Question

consider the isoelectronic ions Cl- and K+. Which ion is smaller?

ssuming the core electrons contribute 1.00 and valence electrons contribute nothing to the screening constant, S, calculate Zeff for these two ions.

Repeat this calculation using slater's rules to estimate the screening constant, S. For esoelectronic ions how are effective nuclear charge and ionic radius related?

Answer 1

k+ ion is smaller in size

Zeff = Z - S Zeff is the effective nuclear charge on an electron; Z is the nuclear charge and S is the screening of that charge on the electron by all the other electrons.
Assume core electrons S = 1, valence electrons S = 0
Cl^- 1s^2 2s^2p^6 3s^2 3p^6 1s^2 2s^2p^6 S = 10; 3s^2 3p^6 S = 0
Zeff = Z-S = 17- 10 =7
K^+ 1s^2 2s^2p^6 3s^2 3p^6; 1s^2 2s^2p^6 S = 10; 3s^2 3p^6 S = 0
Zeff = Z-S = 19- 10 = 9

Firstly, the electrons are arranged in to a sequence of groups in order of increasing principal quantum number n, and for equal n in order of increasing azimuthal quantum number l, except that s- and p- orbitals are kept together. Well ignore 3d electrons etc: don’t apply
[1s] [2s,2p] [3s,3p] Each group is given a different shielding constant which depends upon the number and types of electrons in those groups preceding it.
The shielding constant for each group is formed as the sum of the following contributions:
An amount of 0.35 from each other electron within the same group except for the [1s] group, where the other electron contributes only 0.30.
If the group is of the [s p] type, an amount of 0.85 from each electron with principal quantum number (n) one less and an amount of 1.00 for each electron with an even smaller principal quantum number
Cl^- 1s^2 2s^2p^6 3s^2 3p^6; 1s^2 S = 2; 2s^2p^6 S = 8×0.85; 3s^2 3p^6 S = 7×0.35 (don’t count the electron under consideration)
S = 2 + 6.8 + 2.45 = 11.25
Zeff(Cl^-) = 17 – 11.25 = 5.75
K^+ 1s^2 2s^2p^6 3s^2 3p^6 same S as for Cl^- but Z increases by 2 hence
Zeff(K^+) = 19 - 11.25 = 7.75