What is the packing efficiency of a body-centered cubic unit cell?

Verified step by step guidance

1. Understand the concept of packing efficiency, which is the fraction of volume in a crystal structure that is occupied by atoms.
2. Recognize that in a body-centered cubic (BCC) unit cell, there is one atom at each corner of the cube and one atom in the center of the cube.
3. Calculate the number of atoms per unit cell in a BCC structure: 8 corner atoms each contributing 1/8th of an atom to the unit cell, plus 1 center atom, totaling 2 atoms per unit cell.
4. Determine the relationship between the atomic radius (r) and the edge length (a) of the BCC unit cell: \( \sqrt{3}a = 4r \).
5. Calculate the packing efficiency using the formula: \( \text{Packing Efficiency} = \frac{\text{Volume of atoms in the unit cell}}{\text{Volume of the unit cell}} \times 100\% \).