher J are lower in energy. W98 442V art‘in 1Ifiéiééfiflfiifiwedgiiclecm s1:;; , awe fi=0 aagfigm_m _m_aonJrllgcw2r19/_zf7_2'_7.afcmmfe’mfzfa‘ldgfigimw 412,4 ans/g, =5 éwmw ;.W.w_35_P ' _&i_fl_3b;mfio_wm_fl__WW/W_ ., . . ___.. , w ._mn“._m.)___n _ meg/59m r, W LMe/MQW ‘ il :1 :1 [i u . if"::ii::fi@)fi“fi§o2 «/__ _ 9;“W2fmg77za“@jam”255w 1:244:15 j” W ‘ . ifiLfiM 51%,;ngflg [email protected]_ 1 414g, flat 5 p” b méL/kfififllgmfl , ‘ do} a A; b» 143%.". ° ‘ 5 MngJ ' {@ém;__ MMMQM¥££_-W :ELEanmdkoayézr 0" Ewell—241;;H, _[g/gw)71 ' = y = ¢_,gmz;s 579/717—7712”?- r/mr-mm‘ltmwé/ée—w: cm fim7/i3WW’7_W—k*U—fle—fimkr~—~ WWI—w 21".}; T: _.__L_ Ma If mz‘cmzhfi:: “me_wwmflmwmwfi “M ; ._‘:}2, ‘ _; )3, *' ‘fIflZ:E_’:3 * \ F [N I 1 1 l 1 1 HHle 1 t “90>x0&$5 H k ; *FH'FHWH I” I” *‘WW W i L§9T°Lo Liifi 1 '* L l l t i I g . y \ £ ' ‘ ‘ 1 ‘ i 111mg” ._ :10 lift/(520% 7 Lilian _fl.c./IL lxfligzzeffi _¢’I_WM_M M6 dz, flue. Hack [liflélQllLCflflé/fiéélhw. _ EL_~fl5/, ,, ., ‘,,_V,,,V___m.fi J 1 ymh/ Me I» J _ . W 6t fan 7 JAM 411161165 3—127 fem; Jfli7iat mm J/zfa a wt w/mp/ _____.. m am all mam/$2 “" “—"'—‘“7m—Tr F I W—w —a~, H24 —_,,; I” mth a" I" WWW—m a’m all (wva —fl_,— 2 b I way—fl w i “ “HM—w Mun...“— l ~ M51L11_:1:fl_1_1_1mw ...
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