Which has lower atomic radius: Ca or Ba? Why?

Atomic radius of any two atoms can be compared by knowing their relative position in the periodic table of elements. As we move down a group, an extra shell of electrons is added between any two successive elements. This causes the atomic radius to increase down a group. This also causes the nuclear attraction for valence electrons to decrease, since the distance between the nucleus and valence electrons increases, thus making electron loss easier. In comparison, atomic radius decreases as we move across a period, since only one electron is added at a time. This makes the electron loss difficult.

When comparing calcium and barium, both of these elements are members of group 2 (thus making them alkaline earth metals), although calcium is a member of period 4, while barium is a member of period 6. This means that barium atom has two more layers of electrons than calcium and hence has a bigger atomic radius than calcium.

Thus, of the two, calcium has lower atomic radius.

Hope this helps.