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Chapter08 Atomic Structure and the Periodic Table

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.

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Chapter08 Atomic Structure and the Periodic Table

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  1. Chapter08Atomic Structure and the Periodic Table General Bibliography 1) Various wikipedia, as specified 2) Thornton-Rex, Modern Physics for Scientists & Eng, as indicated

  2. Outline • 8.1 Atomic Structure and the Periodic Table • 8.2 Total Angular Momentum

  3. H-atom Energy Level Scheme 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s

  4. 8.2 Multi-Electron Atoms Z

  5. n = 1

  6. n = 1

  7. n = 2

  8. n = 2

  9. n = 3

  10. n = 3

  11. orbitals get sucked down the most Crossings occur for the upper orbitals 4p 3d 4s 3p 3s 2p 2s 1s 1s sucked off bottom of page

  12. 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=0wOqTqLOGYn20gHE-ZSIDw&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=55http://chemistry.about.com/od/periodictables/Periodic_Tables.htm&docid=vGs4R7cWOxUJLM&imgurl=http://www.ithaca.edu/hs/chemistry/tablebig.jpg&w=600&h=327&ei=0wOqTqLOGYn20gHE-ZSIDw&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=55

  13. http://www.forevergeek.com/2010/10/there-is-a-periodic-table-for-that-15-periodic-tables-for-your-geekgasmic-pleasures/http://www.forevergeek.com/2010/10/there-is-a-periodic-table-for-that-15-periodic-tables-for-your-geekgasmic-pleasures/

  14. http://www.gamepro.com/article/news/224076/the-periodic-table-of-pokemon/http://www.gamepro.com/article/news/224076/the-periodic-table-of-pokemon/

  15. http://antoine.frostburg.edu/chem/senese/101/index.shtml

  16. http://willnicholes.com/PeriodicTableofUSPresidents.html

  17. http://clockworkrealm.wordpress.com/2010/09/11/lolwut-periodic-tables/http://clockworkrealm.wordpress.com/2010/09/11/lolwut-periodic-tables/

  18. http://www.rsc-northwest.ac.uk/acl/eMagArchive/RSCeMags2007/July07/012eMagazine/internet_periodic_table.htmlhttp://www.rsc-northwest.ac.uk/acl/eMagArchive/RSCeMags2007/July07/012eMagazine/internet_periodic_table.html

  19. http://www.geekologie.com/2009/03/scientific-a-periodic-table-of.phphttp://www.geekologie.com/2009/03/scientific-a-periodic-table-of.php

  20. http://clounaghscience.wordpress.com/elements-compounds-and-the-periodic-table/http://clounaghscience.wordpress.com/elements-compounds-and-the-periodic-table/

  21. http://clockworkrealm.wordpress.com/2010/09/11/lolwut-periodic-tables/http://clockworkrealm.wordpress.com/2010/09/11/lolwut-periodic-tables/

  22. Two kinds of Angular Momentum • Classical Angular Momentum • L = r x p • 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 = r x p • 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

  23. 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

  24. Vector Model of QM Ang. Momentum quantum numbers E&R Fig 7-12

  25. 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) e-iwt

  26. Morrison, Estle, Lane “Understanding More QM”, Prentice-Hall, 1991

  27. Addition of Orbital Angular Momentumfor two electrons L2 L1 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

  28. Ltot = L1 + L2

  29. Ltot = L1 + L2

  30. Addition of Angular Momentum www.bokerusa.com aligned configuration “aligned” does not mean straight jack-knife configuration www.cartowning.co.za/DBNRECGC.htm “jack-knife” does not mean antiparallel

  31. Addition of Intrinsic SpinAngular Momentum Stot = S1 + S2 S1 S2 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

  32. Total Angular Momentumfor a single electron L1 Jtot = L1 + S1 S1

  33. Add It All Up for Two Electrons L2 L1 S2 S1 What is the “total” total angular momentum, Jtot ? LS Coupling JJ Coupling

  34. 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.

  35. Hund’s Rules L2 • 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 L1 S2 S1 http://en.wikipedia.org/wiki/Friedrich_Hund 4 February 1896 - 31 March 1997

  36. 4p-4d Example

  37. Multi-e Spectroscopic Notation QUANTUM NUMBERS principal: n ltot , stot jtot . stot = 1, ltot=0, jtot=1 3S1 Stot = S1 + S2 + … Ltot = L1 + L2 + … Jtot = Ltot + Stot

  38. Where an individ electron is at n l j 1s1/2 2s1/2 2p1/2 2p3/2 A.M. for whole atom 2Stot+1LtotJtot 1S0 3S1 3P0 , 3P1, 3P2 Two Kinds of Spectroscopic Notation

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