Atomic Radii and Effective Nuclear Charge

An atom’s size is dictated by the electrons or their orbitals. However, orbitals do not describe a confined space, but rather the statistical probability of where an electron can be found. So how is the atomic size defined, and what influences it?

An atomic radius can be described in two ways. Nonbonding atomic radius, or van der Waals radius of an atom, is one-half of the distance between adjacent nuclei in the atomic solid. 

Conversely, a bonding atomic radius, or covalent radius, distinguishes between metals and nonmetals. In metals, the radius is described for atoms in their crystal structure as one-half of the distance between the centers of two neighboring atoms. 

In nonmetal, diatomic molecules, the radius is described as one-half of the distance between the centers of bonded atoms.

The periodic table depicts variations in covalent radii that are often called atomic radii, which are influenced by two factors; the number of principal energy levels of valence electrons, and the effective nuclear charge. 

The trend in atomic radii for main group elements down the columns is depicted here.

Moving down a group, the principal quantum number, n, increases by one for each element. Thus, as outer electrons get farther from the nucleus, the atomic radius increases down the group. 

For example, moving down group 1, the atomic radius increases from lithium to cesium. This trend is demonstrated by the entire periodic table.

Further, the plot reveals that the atomic radius is maximum for each alkali metal and falls to a minimum with each noble gas across the period. The decreasing atomic radii across a period can be explained by the effective nuclear charge.

Recall the concept of an effective nuclear charge. In any multi-electron atom, the inner shell electrons partially shield the outer shell electrons from the pull of the nucleus. Thus, the effective nuclear charge, the charge felt by an outer electron is lesser than the actual nuclear charge.

Electrons in the same valence shell do not shield one another very effectively. Across the period, the nuclear charge increases while the number of inner shell electrons remains constant.

Thus, as the effective nuclear charge increases steadily, the shielding of outer electrons becomes less, and this leads to a decrease in atomic radii.

The radii of most transition elements, however, stay roughly constant across each row. This is because the number of electrons in the outermost principal energy level is nearly constant.