Ask A Scientist Chemistry Archive

name         Aimee D.
status       student
age          16
Question -   If the Nobel gases are monoatomic, how can atomic radii be
found of the atoms in this period?  For example, we know that Argon's atomic
radius is about 97 picometers.  I do not understand how one half the distance
between the nuclei of identical atoms that are bonded together be found if
Nobel gases don't bond together?
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Dear Aimee,

Good question. I should start this answer by stating that
the determination of atomic size is controversial, and
that different methods give different results for individual
cases. There is no direct experimental means for determining
atomic size, nor is there a direct theoretical definition of
atomic size. However, covalently bond distances can be used in
many combinations to yield average atomic sizes. However,
as you point out most of the rare gas elements do not form
covalent bonds at all (an exception is Xe; XeF4 exists, as
do a number of other Xe compounds). So how are these handled?

Basically, the atomic radii of noble gases are estimated using
a variety of methods. Argon's atomic radius can be estimated
by freezing argon into a solid, which can be done easily
using a fairly low-tech vacuum pump and liquid nitrogen
(I've taught this experiment myself to students in a college
physical chemistry lab). In the solid state, all you need to
know is the crystal packing structure (which has been
determined by a number of different methods) and the density,
and then you can estimate the atomic radius. All of the
rare gases except helium can be treated in this sort of way,
although the lighter the gas is, the harder it is to get it
to crystallize (helium is especially tough). The noble gases
can also be liquefied by cooling, and the liquid "structure"
determined by neutron scattering and other methods. This also
can be used (often together with computer simulations) to get
an estimate of atomic size, and these results usually agree
well with the solid state results.

There are also other kinds of experiments. For example,
there are scattering experiments where you bang atomic beams together at
various angles and use the scattering pattern to backtrack and estimate
the size of the atom and the strength of the atomic forces.

Finally, there are calculations. The theory of quantum mechanics
can be implemented on a computer, and solved pretty accurately for
most of the rare gas elements. From the calculated probability
functions predicted by the theory, you can make estimates of
atomic size. These estimates correlate extremely well with experiments.

Hope this helps.

best, prof. topper
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Atomic radii of all atoms is very "method dependent" -- a point many texts
do not adequately warn the readers. Atoms are "squishy" so it depends upon
how hard you push them together when making an estimate of the atomic radii.
It is not a precisely defined. However, it is useful to distinguish "big"
atoms from "little" atoms. The best you can hope for is that the radii are
internally consistent.

For a detailed discussion check the index of the text: "Atoms and Molecules"
by Martin Karplus and Richard N. Porter. They discuss the concepts in
several places in their text.

Vince Calder
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A astute observation!

Any atom that can be studied as a free / unbonded atom uses the normal
definition for the radius of a sphere.  When free atoms cannot be conveniently
studied we are forced to work with bonded atoms.  However, we are still
interested in the concept of an atomic radius for ESTIMATING the length of 
bonds
between atoms of different types.  In this case scientists use the definition
you have cited.

Greg Bradburn
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