When atoms become ions (Predicting Ion Charges), their sizes change a lot. Shielding and Effective Nuclear Charge explains which way, and it settles the hardest comparison: ions that have the same number of electrons.
Key idea
Cations are smaller than their atoms: $\mathrm{Na^+}$ (102 pm) is much smaller than Na (166 pm). Anions are larger than their atoms: $\mathrm{Cl^-}$ (181 pm) is larger than Cl (102 pm). In an isoelectronic series (same number of electrons), more protons make a smaller ion: $\mathrm{O^{2-}} > \mathrm{F^-} > \mathrm{Na^+} > \mathrm{Mg^{2+}} > \mathrm{Al^{3+}}$.
Why it works
A sodium atom that loses its $3s$ electron loses its whole outer shell; what is left is the neon-like core, held by 11 protons, so it is far smaller. A chlorine atom that gains an electron keeps the same 17 protons but now has 18 electrons repelling one another, so the cloud spreads out. In an isoelectronic series, every ion has the same 10 electrons in the same arrangement, $1s^2 2s^2 2p^6$; the only difference is the nuclear charge, from 8 in $\mathrm{O^{2-}}$ to 13 in $\mathrm{Al^{3+}}$. More protons pull the same cloud in tighter.
Worked example: An isoelectronic series
Rank $\mathrm{S^{2-}}$, $\mathrm{Cl^-}$, $\mathrm{K^+}$ and $\mathrm{Ca^{2+}}$ from largest to smallest.
- Count electrons: S has 16, so $\mathrm{S^{2-}}$ has 18; $\mathrm{Cl^-}$ 18; $\mathrm{K^+}$ 18; $\mathrm{Ca^{2+}}$ 18. All isoelectronic with argon.
- Protons: S 16, Cl 17, K 19, Ca 20. More protons, smaller ion.
Answer: $\mathrm{S^{2-}} > \mathrm{Cl^-} > \mathrm{K^+} > \mathrm{Ca^{2+}}$ (184, 181, 138, 100 pm).
Worked example: Two ions of one element
Which is smaller, $\mathrm{Fe^{2+}}$ or $\mathrm{Fe^{3+}}$?
- Same nucleus (26 protons). $\mathrm{Fe^{3+}}$ has one electron fewer.
- Fewer electrons, less repulsion, and the same charge pulling them in: a smaller ion.
Answer: $\mathrm{Fe^{3+}}$ (65 pm against 78 pm).
Worked example: Down a group
Rank $\mathrm{Li^+}$, $\mathrm{Na^+}$ and $\mathrm{K^+}$ by size.
- Each has one more filled shell than the one before, and the simple $Z_\text{eff}$ for the outer shell stays about the same.
- More shells, larger ion.
Answer: $\mathrm{Li^+} < \mathrm{Na^+} < \mathrm{K^+}$ (76, 102, 138 pm).
Common mistake
Thinking the ion with more protons is bigger in an isoelectronic series ("aluminum is a bigger atom than oxygen, so $\mathrm{Al^{3+}}$ is bigger than $\mathrm{O^{2-}}$"), or that anions shrink. With the electron count fixed, protons only pull; they add no size. Check: in an isoelectronic series the anions are the big ones and the most highly charged cation is the smallest.