PS8-08-Solution - Chem 442 Homework Set #8 DUE: Friday,...

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Chem 442 Homework Set #8 DUE: Friday, November 14, 2008 1) McQ&S, 8-22 () () () ( ) () ( ) () () ( ) ,1 2 1 2 12 In this problem we are only concerned with the spin part of the wavefunciton: 11 22 1 ˆˆ ˆ ˆ ˆ 2 1 2 z total z z z z zz SS S S S αβ ψ βα ψψ α β == =+ =− +− ⎛⎞ ⎜⎟ ⎝⎠ 1 2 11 1 1 11 2 2 1 01 2 1 2 2 In this case the eigenvalue is 0 . + = Problem Set #8 - Solutions - 1 -
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() 111 = 1 23 23 1 23 32 666 1 123 123 123 132 123 132 6 Here, since we are considering only the spin part of the wavefunction, we can 'cancel' two of the terms. 1 =1 2 3 6 ψ αβα αβ βαα αα ααβ αβ αβα αα β βαα ααβ −− −+ = −−++− ,1 2 3 1 2 3 z1 z2 123 132 132 1 ˆˆ ˆ ˆ ˆ ˆ ˆ 123 123 132 132 6 ˆ ( F r om S) 26 ˆ ( F r 123 123 132 z total z z z z z z SS S S S S S βα α ψαβ α β −+− =+ + + + +− + + + = = = z3 ˆ 132 ( F r 1 2 31 2 3 21 3 2 2 So, the eigenvalue is 2 =− + = == = 2) McQ&S, 8-32 2S+1 1 1 1 3 3 , ... Term Symbol: :0 ,0 0 :2 2 :4 4 :1 2 , 1 , 0 :3 , 1 4 , 3 , 2 Ground state, according to Hund's rule is the term with largest value of S. Thus J JLS JLSLS L SL S J
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This note was uploaded on 02/12/2011 for the course CHEMISTRY 442 taught by Professor Lizzy during the Spring '10 term at Hanoi University of Technology.

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PS8-08-Solution - Chem 442 Homework Set #8 DUE: Friday,...

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