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Chapter08 Atomic Structure and the Periodic Table General Bibliography 1) Various wikipedia, as specified 2) Thornton-Rex, Modern Physics for Scientists & Eng, as indicated Outline • 8.1 Atomic Structure and the Periodic Table • 8.2 Total Angular Momentum H-atom Energy Level Scheme 4s 4p 4d 3s 3p 3d 2s 2p En 1s 4f 13.6 eV Z2 n2 8.2 Multi-Electron Atoms Z n=1 n=1 Z eff ~ Z En 13.6 eV 2 Z eff n2 n=2 n=2 n=3 n=3 0 orbitals get sucked down the most Crossings occur for the upper orbitals 4s 3d 3s 2s 1s 4p 3p 2p http://chemistry.about.com/od/periodictables/Periodic_Tables.htm&docid=vGs4R7cWOxUJLM&imgurl=http://www.ithaca.edu/hs/chemistry/tablebig.jpg&w =600&h=327&ei=0wOqTqLOGYn20gHEZSIDw&zoom=1&iact=rc&dur=404&sig=111472812632995117326&page=2&tbnh=104&tbnw=191&start=16&ndsp=16&ved=1t:429,r:9,s:16&tx=111&ty=5 5 http://www.forevergeek.com/2010/10/there-is-a-periodic-table-for-that-15-periodic-tables-for-your-geekgasmic-pleasures/ http://www.gamepro.com/article/news/224076/the-periodic-table-of-pokemon/ http://antoine.frostburg.edu/chem/senese/101/index.shtml http://willnicholes.com/PeriodicTableofUSPresidents.html http://clockworkrealm.wordpress.com/2010/09/11/lolwut-periodic-tables/ http://www.rsc-northwest.ac.uk/acl/eMagArchive/RSCeMags2007/July07/012eMagazine/internet_periodic_table.html http://www.geekologie.com/2009/03/scientific-a-periodic-table-of.php http://clounaghscience.wordpress.com/elements-compounds-and-the-periodic-table/ http://clockworkrealm.wordpress.com/2010/09/11/lolwut-periodic-tables/ Two kinds of Angular Momentum • Classical Angular Momentum – – – – L=rxp r vector, p vector L vector L obeys vector math Any L possible, no contraints on Lx Ly Lz • Quantum – – – – – – Quantum Mechanical Angular Momentum L=rxp r vector, p vector operator L 3 component operator L obeys …… got to be careful L described by two labels l , m L and Lz can be known, Lx and Ly cannot Bohr Model of Ang Momentum Classical or Semi-classical description Note: s-states (l=0) have no Bohr model picture Eisberg & Resnick: Fig 7-11 Vector Model of QM Ang. Momentum quantum numbers m E&R Fig 7-12 Edmonds “A.M. in QM” pg 19: “We might imagine the vector moving in an unobservable way about the z-axis...” pg 29: “The QM probability density, not being time dependent, gives us no information about the motion of the particle in it’s orbit.” Y*(r,t) Y(r,t) Y(r,t)=Y(r) eiwt Morrison, Estle, Lane “Understanding More QM”, Prentice-Hall, 1991 Addition of Orbital Angular Momentum for two electrons L1 L2 Ltot = L1 + L2 Problem: Two objects each travel in a p-orbit ( l=1 ). What are the allowed values of ltot, mtot ? L1 Ltot L2 Ltot = L1 + L2 tot 1 m1 2 Yl1m1 , Yl2 m2 , m2 mtot Ylto tmto t , Ltot = L1 + L2 1 m1 tot mtot 1 2 tot 1 2 mtot m1 m2 2 m2 Addition of Angular Momentum www.bokerusa.com aligned configuration “aligned” does not mean straight www.cartowning.co.za/DBNRECGC.htm jack-knife configuration “jack-knife” does not mean antiparallel Addition of Intrinsic Spin Angular Momentum S1 Stot = S1 + S2 stot s2 ms ,tot s1 s2 S2 s1 stot mtot ms , 2 ms ,1 s1 s2 m1 m2 Because objects are all spin-1/2 stot = 0, 1 singlet triplet WARNING: CAN’T MAKE TRIPLET IF BOTH ELECTRONS ARE IN THE SAME ORBIT BECAUSE THEY WOULD BE IN THE SAME ms SUBSTATE. i.e. ms = + ½ and + ½ Total Angular Momentum for a single electron L1 Jtot = L1 + S1 S1 jtot s2 m j ,tot 1 s1 1 mj ms , 2 m ,1 jtot 1 s1 m ms Add It All Up for Two Electrons L1 S2 L2 S1 What is the “total” total angular momentum, Jtot ? LS Coupling JJ Coupling Two Ways to Add • LS Coupling (aka Russell-Sanders Coupling) – Ltot = L1 + L2 and Stot = S1 + S2 – Jtot = Ltot + Stot – Preferred for lighter atoms, Z<30 • JJ Coupling – J1 = L1 + S1 and J2 = L2 + S2 – Jtot = J1 + J2 – Preferred for heavier atoms, where the nucleus has a lot of charge and creates big internal magnetic fields from the point of view of the electrons. Hund’s Rules L1 S2 L2 S1 http://en.wikipedia.org/wiki/Friedrich_Hund 4 February 1896 - 31 March 1997 • Hund observed in lighter atoms that – The S1 – S2 orientation energy is very strong – Bigger Stot have lower energy – The L1 – L2 orientation energy is not as strong – Bigger Ltot have lower energy – If shells are less than half full, smaller Jtot have lower energy 4p-4d Example Multi-e Spectroscopic Notation QUANTUM NUMBERS principal: n ltot , stot jtot . 2 stot 1 tot j tot Stot = S1 + S2 + … Ltot = L1 + L2 + … Jtot = Ltot + Stot stot = 1, ltot=0, jtot=1 3S 1 Two Kinds of Spectroscopic Notation • Where an individ electron is at • nlj – – – – 1s1/2 2s1/2 2p1/2 2p3/2 • A.M. for whole atom • 2Stot+1 Ltot Jtot – 1S0 – 3S1 – 3P0 , 3P1, 3P2