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When a highly charged cation has the ability to distort the electron cloud of an anion, this process is known as polarization. Highly distorted electrons are described as highly polarizable. When atoms and ions have electron clouds that undergo large distortion, they have highly polarizing power.
To be highly polarizable means that a molecule has so many electrons that sometimes a high density of electrons can be found on just one side of the atom. This high density all one one side creates a very temporary moment of unusually high negative charge, which means the other side without all these electrons is partially positively charged. What this means is even a neutrally charged molecule of atom can become charged. So if a molecule is "highly polarizable" that means it is highly likely for it to become charged or polarized, it literally means "able to become polarized." Just think more electrons in an atom/molecule = more polarizable.
By definition, you can think of polarizable as the capability to form poles - as in a negative and a positive side. As stated above, atoms with a large number of electrons are more susceptible to being polarized, as the pull on the electrons from the positive nucleus is weaker. Therefore, these atoms with many electrons are polarizable in the sense that if a small ion with high polarizing power were to bond with it, then the electrons would be attracted to one side, creating "poles."
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