

Measuring Atomic Sizes
Name: Clara F.
Status: student
Age: 15
Location: N/A
Country: N/A
Date: Thursday, November 28, 2002
Question:
How scientists measure the size of an atom?
Replies:
There are numerous ways to determine the sizes of atoms, depending on
what you can assume is known. For example, if you know that one mole
of any substance contains Avogadro's number of atoms and weighs the
atomic weight in grams of that substance, you can trim a piece of that
material until its mass in grams equals its atomic weight. Then
measure the volume and divide by Avogadro's number to find the volume
of one atom. Taking the cube root of that volume give the length of a
side of a cube which would just contain that atom.
For example, consider iron whose atomic weight is 55.847 and density
is about 7.874 gm/cm^3. So 7.09 cm^3 of iron has a mass of 55.847 gm
and contains Avogadro's number of atoms. Dividing 7.09 cm^3/mole
by 6.022 x 10+23 atoms/mole, you get 1.18 x 1023 cm^3/atom. Taking
the cube root of this gives a size of 2.28 x 108 cm.
A more direct way, though not as simple to understand, is by
scattering xrays off a crystal of the material. The crystal acts
like a diffraction grating with a slit spacing equal to the atomic
spacing (which is just the size of the atoms). From analyzing the
diffraction patterns, it is possible in a straightforward way to
determine the relative positions of the layers of atoms.
Best, Dick Plano...
Let us start with the notion that the atoms in a solid or liquid are
touching their nearest neighbors, so the size of an atom is the same
as the distance between them. You can infer the distance between
atoms from the pattern made by xrays scattered from a bunch of them.
You're going to get a pretty complicated pattern, because the x rays
will scatter from all the atoms, but in the simplest case  all the
atoms arranged in a regular pattern (i.e., a crystal)  the pattern
is just a bunch of spots. If you know some trigonometry and something
about how waves interfere, you can calculate the interatomic distance
from the angle by which an incoming ray of (monochromatic) xray light
was diffracted. If you want to know more, look for information about
"Bragg's Law".
Tim Mooney
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Update: June 2012

