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Chapter 20

Q. 20.5

Write an orbital wave function without antisymmetrization or normalization for the diatomicb boron molecule in its ground level.

Step-by-Step

Verified Solution

Ψ = ψ_{σ_{g}1_{s}} (1)α(1)ψ_{σ_{g}1s}(2)β(2)ψ_{σ_{u}^{∗}1s}(3)α(3)ψ_{σ_{u}^{∗}1s}(4)β(4)×ψ_{σ_{g}2s}(5)α(5)ψ_{σ_{g}2_{s}}(6)β(6)ψ_{σ_{u}^{∗}2s}(7)α(7)ψ_{σ_{u}^{∗}2s}(8)β(8)× ψ_{π_{u}2p_{x}}(9)α(9)ψ_{π_{u}2p_{y}}(10)α(10)

This wave function is one of the three triplet wave functions making up the ground level. Another triplet function contains twoβ spin functions instead ofαfactors for electrons 9 and 10 and the third triplet function contains the symmetric spin factor \sqrt{\frac{1}{2} } [α(9)β(10) + β(9)α(10)].

There is also a singlet function containing the antisymmetric spin factor \sqrt{\frac{1}{2} } [α(9)β(10)-β(9)α(10)].