Re: HOW ARE ATOMIC RADII CALCULATED FROM COVALENT BOND LENGTH?

"Atomic radius" is a somewhat artificial number, not because atoms have zero size, but because the radius of a particular atom will depend on its particular chemical state (not so much solid/liquid/gas as whether it's neutral or an ion; whether it's in one compound--or allotrope--or another).

The easiest number to measure is the distance between nuclei in a solid. Atomic nuclei have approximately zero size compared to the size of an atom. So atomic radius is calculated, most simply, by taking the distance between any two atomic nuclei in a compound and dividing by two.

It's easier when an element forms bonds to itself; for example, we could take the "covalent radius" of carbon as half the distance between the two carbon atoms in ethane--except that we'd get a different number for ethene (double bond) or ethyne (triple bond).

So, to the best of my knowledge, atomic radii are calculated by taking the average of an atom's covalent radius in a range of its compounds. "Ionic radii" are determined using ionic compounds. There's some adjustment made for theory as well as for how closely-packed the atoms happen to be in a particular compound.

If you're lucky, you can measure an atom's radius more directly, for example by imaging atoms on the surface of a solid by scanning tunneling microscopy. But that method has at least as many pitfalls as the traditional one!

Dan Berger