Classification of Elements and Periodicity in Properties - Atomic Radii

Atomic Radius is the distance from the center of the nucleus to the outermost shell of electrons. Since the boundary of an atom is not sharp, it is measured as covalent, metallic, or van der Waals radius.

Covalent Radius: One-half of the distance between the nuclei of two identical atoms joined by a single covalent bond. For example, in $Cl_2$, the distance is $198\,pm$, so the radius is $99\,pm$.

Van der Waals Radius: Half of the internuclear distance between two adjacent identity atoms belonging to two neighboring molecules of the same substance in the solid state. Generally, $r_{vdw} > r_{metallic} > r_{covalent}$.

Variation in a Period: Atomic radii generally decrease across a period from left to right. This is due to an increase in the effective nuclear charge ($Z_{eff}$), which pulls the outer electrons closer to the nucleus.

Variation in a Group: Atomic radii increase down a group because the principal quantum number ($n$) increases, adding new energy shells that outweigh the increase in nuclear charge.

Ionic Radius: The effective distance from the center of the nucleus of an ion up to which it exerts influence on its electron cloud.

Cation Size: A cation is always smaller than its parent atom (e.g., $Na^+ < Na$) because it has fewer electrons while the nuclear charge remains the same, leading to increased attraction.

Anion Size: An anion is always larger than its parent atom (e.g., $F^- > F$) because the addition of electrons increases inter-electronic repulsion and decreases effective nuclear charge per electron.

Isoelectronic Species: Atoms and ions that have the same number of electrons (e.g., $O^{2-}, F^-, Na^+, Mg^{2+}$). For these, the radius decreases as the atomic number ($Z$) increases.