Atomic Radii and Effective Nuclear Charge

Van der Waals radius, or nonbonding atomic radius, is one-half the distance between adjacent nuclei in atomic solids. Covalent radius, or bonding atomic radius, differs for metals and nonmetals. In metals, it's one-half the distance between neighboring atom centers in crystal structures. In nonmetal diatomic molecules, it's one-half the distance between bonded atom centers.

As you move down a group, the principal quantum number increases by one for each element, placing outer electrons farther from the nucleus. Although nuclear charge increases, the additional inner shell electrons shield outer electrons more effectively. This greater distance outweighs the increased nuclear charge, causing atomic radius to increase down the group.

Across a period, nuclear charge increases while the number of inner shell electrons remains constant. Outer electrons in the same valence shell do not shield each other effectively. As effective nuclear charge increases, the nucleus pulls outer electrons closer, decreasing atomic radius. This stronger pull creates the periodic trend of decreasing size from left to right.

Inner shell electrons partially shield outer shell electrons from the nucleus's pull, reducing the effective nuclear charge felt by valence electrons. Core electrons shield efficiently, but outermost electrons do not shield one another effectively. The greater the effective nuclear charge after accounting for shielding, the stronger the nucleus holds outer electrons, resulting in a smaller atomic radius.

Transition elements maintain roughly constant atomic radii across each row because the number of electrons in the outermost principal energy level remains nearly constant. Although nuclear charge increases, the additional electrons enter inner d orbitals, not the valence shell. This results in a roughly constant effective nuclear charge experienced by outer electrons.

Alkali metals show maximum atomic radius at the beginning of each period. Moving down group 1 from lithium to cesium, atomic radius increases significantly. This trend reflects the increasing principal quantum number for valence electrons, placing them progressively farther from the nucleus despite increasing nuclear charge.

Bonding radius applies when atoms form covalent bonds, measured as one-half the distance between bonded atom centers in molecules or crystal structures. Nonbonding radius applies to isolated atoms in solids, measured as one-half the distance between adjacent nuclei. The choice depends on whether atoms are chemically bonded or simply in contact within a solid structure.