# How do you find the diameter of certain atoms?

1. Oct 13, 2009

### thename1000

I only have one example that I can find, and thats finding the diameter of a copper atom. Do most elements follow these steps?

1.) Make sure density is in kg/m^3
2.) find number of copper atoms in a 1 meter by 1 meter cube.
3.) find number of atoms in one edge(row?) of said cube.
4.) find diameter of one atom in that edge.

I understand this assuming its correct. What I don't understand is the math, and how it will differ with different elements.

So can we do an example of say, lead? one mole of it has a mass of 207.2g and a density of 11.4 g/cm^3.? How do you do each step and WHY?

Assume I know nothing besides what I've said lol

2. Oct 13, 2009

### thename1000

BUMP.

Nobody knows how to do this? Help if you can :)

3. Oct 13, 2009

### Bob S

At one time, diffraction of x-rays of known wavelength were Bragg-diffracted off of simple crystals to determine the separation of crystal planes, thus determining the size of the crystal lattice and the volume occupied by single atoms.
Bob S

4. Oct 13, 2009

### kanato

That's a roundabout way of doing it.

1. Calculate volume per mole as molar mass / density.
2. Divide by N_A and convert units to something small, like nm or Angstroms to get volume per atom.
3. Plug into volume for a sphere and solve for radius.

The procedure is not different for different elements. Keep in mind that the size of an atom is not something that can be well defined; the same kind of atom will be different sizes in different chemical environments.

5. Oct 13, 2009

### Bob S

Finding the number of atoms in a single row on an edge of some elements is very dependent on the crystal structure of the element, and the specific allotrope. See
http://en.wikipedia.org/wiki/Allotropes_of_carbon
Graphite for example is a staggered hexagonal structure. Is the atomic spacing the same on all edges? Does the spacing change depending on allotrope (compare diamond and graphite)? Is the atomic diameter depend on whether the spacing is cubic (same dimension in x, y, z) or rectangular (like in graphite)? This cannot be done with a meter stick and a scale. Lead is an unusual element in that the isotopic abundance varies depending on where it is mined. So if all isotopes have different densities, does this mean that the atomic sizes are different?
Bob S