We examine the dependence of atomic properties on a new atomic size, r(n)(Z)(c), that has been rigorously defined by the presence of an interaction without depending on the strength or nature of the interaction. We have thus related the static dielectric polarizability radius, r(alpha), the inverse of the first ionization potential, I(-1), the inverse of Pauling electronegativity scale, chi(-1)(P) and the size CR of atoms that contribute to interatomic distance involving atoms of the main group elements in the periodic table. There is a linear relationship between r(n)(Z)(c) and a size-dependent atomic property P of the form P = C(P)r(atom) + D(P), where r(atom) is a simple and transparent function of r(n)(Z)(c) and DP is simply related to the property of the hydrogen atom, except for P = I(-1) when DP is a property of the occupancy of the valence s-and p-electrons. We find a strict criterion for metallicity in elements based on atomic sizes and show how this criterion can be used to account for changes in descriptions of interatomic distance for gas-phase MX compounds of metallic elements.