Determine the atom density of (100), (110), and (111) planes of a Silicon crystal

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Homework Statement



For the (100), (110), and (111) planes of a Silicon crystal sketch the placement of atoms on the plane and determine the atom density (atoms/cm^2) on the plane.

Homework Equations



As of now I think the only relavent equation would be the atom density which is:

Atoms per unit cell / (area of the square = Atoms per unit cell/a^2

Where a is the lattice constant.

The Attempt at a Solution



I've already sketched the planes, but don't know how to find the atom density. I know that silicon has a diamond structured lattice meaning that it has 8 atoms in a square.

For the (100) plane it's just a square at located at the x, so this means the facing square contains 8 atoms, because silicon has a diamond lattice.

Does that mean the atom density is 8/a^2? Atleast for the (100)?

I'm not exactly sure how you find the (110) and the (111), the planes in the unit cell look odd to mean. How do I determine the number of atoms?

Any help would be appreciated! Thanks.
 

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