My textbook says it is possible to determine the atomic radius of the inert gases like He, Ne, Ar etc because they roam freely and are incapable of forming bonds. However it is very difficult to find out the atomic radius of elements that are chemically active because the position of electron in an atom is uncertain (according to Heisenberg's principle I guess). I am just curious that the principle is true for the electrons of inert gases too, then why did they say it was possible for those gases but very difficult for the chemically active atoms?

  • $\begingroup$ Not quite the right focus. The inert gases, in the gaseous state, have one "pure" electronic configuration, and one "pure form. For an ion like Sodium +1, it forms numerous compounds. The "pure" ionic charge of +1 is an abstraction. So sodium salts are in a variety of crystal lattices with various "partial" charges (something between a pure ionic bond and a pure covalent bond). So for every salt sodium would have a slightly different radius for sodium. $\endgroup$ – MaxW Dec 19 '15 at 15:37

There are several definitions of atomic radius. Guessing from context of your answer, I assume you are talking about van der Waals atomic radius. By definition, it is a radius of atom in respect of equilibrium position with other atoms when only van der Waals forces are acting between the atoms. Since atoms of inert gases do not tend to make covalent bonds, the equilibrium distance between two in solid equals double atomic radius - plain and easy. Not so easy for other elements.

Since most metals and some non-metals form closely packed lattice in elemental form, there is no simple way to obtain their vdW radius. It is required to find a compound with the atom sterically unhindered and forming a crystal lattice containing close contact with said atom involved. Since most metals are electron-deficient and tend to interact with almost anything, no such experimental data are available for metals in a strict sense (though I can come with few examples when it may make sense). As such, vdW radii can be measured (and, actually, are meaningful) only for atoms of top-right corner of periodic table plus hydrogen. Furthermore, even for them vdW radius may fluctuate from compound to compound depending on the oxidation state and atomic neighborhood. Furthermore, the radius is pressure-dependent and, for chemically bound atom, may be unequal in different directions.

For covalent radii the problem is even larger, as the radius is dependent on near neighborhood and valence state in significant way (N-N bond legnth may vary from 1.10 Angstrom in dinitrogen to 1.45 in hydrazine)

As such, even if people talk about larger and smaller atoms, larger and smaller substituents, there is no strong definition for such relations.

As for atomic radius no related to vdW and/or covalent interaction, it depends on the definition of atomic border, which does not exist. A free atoms does not have a clear border, its electronic density fades exponentially with distance, but is non-zero for all finite distances.

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