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Atoms with valence electrons in further shells from the nucleus experience less attraction from the nucleus. These electrons are not held onto as strongly and are able to be attracted by other atom's positive charges, therefore when a small cation such as Na+ is near a large atom with electrons far from the nucleus, such as Br-, Br-'s valence electrons are attracted to the Na+. The valence electrons will be distorted towards the Na+ and stay around the Na+ side. Then, you can say the polarizability increases with increasing size of anions. Polarizing power increases by decreasing the size of a cation because there is less electron shielding of its own electrons and the positive attraction is greater.
Pretend that the nucleus of each atom has a large circle around it. This is the electron cloud, the region where electrons could be found (we can't say where electrons are exactly so we kinda just create an area where they're most likely to be found—hence the electron cloud). Now say you have sodium chloride (NaCl), which is made up of two ions: Na+ and Cl-. When they're bonded, the positive nature of sodium will actually pull the electrons from chlorine closer to sodium. We represent this by taking the large circle around chlorine and distorting it, making the cloud appear like it's being sucked by the Na+ ion.
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