So first, it's important to know how radius is determined o the periodic table:
The higher you go UP the periodic table, the smaller the radius. This is because as you go down the periodic table, there is more electron shielding. The more electron shells means that there is more distance between the positively charged nucleus and the negatively charged valence shell of electrons. Its like those Russian nesting dolls: the more layers, the bigger the total volume. And the bigger the total volume, the further away the valence shell is from the nucleus. Its like holding a magnet 1 inch away versus holding it 1 foot away: you feel less attractive forces.
Now how does size affect going across the periodic table horizontally? As you go from left to right, the radius of NEUTRAL atom decreases. This is because as you go from left to right, the number of shells stays the same, but the number of protons increase. That's like comparing the strength of one magnet on a rock vs 2 magnets on a metal rock. Double the magnets means double the strength! (Kinda lol, but its a good example).
Now let's look at the question. We can rule out Cl- since its isoelectronic with I- but the only difference is that I- is lower on the periodic table so it would be bigger. With the same logic, we can rule out Mg2+ as Ca2+ is isoelectronic with it, but Ca is lower so it will be bigger than Mg.
Now how does ions affect sizes? When an atom gains an electron, the radius increases. This is because there is more electrons than protons so there is less "energy" to hold everything together. It's like asking John to go from carrying 40 pounds to 80 pounds of dumbbells': You have the same weak person but you increase the work load so he cant carry them as easy. Conversely, if you remove electrons from an atom, what do you think will happen? Using the same analogy, its like making the dumbbells' lighter which makes it easier for John to carry. Thus the radius decreases.
With all of that out of the way, which answer is correct between Ca2+ and I-? Ca2+ would be isoelectronic to Ar but have a smaller radius than it since it has more protons. Meanwhile, I- would be isoelectronic to Xe, but it would have a larger radius than Xe since it has less protons than it. Thus I- would have the largest radius since it gains an electron and it is lower than all of the other choices on the periodic table.
