APF is defined as which ratio?

• A. The volume of atoms in a unit cell divided by the volume of the unit cell.
• B. The ratio of the surface area to the volume of the unit cell.
• C. The number of atoms per unit cell.
• D. The volume of the unit cell divided by the volume of atoms.

Answer: (A)

Atomic packing factor measures how much of a unit cell’s volume is actually filled by atoms. It is defined as the volume occupied by the atoms inside the unit cell divided by the total volume of the unit cell. In practice, you estimate this by taking the number of atoms in the cell, multiply by the volume of a single atom (approximated as a sphere with the atomic radius), and divide by the unit cell volume. This fraction lies between 0 and 1 and reflects packing efficiency, not the surface or a simple count. The given definition—volume of atoms in the unit cell divided by the volume of the unit cell—is exactly what APF measures. The other ideas correspond to different quantities: a surface area to volume ratio, a simple count of atoms, or the reciprocal of the packing factor.