Final answer:
The atomic radius increases down a group in the periodic table due to the addition of more principal energy levels, which outweighs the increase in nuclear charge, resulting in larger atomic sizes.
Step-by-step explanation:
The trend for atomic radius down a group in the periodic table is characterized by an increase in size. This trend is due to the addition of more occupied principal energy levels (shells) as one moves down a group, with each subsequent level being further from the nucleus than the last. Although there is an increase in positive nuclear charge that attracts the electrons towards the nucleus, this is outweighed by the addition of these larger, more distant shells, resulting in an overall increase in the atomic radius.
Furthermore, each new energy level consists of orbitals that are more spread out, meaning that the valence electrons are farther from the nucleus. This lessens the effect of the positive charge that would otherwise pull electrons inwards, thus contributing to the larger atomic radii seen down a group. This increase in atomic size is critical in understanding many properties of elements, such as their ionization energies and reactivities.
Reflecting on periodic trends, such as atomic radii, in comparison to covalent radius and electron affinity, reveals the relationship between an element's position on the periodic table and its chemical properties. Therefore, the atomic radius plays a significant role in the periodic behavior of elements.