Unit Cells

To determine the density of a face-centered cubic (FCC) crystal structure, we follow these steps:
Step 1: Identify the number of atoms per unit cell in FCC. In an FCC structure, each unit cell contains 4 atoms. This is because each corner atom is shared among 8 adjacent unit cells and each face-centered atom is shared between 2 unit cells:
Step 2: Express the mass of the unit cell. The mass of the unit cell is the product of the number of atoms per unit cell and the atomic mass :
Step 3: Calculate the volume of the unit cell. The volume of the cubic unit cell is given by the cube of the edge length :
Step 4: Formulate the density equation. Density is defined as mass per unit volume. Substituting the mass and volume of the unit cell:

Conclusion: The density of an FCC crystal structure is given by: where is the atomic mass and is the edge length of the unit cell.

In a Body-Centered Cubic (BCC) unit cell, the atoms are arranged such that there is one atom at each corner of the cube and one atom at the center of the cube. The distance between the centers of two atoms along the body diagonal of the cube is equal to four times the radius of an atom.
Step 1: Relationship between edge length and radius Let the edge length of the BCC unit cell be . In a BCC unit cell, the body diagonal is related to the edge length by the Pythagorean theorem: Since the body diagonal of a BCC unit cell passes through two atoms (one at the center and one at the corner), the body diagonal is also equal to , where is the radius of the atoms. Thus, we have the equation:
Step 2: Solve for the radius Rearranging the equation to solve for :
Step 3: Substitute the given edge length We are given that the edge length . Substituting this into the equation: Thus, the radius of the BCC molecule is .