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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.