Which among the following elements has the largest atomic radii?
Option (c) is correct.
Na and Mg belong to period 3 and K and Ca belong to period 4 of the modern periodic table.
Across a period, nuclear charge increases, hence the atomic radius decreases. So, Mg that lies to the right of Na will have a smaller radius than Na. Similarly, Ca that lies to the right of K will have a smaller radius than K.
Down the group, there is an increase in atomic radius because of filling of electrons in a new shell (increase in nuclear charge is dominated by an increase in distance).
So K that belongs to period 4 will have the largest radius.