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Unit 1, Day 8 Suggested Problem for Slater’s Rules Use Slater's rules to evaluate the following three possible electron configurations for scandium and comment on your results: [Ar]4s23d1, [Ar]4s13d2, and [Ar]3d3 The effective nuclear charge, Zeff, is given as Z – S where Z is the actual charge on the nucleus and S is a shielding constant the value of which is determined using the following set of rules: 1. write out the electron configuration in groups using the following order (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) … 2. identify the group in which the electron of interest lies; ignore electrons to the right of this group 3. if the electron of interest is an s or p electron, then each additional electron in its (ns, np) group contributes 0.35 to S, each electron in the n – 1 shell contributes 0.85 to S, and each electron further to the left contributes 1.00 to S 4. if the electron of interest is a d or f electron, then each additional electron in its (nd) or (nf) group contributes 0.35 to S and each electron further to the left contributes 1.00 to S [Ar]4s 23d 1 For the 4s electrons we use rules 1–3. The grouped electron configuration is (1s2) (2s2, 2p6) (3s2, 3p6) (3d1) (4s2) and the effective nuclear charge is Zeff = Z – S = 21.00 – (1!0.35 + 9!0.85 + 10!1.00) = 21.00 – 18.00 = 3.00 For the 3d electron we use rules 1, 2 and 4. The grouped electron configuration is (1s2) (2s2, 2p6) (3s2, 3p6) (3d1) (4s2) and the effective nuclear charge is Zeff = Z – S = 21.00 – (18!1.00) = 21.00 – 18.00 = 3.00 [Ar]4s 13d 2 For the 4s electrons we use rules 1–3. The grouped electron configuration is (1s2) (2s2, 2p6) (3s2, 3p6) (3d2) (4s1) and the effective nuclear charge is Zeff = Z – S = 21.00 – (10!0.85 + 10!1.00) = 21.00 – 18.50 = 2.50 For the 3d electrons we use rules 1, 2 and 4. The grouped electron configuration is (1s2) (2s2, 2p6) (3s2, 3p6) (3d2) (4s1) and the effective nuclear charge is Zeff = Z – S = 21.00 – (1!0.35 + 18!1.00) = 21.00 – 18.35 = 2.65 [Ar]3d 3 For the 3d electrons we use rules 1, 2 and 4. The grouped electron configuration is (1s2) (2s2, 2p6) (3s2, 3p6) (3d3) and the effective nuclear charge is Zeff = Z – S = 21.00 – (2!0.35 + 18!1.00) = 21.00 – 18.70 = 2.30 Comments on Results The table below summarizes the results of these calculations: electron configuration Zeff for 4s Zeff for 3d Average Zeff [Ar]4s23d1 [Ar]4s13d2 [Ar]3d3 3.00 2.50 — 3.00 2.65 2.30 3.00 2.60 2.30 The average Zeff is determined by accounting for the number of 3d and 4s electrons. Greater values for Zeff provide for a stronger attractive force between the electron and the nucleus. We see in these results that the most stable electron configuration is [Ar]4s23d1.