Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells.

Going across a period from left to right, a proton is added to the nucleus and an electron to the valence shell with each successive element. Going down the elements in a group, the number of electrons in the valence shell remains constant, but the principal quantum number increases by one each time. An understanding of the electronic structure of the elements allows us to examine some of the properties that govern their chemical behavior. These properties vary periodically as the electronic structure of the elements changes. 

Variation in Atomic Radius

The quantum mechanical picture makes it difficult to establish a definite size of an atom. However, there are several practical ways to define the radius of atoms and, thus, to determine their relative sizes that give roughly similar values.

The atomic radius in metals is one-half of the distance between the centers of two neighboring atoms. It is one-half of the distance between the centers of bonded atoms for elements that exist as diatomic molecules.

Moving across a period from left to right, generally, each element has a smaller atomic radius than the element preceding it. This might seem counterintuitive because it implies that atoms with more electrons have a smaller atomic radius. This can be explained based on 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 electron, is lesser than the actual nuclear charge (Z) and can be estimated by the following:

Z_eff = Z – σ              

where, Z_eff is the effective nuclear charge, Z is the actual nuclear charge, and σ is the shielding constant, where the shielding constant is greater than zero but smaller than Z.

Each time we move from one element to the next across a period, Z increases by one, but the shielding increases only slightly. Thus, Z_eff increases as we move from left to right across a period. The stronger pull (higher effective nuclear charge) experienced by electrons on the right side of the periodic table draws them closer to the nucleus, making the atomic radii smaller.

Core electrons efficiently shield electrons in the outermost principal level from nuclear charge, but outermost electrons do not efficiently shield one another from the nuclear charge. The larger the effective nuclear charge, the stronger the hold of the nucleus on outer electrons, and the smaller the atomic radius.

However, the radii of some transition elements stay roughly constant across each row. This is because the number of electrons in the outermost principal energy level is nearly constant, and they experience a roughly constant effective nuclear charge.

Within each period, the trend in atomic radius decreases as Z increases;  Within each group, the trend is that atomic radius increases as Z increases.

Scanning down a group, the principal quantum number, n, increases by one for each element. Thus, the electrons are being added to a region of space that is increasingly distant from the nucleus. Consequently, the size of the atom (and its atomic radius) must increase as we increase the distance of the outermost electrons from the nucleus. This trend is illustrated for the atomic radii of the halogens in the table below.

This text is adapted from Openstax Chemistry 2e, Section 6.5: Periodic Variations in Element Properties.