Explain the pauling method for the determination os ionic radius.

Explanation

(i) Ionic radius of uni - univalent crystal can be calculated using Pauling's method from the inter ionic distance between the nuclei of the cation and anion.
(ii) Pauling assumed that ions present in a crystal lattice are perfect spheres, and they are in contact with each other therefore,
`d=r_(C )^(+)+r_(A)^(-) " "` ....(1)
Where d is the distance between the centre of the nucleus of cation `C^(+)` and anion `A^(-)` and `r_(C )^(+), r_(A)^(-)` are the radius of the cation and anion respectively.
(iii) Pauling also assumed that the radius of the ion having noble gas electronic configuration is inversely proportional to the effective nuclear charge.
`r_(C )+alpha (1)/((Z_(eff))_(C^(+)))" "` ...(2)
`r_(A)-alpha (1)/((Z_(eff))_(A^(-)))" "` ...(3)
Where `Z_(eff)` is the effective nuclear charge and `Z_(eff)=Z-S`
Dividing the equation 1 by 3
`(r_(C^(+)))/(r_(A^(-)))=((Z_(eff))_(A^(-)))/((Z_(eff))_(C^(+)))" "` ....(4)
On solving equation (1) and (4) the values of `r_(C^(+))` and `r_(A^(-))` can be obtained.