The first ionization energy decreases down a group

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The first ionization energy decreases down a group. Because highest energy e - s are, on average, farther from nucleus. As principal quantum number increases, size of orbital increases and e - is easier to remove. e.g., I 1 ( Na ) > I 1 ( Cs ) and I 1 ( Cl ) > I 1 ( I ) . P. J. Grandinetti (Chem. 4300) Multi-electron Atoms Nov 20, 2017 21 / 39
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Electron Affinity Energy associated with addition of electron to gaseous atom is called electron affinity . Cl(g) + e - Cl - (g) Δ E = - E EA = - 349 kJ/mol . Sign on energy change is negative because energy is usually released in this process. More negative Δ E corresponds to greater attraction for e - . An unbound e - has an Δ E of zero. Convention is to define e - affinity energy, E EA , as negative of energy released in reaction. P. J. Grandinetti (Chem. 4300) Multi-electron Atoms Nov 20, 2017 22 / 39
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Electron Affinity 10 20 30 40 50 50 0 100 150 200 250 300 350 atomic number electron affinity / kJ/mol Period 1 Period 2 Period 3 Period 5 Period 6 Li Be B C O F Cl I Ne Kr Na Mg Al Si P S He He H N Ar 2 rules that govern periodic trends of e - affinities: 1 e - affinity becomes smaller down group. 2 e - affinity decreases or increases across period depending on electronic configuration. P. J. Grandinetti (Chem. 4300) Multi-electron Atoms Nov 20, 2017 23 / 39
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Electron Affinity 1 e - affinity becomes smaller down group. As principal quantum number increases, size of orbital increases and affinity for e - is less. Change is small and there are many exceptions. 2 e - affinity decreases or increases across period depending on electronic configuration. This occurs because of same sub-shell rule that governs ionization energies. e.g., E EA ( C ) > E EA ( N ) . Since a half-filled p sub-shell is more stable, C has a greater affinity for an electron than N. Obviously, the halogens, which are one electron away from a noble gas electron configuration, have high affinities for electrons. F’s electron affinity is smaller than Cl’s because of higher electron–electron repulsions in smaller 2p orbital compared to larger 3p orbital of Cl. P. J. Grandinetti (Chem. 4300) Multi-electron Atoms Nov 20, 2017 24 / 39
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Angular Momentum in Multi-electron Atoms P. J. Grandinetti (Chem. 4300) Multi-electron Atoms Nov 20, 2017 25 / 39
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Angular Momentum in Atom with N electrons In absence of external fields split ̂ for multi-electron atom into 3 parts: ̂ = ̂ 0 + ̂ ee + ̂ SO ̂ 0 is electron kinetic energy and nuclear Coulomb attraction: ̂ 0 = N i = 1 [ - 2 2 m e 2 i - Zq 2 e 4 𝜋𝜖 0 r i ] ̂ ee is electron repulsion: ̂ ee = N - 1 i = 1 N j = i + 1 q 2 e 4 𝜋𝜖 0 r ij ̂ SO is spin-orbit coupling: ̂ SO = N i = 1 𝜉 ( r i ) 𝓁 i s i There are additional interactions we could add to total ̂ , but these can be handled later as perturbations to ̂ . P. J. Grandinetti (Chem. 4300) Multi-electron Atoms Nov 20, 2017 26 / 39
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Angular Momentum in Atom with N electrons In absence of external fields split ̂ for multi-electron atom into 3 parts: ̂ = ̂ 0 + ̂ ee + ̂ SO In H-atom we saw that spin orbit coupling was small correction to ̂ 0 .
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