Calculation of Ionic Radii in Pauling’s Method - QS Study

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; this calculation named Pauling’s Method. In each ionic crystal the cations and anions are isoelectronic with inert gas 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) … … … … (1)

where,

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+) α 1/ Z*(C+) … … … (2)

r(A+) α 1/ Z*(A) … … … (3)

where, Z*(C+) & Z*(A) are the effective nuclear charges of cation (C+) and anion (A) respectively. On combining (2) & (3)

r(C+)/ r(A+) = Z*(A)/ Z*(C+) … … … … (4)

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.