Final answer:
The increasing atomic radius within a group on the periodic table is due to the increasing number of electron shells, which results from the addition of electrons in higher principal quantum number shells as the atomic number increases down the group.
Step-by-step explanation:
The reason for the increasing atomic radius within one group on the periodic table is primarily due to the increasing number of electron shells. As one moves down a group, the atomic number increases, which means there are more protons in the nucleus and more electrons surrounding it. These additional electrons reside in higher principal quantum number shells, which are physically larger, leading to a larger atomic radius. This effect is related to electron shielding, where inner electron shells shield the outer electrons from the full charge of the nucleus, thus the outer electrons are less tightly held and may occupy a greater volume.
This trend can be observed as we go down a column of the periodic table, where the increase in principal energy levels outweighs the increase in nuclear charge, resulting in an increased atomic radius. This contrasts with the horizontal trend across a period where atomic radius decreases as the nuclear charge increases without an increase in principal energy levels, which pulls electrons closer to the nucleus and reduces atom size.