This preview shows pages 1–19. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 mbolsLa 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 threehalves”
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 LMAxalMAX—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, RussellSaunders 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 sginorbit 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 spinorbit 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 spinorbit 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 halffull, 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;[email protected] 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 ' [email protected];__ MMMQM¥££_W :ELEanmdkoayézr 0" Ewell—241;;H, _[g/gw)71 ' = y = ¢_,gmz;s 579/717—7712”? r/mrmm‘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 ...
View
Full
Document
This note was uploaded on 07/17/2008 for the course CHEM 861 taught by Professor Dr.coe during the Fall '04 term at Ohio State.
 Fall '04
 DR.COE
 Quantum Chemistry

Click to edit the document details