Final answer:
The atomic packing factor for the body-centered cubic (BCC) structure is 0.68, indicating that BCC structures are densely packed, with atoms occupying about 68% of the total volume in the unit cell.
Step-by-step explanation:
The atomic packing factor (APF) for the body-centered cubic (BCC) crystal structure is calculated based on the volume occupied by the atoms in a unit cell in relation to the total volume of the unit cell. In a BCC unit cell, there are two atoms: one-eighth of an atom at each of the eight corners (1 atom total from corners) and one atom at the center. The atomic radius can be determined from the geometry of the unit cell, allowing for the calculation of the volume occupied by the atoms. Given that the atoms in a BCC crystal occupy about 68% of the total volume, the atomic packing factor for BCC is thus 0.68, meaning BCC structures are quite densely packed, though not as densely as the face-centered cubic (FCC) structures, which have an APF of 0.74.