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Polarizability is the inclination of electrons to be distorted in an anion. Polarizing power is the ability of a cation to distort electrons of an anion. The size of cations are pretty small in comparison to the size of anions, since the radii of cations are small, their nucleus has enough pulling energy to pull onto (or distort) the electrons of an anion, and an anion's size is bigger and their electrons are farther from the nucleus and the nucleus cannot hold onto the electrons that are further away from it. I think of it as, polarizability = anions, polarizing power = cations.
The tendency of an anion to become polarized by the cation is polarizability while the ability of a cation to distort an anion is polarization power. When looking at more polarizability you would look at a higher electron to proton ration and when looking at polarization power you would look at higher proton to electron ratio.
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