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Electrons make the atom bigger because they increase the number of shells the atom has. So losing electrons (becoming cation) would mean you are reducing the number of energy levels and therefore decreasing the size of the atom. Vice versa, since an anion is gaining electrons, it has more shells than the neutral atom, meaning it is bigger than the original element.
Well the previous reply is not always true because sometimes the ions doesn’t lose or gain enough electrons to subtract or add an energy level. Sometimes you can remove one electron and it would still have the same principal quantum number. Cations are smaller because cations have less electrons than their parent atoms. Less electrons mean less electron-electron repulsions, so the ionic radius is smaller. Conversely, anions are larger because they have more electrons, and therefore, more electron-electron repulsions, than the parent atom.
Hannah is correct, the atom doesn't necessarily lose or gain an entire shell when it loses or gains electrons. When e- are lost, the atom is a cation and has more protons than e-. Therefore, the positive charge of the protons can pull more on each e- than it could in the atom's neutral state. The e- will get pulled closer to the nucleus and the atom is smaller. When e- are gained, there are more e- than protons, so the protons have less "pull" on the e-. The e- can spread out easier and the e- cloud increases in size away from the nucleus.
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