Final answer:
The atomic radius of K is larger than that of Na because K has an additional electron shell, increased electron shielding, and a higher principal quantum number.
Step-by-step explanation:
The atomic radius of potassium (K) is larger than that of sodium (Na) because of its position on the periodic table. When moving from Na to K within the same group, one progresses from the third period to the fourth period, resulting in an increase in the principal quantum number, n. Each successive element down a group has one additional electron shell compared to the element above it, leading to a greater distance of the valence electrons from the nucleus and thus a larger atomic radius.
Moreover, although both K and Na are alkali metals, with each additional electron shell, the effect of electron shielding increases and counteracts the pull of the increased nuclear charge due to additional protons. The outermost electrons are held less tightly and are further from the nucleus in K than in Na, contributing to the increased atomic radius of potassium compared to sodium.