Which Ion from Na+ and Mg2+ has a smaller atomic radii? Explain why?

The smaller ion of the two would be Mg²⁺. Both ions have the same electronic arrangement so the amount of shielding occuring for both ions is the same. The key difference between the ions that causes the Mg²⁺ to have a smaller atomic radii, is that it has more protons within its nucleus, hence a greater nuclear charge than Na⁺ which means it will attract the valence electrons on the ion to a greater degree, shortening the distance between the nucleus and valence electrons and so making the ion smaller.