Final answer:
Barium (Ba) has the largest atomic radius out of the given elements because it is located further down in the periodic table, indicating it has more electron shells compared to the others.
Step-by-step explanation:
The element with the largest atomic radius among Mercury (Hg), Calcium (Ca), Barium (Ba), and Boron (B) is Barium (Ba). The atomic radius tends to increase as we move down a group in the periodic table because additional electron shells are added, making the atom larger.
Barium is located in Group 2 and is further down the group than Calcium, hence it has more electron shells and a larger atomic radius. Boron is located in Group 13 and Mercury in Group 12, but they are much higher up in the periodic table compared to Barium and Calcium, which means they have fewer electron shells and thus smaller atomic radii.