Final answer:
Atomic radii within a group increase as you move down the periodic table due to the addition of principal energy levels, which makes the valence electron shell larger and placed farther from the nucleus, outweighing the increase in nuclear charge.
Step-by-step explanation:
The trend in atomic radii within a group can be accounted for by considering the number of occupied principal energy levels and the positive nuclear charge as you move down a group in the periodic table. As the atomic number increases down a group, we see an increase in the number of principal energy levels. These energy levels consist of orbitals that are larger in size than those in lower levels. While there is also an increase in nuclear charge, the effect of the greater number of energy levels outweighs this, leading to an increase in the atomic radius.
Atomic radii plotted against atomic number results in a trend where the atomic radii increase as we descend down a group in the periodic table. This is because with each step down, a new principal energy level is added, which places the valence electron shell physically farther away from the nucleus despite the growing nuclear charge.
In summary, the trend in atomic radii within each group is directly linked to the increase in occupied principal energy levels as you move down the periodic table, with valence electron shells getting larger and extending further out from the nucleus.