Helium and Nitrogen Sizes

name         James W.
status       other
age          40s

Question -   What is the physical size of an air molecule (assuming 79.1% Nitrogen),
and what is the physical size of a Helium molecule.  I am looking for
the relative size difference between the two.
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James,

Without getting too theoretical, I offer the following: According to my copy
of the Periodic Table of the Atoms, the atomic radius of a helium atom is
0.49 Angstroms -- the diameter is therefore 0.98 Angstroms. The radius of a
nitrogen atom is 0.75 Angstroms -- the diameter is 1.5 Angstroms.

A nitrogen molecule is composed of two nitrogen atoms bonded to each other.
The molecule is shaped a little like a very short sausage -- kinda
elliptical. Helium atoms do not bond to each other. Thus the "molecule" is
represented by a single helium atom. We are comparing a sphere of 0.98
Angstroms in diameter for the helium atom and an ovoid whose longest length
is about 3 Angstroms for the nitrogen molecule.

This admittedly crude (approximate) comparison of the two has the nitrogen
molecule at about 3 times the size of a helium atom. I hope this is helpful.

Regards,
ProfHoff
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Another tough answer hiding behind a simple question!! Unfortunately,
chemists throw around bond lengths, and the sizes of molecules much too
carelessly. Atoms and molecules are "squishy" not "hard spheres", so the
"size" of molecules and atoms depends upon how you measure it.

For example, the excluded volume constant -- the 'b' term in the van der
Waals equation of state for a gas (P+a/V^2)*(V-b) = RT , which for He and N2
is 0.02370 and 0.03913 liters/mol, respectively. From this you can calculate
a volume and from that a radius, assuming the spherical shape for He and
N2 -- not a bad assumption. The result is 340 and 220 picometers for He and
N2 respectively.

The interatomic distance for N2 obtained from electronic spectra is 109.7
picometers compared to 298 picometers for diatomic He2 obtained from quantum
mechanical calculation. Quantum mechanical calculation of the orbital radius
of He and N atoms is 291 and 521 picometers respectively.

So the physical size of N2 and He is not a quantity cast in stone. It
depends upon how the quantity is arrived at.

Vince Calder
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