Question

Explain the Pauling method for the determination of ionic radius.

Answer 1

1. Ionic radius is defined as the distance from the center of the nucleus of the ion up to which it exerts its influence on the electron cloud of the ion.
2. Ionic radius of the uni-univalent crystal can be calculated from the inter-ionic distance between the nuclei of the cation and anion.
3. 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 = distance between the center of the nucleus of cation C⁺ and the anion A^-. `"r"_("C"^+)` = radius of cation and `"r"_("A"^-)` = radius of the anion.
4. Pauling assumed that the radius of the ion having noble gas configuration (Na⁺ and F^– having 1s², 2s², 2p⁶ configuration) is inversely proportional to the effective nuclear charge felt at the periphery of the ion.
   i.e. `"r"_("C"^+)  α 1/(("Z"_"eff")_("C"^+))` .........(2)
   `"r"_("A"^-)  α 1/(("Z"_"eff")_("A"^-))` .........(3)
   Where Z_eff is the effective nuclear charge
   Z_eff = Z – S
5. Dividing the equation (2) 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.