Complex Atoms; The Exclusion Principle and the Periodic System
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1 Complex Atoms; The Excluson Prncple and the Perodc System In order to understand the electron dstrbutons n atoms, another prncple s needed. Ths s the Paul excluson prncple: No two electrons n an atom can occupy the same quantum state. The quantum state s specfed by the four quantum numbers; no two electrons can have the same set. Wolfgang Paul The Nobel Prze n Physcs 1945 "for the dscovery of the Excluson Prncple, also called the Paul Prncple"
2 Queston 1: why can we use 1-electron orbtals n ths problem Queston : why do l-values for the same n have dfferng energes The potental energy n a mult-electron atom: V e r j r rj attracton to nucleus e 1 repulson between electrons V s a non-central potental Central Feld Approxmaton: The overall effect of V r s centrally drected toward the nucleus V c r e for r 0 4 r 0 e for r 4 r Then V can be wrtten n terms of an effectve screened nuclear charge V cfa r eff 0 r e 4 r 0 Ths s a central potental!!
3 Separaton of varables n the central feld approxmaton Product wave functon r, r, r r r r 1, 1 1 Potental and egenenergy 1 V V c r E 1 E Inserton of tral yelds a set of equatons: m r V r r E r c 1. Angular part of the wave functon s the same, hence angular functons l m,. Radal part of the wave functon mr d dr rr eff r r 1 mr Energy E depends on R Energy E does not depend on m E R The potental functon s not Coulombc.e. s not 1/r but eff r r Wave functons for sngle orbtal r R r, lm,
4 Radal part of the wave functon mr d dr rr eff r r 1 mr R E R Energy E depends on Energy E does not depend on m Hgh classcal pcture Low For low values (and same n) electron comes closer to the nucleus More Coulomb attracton More bndng energy s-states have hgher densty near the nucleus Wave functons for sngle orbtal r R r, lm,
5 Lowerng of low quantum states as an effect of screenng
6 Complex Atoms; the Aufbau Prncple Ths chart shows the occuped and some unoccuped states n He, L, and Na.
7 The Perodc Table of the Elements Each value of s gven ts own letter symbol. Electron confguratons are wrtten by gvng the value for n, the letter code for, and the number of electrons n the subshell as a superscrpt. For example, here s the groundstate confguraton of sodum: 1s s p 6 3s 1
8 The Perodc Table of the Elements subshells
9 Aufbau prncple for mult-electron atoms Egenfunctons n mult-electron atom r, r, r r r r 1, 1 1 1) Electrons fll the one-electron orbtals r R r, lm nto a confguraton :, ) Paul prncple dctates: sngle occupancy r 3) For flled shells shell shell m s 0 L 0 tot 0 S 0 tot Degeneracy n structures the Perodc System Note: ths s about ground states of the atoms
10 Electron spn and the atom Addtonal quantum number m sm l m s Wave functons m t / r, t R r, e En, lm No effect on energy levels, except for magnetc couplng to other angular momenta Degeneracy 1 n Selecton rules s s not a spatal operator, so no effect on dpole selecton rules
11 Ground state orbtal confguratons for mult-electron atoms Noble gases 1s He confguraton Ne conf. 6 ; closed shell s ; closed shell s p 6 3s 3 ; closed shell 1s p Ar conf. 1 s p 6 Alkal metals L ss Na 1 ss (p) 3s K ss (p) 3s 3 p4s 1 one open shell electron 6 one open shell electron Earth alkal metals... Mg 6 s (p) 3 1s s closed Ca 6 6 s (p) 3s 3p 4 1s s Bndng energes of the one-electron orbtals vary wth : Screenng effects
12 Irregulartes and degeneraces Term Value (S+1) L J Transton metals; effect of 3d orbtals: Ca 6 6 s (p) 3s 3p s s Sc 1 ss (p) 3s 3 p4s3d T 6 6 s (p) 3s 3p 4s 3 s (p) 6 3s 3p 6 4s 3 s (p) 6 3s 3p 6 4s 3 s (p) 6 3s 3p 6 4s 3 1s d V 1 s d 3 Cr 1 s d 5 Mn 1 s d 5 Fe 1 s s (p) 6 3s 3 p 6 4s d 6 Co 1 s s (p) 6 3s 3 p 6 4s d 7 N 1 s s (p) 6 3s 3 p 6 4s d 8 Cu 1 s s (p) 6 3s 3 p 6 4s d 10 n 1 s s (p) 6 3s 3 p 6 4s d 10 ground term 1 S 0 D 3/ 3 F 4 F 3/ 7 S 3 6 S 5/ 5 D 4 4 F 9/ 3 F 4 S 1/ Near degeneracy of 3d and 4s orbtals Competton n allocaton of electrons 1 S 0 Couplng of the Angular momenta
13 4d electrons 3d electrons p electrons 3p electrons 5f 5d 6f One electron systems Alkal metals L(s), Na(3s),K(4s), Rb (5s) Two-electron systems Earth-alkal metals Flled shells He(1s ), Ne(p 6 ) Noble gases
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SUPPLEMENTARY INFORMATION
do: 0.08/nature09 I. Resonant absorpton of XUV pulses n Kr + usng the reduced densty matrx approach The quantum beats nvestgated n ths paper are the result of nterference between two exctaton paths of
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-"l" also contributes ENERGY. Higher values for "l" mean the electron has higher energy.
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-"l" also contributes ENERGY. Higher values for "l" mean the electron has higher energy.
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