Why does calcium have a larger atomic radius than magnesium

Down the group , atomic radius of atoms increase due to increase in number of shells there by increasing shielding effect and decreasing effective nuclear charge . ( effective nuclear charge pulls the valence shell closer to the nucleus)

the old alchemists made significant contributions to science even though there starting premises were off a bit. their conclusions after failure would steer them into better directions for investigation. science is no more than close observation and the initial mistakes result in rethinking and retrying experiments.