The atomic radius of sodium (Na) is larger than that of chlorine (Cl) because of their positions in the periodic table. Sodium, being in Group 1, has a single electron in its outer shell and a greater number of electron shells compared to chlorine, which is in Group 17. As you move from sodium to chlorine across Period 3, the atomic radius decreases. This is due to the increase in nuclear charge. Chlorine has more protons in its nucleus than sodium, which leads to a stronger attraction between the nucleus and the electrons.
However, when we look at the ionic radii, things change. The ionic radius of Na+ is smaller than its atomic radius due to the loss of its outermost electron, resulting in a greater effective nuclear charge on the remaining electrons. On the other hand, Cl gains an electron to become Cl–, which leads to an increased electron-electron repulsion in the outer shell, making the ionic radius larger. The added electron means that there are now more electrons than protons, reducing the effective nuclear pull on the outermost electrons.
In summary, the atomic radius decreases from Na to Cl due to increasing nuclear charge with no additional electron shells, while the ionic radius increases for Cl– due to increased electron repulsion after gaining an electron, despite the regular trend of decreasing ionic radii in the periodic table.