8-Electronic Structure of Multielectron Atoms

8-Electronic Structure of Multielectron Atoms - 5.111...

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5.111 Lecture Summary #8 September 25, 2009 8.1 Reading for today: Sections 1.12-1.13 Reading for Lecture 9: Sections 1.14-1.18, 1.20 ELECTRONIC STRUCTURE OF MULTIELECTRON ATOMS All 1e states in a multi e atom are lower in E (more negative) than in H atom. Why? n is no longer the sole determining factor in E. << < << < << < < << < < << ±²³²´ ±²³²´ µ µ CLOSE CLOSE 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s < < < << < < ±²³²´ ±²³²´ µ µ CLOSE CLOSE 6s 4f 5d 6p 7s 5f 6d E 4 4s 4f 14 3s E 3 E 2 E 1 MANY ELECTRON ATOM H ATOM E n 3d 3d 3d 3d 3d 4p x 4p z 4p y 3p x 3p z 3p y 4s 3s 2s 1s E 4p E 3d E 4s E 3p E 3s E 2p E 2s E 1s E 3d 3d 3d 3d 3d 4p x 4p z 4p y 3p x 3p z 3p y 2p x 2p z 2p y 1s 2s 2p x 2p z 2p y 4d 4d 4d 4d 4d E nl = - IE nl = - Z eff nl ( ) 2 R H n 2
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5.111 Lecture Summary #8 September 25, 2009 8.2 SHIELDING AND Z eff Energies of states in multi e atom are approximated ( ) = − A A A 2 H 2 n eff n n Z R E IE n where A n eff Z is effective charge experienced by an e in the n A state. This is not the same as Z for nucleus. Because of shielding ! For example: He Atom Z = +2 EXTREME CASE 1: e #1 far from nucleus and e #2 close to nucleus Z = +2 e #2 e #1 e #2 cancels (shields) part of charge experienced by e #1 e #1 experiences force on average of Z eff = +1, not +2. Energy of e #1 is that of H atom.
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