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You have to know that a higher negative charge means that there are more electrons added to the atom to achieve stability. There is greater electron-electron repulsion when electrons are added to the valence shell. As you move left to right across the periodic table, the atomic radius decreases. By adding more electrons, the positive charge of the nucleus is spread out more evenly. Thus, as P has the lowest number of protons and thus the lowest positive charge, it will be the biggest ion, followed by S and then Cl.
To add on, the easiest way I like to remember it is with the amount of protons, since the amount of electrons is the same with these ions. Protons have a positive charge which will draw negatively-charged electrons towards the nucleus, so if an ion has more protons in the nucleus, their radius will be smaller because it can bring outer electrons inwards.
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