Screening and Effective Nuclear Charge (©2007, François G. Amar, All rights reserved)
We've defined the effective nuclear charge, Zeff felt by an electron in an orbital as
Zeff= Z- S
where Z is the nuclear charge or number of protons in the nucleus and S is a screening constant. What this represents is the fact that the chosen electron feels a net Coulomb force that includes the attraction of the nucleus but is partially cancelled (or screened) by the neighboring electrons in the atom.
In 1930, John Slater developed a set of rules to define the value of S for an electron in an orbital
1. S is the sum of contributions from other electrons in shells with the same or smaller principal quantum number.
1a. Any electron in a shell with higher principal quantum number than the electron of interest contributes nothing to S2. If the screening electron is in the same shell (same n) it contributes 0.35 to S. (If we're considering a 1s electron, use 0.30 instead of 0.35).
3. If the screening electron is the next lower shell (n-1), it contributes 0.85 to S.
4. If the screening electron is in any shell below that (n-2, n-3 etc), it contributes 1.00 to S.
These rules can be turned into a formula:
S=0.0Nn+1+0.35 Nn + 0.85 Nn-1 + 1.00Nn-2
Let's apply this rule to the outer shell electrons of Li and B (boron).
Atom Li (1s)2(2s)1 B (1s)2(2s)2(2p)1 2.6
The outer electron of Li and B is, in each case, in the n=2 shell. The Li electron feels half the effective nuclear charge of the B electron and therefore will be further from the nucleus and less tightly bound (in terms of energy). Thus the radius of Li is larger than the radius of B
RLi > RBand the energy required to ionize Li is less than that for B or
IPLi < IPB
Exercise: Apply this procedure to get S and Zeff for the outermost electron of the the following pair of atoms: C and O
Discuss whether the result you get is consistent with the observed trends in atomic radius and ionization potential.
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