The goal of this activity is to have students calculate the empirical formula of a compound given the contents of a unit cell. 

A repeating building block, or unit cell, is used to represent extended structures since shifting a unit cell along its edges by the length of the edge will exactly replicate the extended structure.

In determining stoichiometry for an extended structure only the fraction of an atom within the unit cell counts. In three-dimensions atoms can be shared between unit cells on corners, on edges and on faces of the unit cell. Atoms on corners are shared by eight unit cells, atoms on edges are shared by four cells and atoms on faces are shared by two cells. Therefore only one-eighth of a corner atom, one-quarter of an edge atom and one-half of an atom on a face is in any one unit cell. The total number of atoms in a unit cell is given by:

Assignment:

For five solid state structures determine the empirical formula. Show your work by indicating how many spheres of each type have their centers located inside the unit cell, on faces, on edges, or on corners. (A given sphere only has one location: inside, face, edge, and corner locations are mutually exclusive.)