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They are different sizes in ionic radius because they have a different nuclear charge. All these ions have the same number of electrons, but Cl- has more protons so these protons will pull on the electrons closer to the nucleus, while the extra electrons in P-3 help shield the effective attraction of the nucleus allowing for a greater ionic radius.
Just to add on, we learned that anions are always larger than their parents ions (and cations are smaller). Relating to what Brian said, phosphorus is the the largest anion now with the addition of 3 electrons to shield the attraction by the nucleus, whereas the chloride anion only has one extra election, providing not as much shielding and thus the nucleus has a greater attraction to pull them in for the smallest ionic radius out of the three.
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