Question

The radius of a single atom of a generic element x is 197 picometers (pm and a crystal of x has a unit cell that is face-centered cubic. calculate the volume of the unit cell.

Answer 1

In a face centered cubic unit cell, the volume occupied by the particles of the substance is about 74% of the total unit cell. First, we find the volume of a single atom assuming it to be sphere:
Volume(atom) = 4/3 x π x r³
Volume(atom) = 4/3 x π x (197 x 10⁻¹²)³
Volume(atom) = 2.87 x 10⁻²⁹ m³

There are a total of 4 atoms in a FCC unit cell, so the total volume occupied by atoms is:
2.87 x 10⁻²⁹ x 4
= 1.15 x 10⁻²⁸ m³

Volume of cell = (1.15 x 10⁻²⁸ ) / 0.74
Volume of cell = 1.55 x 10⁻²⁸ m³