Final answer:
The atomic radius of K is larger than that of Na because potassium's valence electrons are in a higher principal energy level, which is farther away from the nucleus compared to sodium's.
Step-by-step explanation:
The atomic radius of K (potassium) is larger than that of Na (sodium) due to the increase in the principal quantum number. As you go down a column of the periodic table, the atomic radii increase. This happens because the valence electron shell is getting larger with each subsequent element, and the highest occupied energy level, represented by the principal quantum number, also increases, thereby positioning the valence shell farther from the nucleus.
Moreover, the increase in the principal quantum number implies that potassium's outermost electrons are in a higher principal energy level (fourth level for K versus third level for Na). This results in a larger atomic radius for potassium as the added shell means that its valence electrons are further away from the positive attraction of the nucleus, despite any increased nuclear charge that results from having more protons.