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Unformatted text preview: 1 Physical Chemistry Lecture 19 Excited States of Helium; Terms Energetics and configuration Helium ground state has two 1s electrons Product representation gives the configuration Configuration indicates number of electrons in each type of orbital Higher-energy configurations Typical minimum increase in energy (to next-lowest configuration) found by promotion of a single electron to the next- lowest available single-electron energy state Can find all configurations by successive promotion s ie E E s 1 2 2 ) 1 ( p s ie s s ie E E E p s E E E s s 2 1 1 1 2 1 1 1 ) 2 ( ) 1 ( ) 2 ( ) 1 ( Energy-level estimation Use independent- electron model as a start Energies of the helium-atom states estimated Promote electrons singly to create configurations Indistinguishability In practice, one cannot distinguish electrons by labels Theory must reflect the ambiguity this fact requires Interchange of labels cannot have a noticeable effect on properties like energy or electron density Requirement on total multi-electron wave function Electrons are fermions , particles whose wave functions change sign upon interchange of two particles Multi-electron wave functions reflect this property Example of the helium atom We use the interchange operator, I ab , to indicate this property 2 1 1 2 2 1 12 , , , r r r r r r I Application to helium-atom ground state Helium-atom state consists of two parts Spatial part Spin part Intechanging the electrons must change the sign of the wave function Spatial part does not change sign Spin part must change sign spin s s gs ) ( ) ( 2...
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