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What is polarizing power and polarizability?

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Hint :We have studied that bonds can be ionic or covalent. But no bond is $100\% $ ionic or covalent. There will always be some covalent character in ionic bonds. Fajan’s rule (based on polarization) can help in deciding the nature of chemical bonds.

Complete Step By Step Answer:
In an isolated anion, the negative charge is evenly distributed but in the presence of cation the negative charge density of anion is distorted. The ability of a cation to distort the electron density of anion towards itself or we can say that ability of cation to pull the electron density of anion towards itself is known as Polarizing power
And the tendency by which the anion undergoes polarization is known as Polarizability.
Based on this, it was said that if the degree of polarization is small, the greater the ionic nature. If the degree of polarization is large, more will be the covalent nature.
Small cation: The smaller cations have more polarizing power. These cations can distort the charge density more strongly than large size cations which have low polarizing power.
Large anion: The larger anions can be easily polarized, as the nucleus doesn’t have much hold on the electrons and are loosely held. Thus large anions show distortion very easily in the presence of cation.
Large charges: As the charges increase the interaction between cation and the outer electrons also increases. Thus, increasing polarization.
Thus, we can conclude by saying that the polarizing power and polarizability determines the nature of bond. Smaller the cation (large polarizing power) or larger the anion (high polarizability) will lead to greater covalent nature in an ionic bond.

Note :
It is observed that ionic compounds with covalent nature are also soluble (appreciably) in non-polar solvents with low dielectric constants. This explains the covalent nature in ionic compounds.