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Polarizing power is the ability of a cation to cause distortions in another atom's or ion's electron cloud. In general, the smaller and more highly charged the cation, the stronger the polarizing power. This is because the smaller radius allows the nucleus of the cation to maintain a stronger pull on the anion's electrons and cause a measurable distortion. Polarizing power increases from left to right across a period because the atomic radius decreases and charge increases. It decreases down a group because the atomic radius increases while the charge stays constant. Whether charge or size is the determining factor of the magnitude of polarizing power is situational. In a group, size would be the determining factor while across a period both factors can be used.
I would say the charge density matters the most--that is the charge/size(surface area) ratio. Cation which has a high polarizing power will have a high charge density so that its charges are very concentrated. Typically, cation with a high charge and a small size has greater polarizing power.
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