Lecture+C5-2

Lecture+C5-2 - = 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1...

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The Periodic Table hydrogenic states Assumption: in z≠1 system, neglect electron-electron repulsion, hamiltonian for each electron is Problem: electron-electron repulsion is large & positive when z is large. Solution: Start from hydrogenic states & use perturbation theory 2 2 2 0 1 2 4 ze m r πε - ∇ - h
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electron configuration n spectroscopic notation 1 1s 2 2s 2p 3 3s 3p 3d 4 4s 4p 4d 4f 5 5s 5p 5d 5f 5g From right-top to left-bottom
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Capital for total. 1 1 2 2 1 | 0, 0 | 0, 0 0. 0 2 1 | 0, 0 2 z z z S S S S S S S L ψ = ⟩ ↑↓ - ↑↓ = = = ⟩ ↑↓ - ↑↓
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2S+1=3 J=0 L=1
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Symmetric! No state! Wrong! Don’t forget the symmetrization requirement! 1 1 2 2 1 1 2 2 st If 2. |1, 1 | 1, 1 symmetric According to 1 rule, 1 = |1, 1 | 1, 1 symmetric l m l m l m l m tot L S ψ χ = = ⟩ → = ⟩ ↑↑
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Unformatted text preview: = 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 2 3 Ground state of has 1 L=1 1 =[a (|1, 1 | 1, 0 |1, 0 | 1, 1 ) 2 1 a (|1, 1 | 1, 1 |1, 1 | 1, 1 ) 2 1 a (|1, 1 | 1, 0 |1, 0 | 1, 1 )] 2 l m l m l m l m tot l m l m l m l m l m l m l m l m Si S and = - + - -- +- -- max occupation = 6 Summary of Hunds Laws 1. S as large as possible 2. At max S, L as large as possible 3. More than half filled, J as large as possible No more than half filled, J as small as possible Practice: Electron configuration & ground state of Boron (5 electrons)....
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Lecture+C5-2 - = 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1...

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