Answer: option (1) Fe
Explanation:
1) The atomic radius change in a predictible way. This is, the atomic radius has a pattern or trend that can be traced by looking at the periodic table.
2) For elements in the same period, the trend is as you go from left to right the atomic radius decreases (due to the greater attraction exerted by a nucleus with more protons over electrons at basically the same distance).
That permits you to compare:
i) Fe and Zn which are in the same period (4). Zn is more to the right than Fe, so Fe is larger than Zn.
ii) Si and Mg are in the same period (3). Si is more to the right than Mg, so Mg is larger than Si.
Now, you have to decide between Fe and Mg which is larger.
3) Fe and Mg are in different periods. The pattern, for elements in the same group is that the atomic radius increases as you go from top to bottom into the group.
That is due to the increase in the size of the orbital (larger principal quantum number means larger orbital).
So, here are two patterns that oppose each other: since Fe is in an larger than Mg orbital it should be larger, but since Fe the nucleus of Fe is bigger than the nucleus of Mg, Fe trends to be smaller. What trend predominates?
You do not know how to predict that, so must go to the data. I did it and found that the atomic radius of Mg is 1.45 angstroms, while the atomic radius of Fe is 1.56 angstroms.
So, the effect of increase of the size of the orbital predominates.
The element on the list that has the largest atomic radius is Fe.
