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Name: Clara F.
Status: student
Age: 15
Location: N/A
Country: N/A
Date: Thursday, November 28, 2002

How scientists measure the size of an atom?

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 10-23 cm^3/atom. Taking the cube root of this gives a size of 2.28 x 10-8 cm.

A more direct way, though not as simple to understand, is by scattering x-rays 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 x-rays 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) x-ray light was diffracted. If you want to know more, look for information about "Bragg's Law".

Tim Mooney

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