lecture_16_07

lecture_16_07 - Covalent bond I H2 N2 CO Symmetry of 2 e...

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05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 1 Covalent bond I H 2 N 2 CO Symmetry of 2 e - wavefunctions shared by 2 atoms First: 1 dimensional model - 2 identical wells - 1 electron symmetric spatial ψ antisymmetric spatial ψ Single particle wavefunctions As the 2 wells get closer together have | ψ S | 2 >0 at center, but A 2 S A
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05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 2 Covalent bond II • H 2 + first. If the 2 wells have + charge they are repelled. So symmetric wave function provides extra attraction. For 2 H nuclei (protons) there is a repulsive energy. o o R ψ 1 + ψ 2 or ψ + negative charge between nuclei
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05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 3 Covalent bond III Nuclei repulsion U protons ( R ) = + k EM e 2 R For R fixed e - sees - k EM e 2 r 1 - k EM e 2 r 2 When R >> a 0 E electron = - 13.6 n 2 eV When R 0 for y + E + - 13.6 n 2 (Z = 2) 2 eV = - 54.4 n 2 eV But for y - must get vanishing at r = 0 when R 0 So y - ( r ) r or y - ~ 2p state Then E _ - 13.6(2) 2 (2) 2 = - 13.6 eV
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05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 4 Covalent bond IV 0 E(eV) -13.6 -16.3 -54.4 0.106 nm R(nm) 0.1 0.2 0.3 U p (R ) U p +E - U p +E + E + Total E has min for ψ + but not ψ - -16.3-(-13.6)=2.7 eV to separate H and H + - Binding Energy Min occurs for R 2a 0 when e - sits between protons - charge is shared or ρ charge has max at 0
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05/07/09 Physics 13 - Fall 07 - G.R. Goldstein 5 Covalent bond V • 2 electrons for H 2 - when separation R have 2x(-13.6 eV)=-27.2 eV for two H atoms U(eV) U - U + R(nm) -31.7 0.074nm 0.1 -27.2 Molecular B.E.
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lecture_16_07 - Covalent bond I H2 N2 CO Symmetry of 2 e...

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