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Question
Explain the Pauling method for the determination of ionic radius.
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Solution
- 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.
- Ionic radius of the uni-univalent crystal can be calculated from the inter-ionic distance between the nuclei of the cation and anion.
- 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. - 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 Zeff is the effective nuclear charge
Zeff = Z – S - 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.
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