Calculation of ionic radii
Pauling has calculated the radii of the ions on the basis of the observed internuclear distances in four crystals namely NaF, KCl, RbBr and CsI. In each ionic crystal the cations and anions are isoelectronic with inert gas configuration.
NaF crystal : Na+ - 2, 8 F- - 2, 8 Ne type configuration
KCl crystal : K+ - 2, 8, 8 Cl- - 2, 8, 8 Ar type configuration
Further the following two assumptions are made to assign the ionic radii.
i) The cations and anions of an ionic crystal are assumed to be in contact
with each other and hence the sum of their radii will be equal to the inter nuclear distance between them.
r(C+) + r(A-) = d (C+-A-)
r(C+) - radius of cation, C+ r(A-)
- radius of anion, A-
d(C+-A-) - internuclear distance between C+ and A- ions in C+A- ionic crystal
ii) For a given noble gas configuration, the radius of an ion is inversely proportional to its effective nuclear charge. i.e.
r(C+ ) á = 1/ Z (C+ )
r(A- ) á = 1/ Z (A- )
Z*(C+) & Z*(A-) are the effective nuclear charges of cation (C+) and anion (A-) respectively. On combining
r(C+ ) / r(A- ) = Z*(A- ) / Z*(C+ )
Hence the above two equations (1) & (4) can be used to evaluate the
values of r(C+) and r(A-) provided that the values of d(C+-A-), Z*(C+) and Z*(A-) are known.
The value of screening constant (S) and effective nuclear charge (Z*) can
be calculated by using Slater's rules. According to these rules the value of "S" for a given electron is estimated as follows.
i) Write down the complete electronic configuration of the element and divide the electrons into the following orbital groups starting from the inside of the atom.
(1s) : (2s, 2p) : (3s, 3p) : (3d) : (4s, 4p) :
(4d) : (4f) : (5s, 5p) : (6s, 6p) .......etc.
ii) Select the electron for which the value of S is to be calculated. For this calculation add up the contributions to S for the other electrons according to the following rules.
Contribution to S for each electron of this type
Type of electron
1. All electrons in groups outside the electron chosen - 0
2. All other electrons in the same group as the chosen one (n) - 0.35 (or 0.30 for 1s electron)
3. All electrons in shell immediately inside (n-1) - 0.85
All electrons further inside - 1.00