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  Paulings Method

Pauling’s Method:

Pauling has evaluated the radii of the ions on the basis of the examined internuclear distances in four crystals that is, NaF, KCl, RbBr and CsI. In each and every ionic crystal the cations and anions are iso-electronic with inert gas configuration.

2153_paulings method.jpg

In addition, the following two suppositions are made to assign the ionic radii.

1) The cations and anions of ionic crystal are supposed to be in contact with each other and therefore the sum of their radii will be equivalent to the inter nuclear distance among them.

r(C+) + r(A-) = d (C+– A- )

Here,
r(C+) - radius of cation, C+
r(A-) - radius of anion, A-
d(C+–A–) - internuclear distance among C+ and A– ions in C+A– ionic crystal.

2) For given noble gas configuration, the radius of ion is inversely proportional to its efficient nuclear charge that is,

1778_paulings method2.jpg

Here,

Z*(C+) & Z*(A–) are the efficient nuclear charges of cation (C+) and anion (A-) correspondingly. On combining the above two:

1523_paulings method3.jpg

Therefore the above two equations (first & last) can be utilized to calculate the values of r(C+) and r(A–) provided the values of d(C+–A–), Z*(C+) and Z*(A–) are acknowledged.

 

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