State pauling univalent radii method to determine the ionic radii ?
Answers
Pauling has calculated the radii of the ions on the basis of the observed inter nuclear distance in four crystals namely.
NaF,KCl,RbCl and Csl.
i) In each ionic crystal, the cations and anions are isolated electronic with inert gas configuration.
K+Cl−−2,8,8−2,8,8∣∣∣
Ar type configuration
ii) 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(K+)+r(Cl−)=d(K+−Cl−) ..... (1)
where : r(K+)= Radius Of Cation K+
r(Cl−)= Radius Of Anion Cl−
d(K+−Cl−)= inter nuclear
distance between K+ and Cl− ions In K+ Cl− ionic crystal
iii) For a given noble gas configuration the radius of an ion is inversely proportional to its effective nuclear charge.
r(K+)∝1Z⋆(K+) .......(2)
r(Cl−)∝1Z⋆(Cl−) .......(3)
Where Z⋆ (K+) and Z⋆ (Cl−) are the effective nuclear charges of cation K+ and Cl− respectively on combining (2) and (3)
r(K+)r(Cl−)=Z⋆(Cl−)Z⋆(K+) ........(4)
The 2 equations (1) and (4) can be used to evaluate the values of r(K+) and r(Cl−), provided that the value of d(K+Cl−)Z⋆(K+) and Z⋆(Cl−) are known.
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