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I find it difficult to understand why the Atomic radius of $\ce{Ar}$ is lower than the ionic radius of $\ce{Mg^2+}$ and $\ce{F-}$, and higher than $\ce{Al^3+}$. According to the tables I've seen:

$$\ce{F- = 119 pm > Mg^2+ = 86 pm > Ar = 71 pm > Al^3+ = 68 pm}$$

Shouldn't Ar be larger than all three since it has a third electron shell, and they only have two? From what I was taught, the number of electron shells is more important then the number of protons in the atom. What differs so much between $\ce{Mg^2+}$ and $\ce{Al^3+}$ that $\ce{Ar}$ atomic radius is right between them?

Is there a way to predict this order, just by looking at the periodic table?

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