Final answer:
A K atom has a larger radius than a Na atom because potassium has more electron shells due to its position lower on the periodic table, leading to a higher principal quantum number.
Step-by-step explanation:
The reason why the K atom has a bigger radius than the Na atom is predominantly due to the increase in principal quantum number, n, as we move down the groups in the periodic table. Both potassium (K) and sodium (Na) atoms have cations that are smaller than their neutral forms, which is a result of losing electrons and having a greater effective nuclear charge. However, potassium (K) is located below sodium (Na) on the periodic table, which means that potassium's outer electrons are in the 4th shell compared to sodium's which are in the 3rd shell. The increase in the principal quantum number corresponds to an increase in the number of electron shells, making the radius of a potassium atom larger than that of a sodium atom.