The radius of the Mg atom increases because the Mg²⁺ has gained 2 extra electrons and a new shell has also been added.
Magnesium atom and ion
General, magnesium atom, Mg has 3 electron shells while magnesium ion, Mg²⁺ has 2 electron shells.
Since Mg is a metal, its atom is bigger that its ion, Mg²⁺.
Thus, to move from Mg²⁺ to Mg, the ion will need 2 extra electrons as shown below:
Mg²⁺ + 2e —> Mg
Since the Mg atom is bigger, it also means that the radius of the Mg is bigger than the radius of the Mg²⁺.
See attached photo for further details
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