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Higher polarizing power refers to "atoms and ions that CAN cause large distortions." I capitalized "can" because that word made me understand what is meant by polarizing power. So basically the higher poloarizing power an atom has, the more it can pull electrons toward it. Small, highly charged cations have high polarizing power because they are pulling electrons toward it, so when they bond with other atoms they are more likely to "distort" the electrons toward themselves.
Another way to look at it is that polarizing power is the ability of the cation to attract electrons (which cause distortions in the electrons of anions). Looking at it this way, smaller, highly-charge cations have the ability to attract electrons more, which makes them have a higher polarizing power. The high charge allows them to be able to pull the negative electrons more and the smaller radius accounts for less shielding from subshells as well as a greater attractive force from the positive nucleus. These two factors greatly increase the polarizing power of a cation.
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