For a simple cubic lattice, the APF equals N(4/3)πR^3/a^3, where N is the number of atoms per cell. What is N for SCC?

• A. 0
• B. 1
• C. 2
• D. 3

Answer: (B)

In a simple cubic lattice, atoms sit at the eight corners of the unit cell. Each corner atom is shared by eight neighboring cells, so its contribution to one cell is 1/8. With eight corners, the total is 8 × (1/8) = 1 atom per unit cell. So the number of atoms per cell, N, is 1.

This is why the APF uses N in the numerator. For a simple cubic lattice, the atoms touch along the cell edge, giving a = 2R. Substituting N = 1 into the expression and using a = 2R yields the packing factor as (4/3)πR^3 / a^3 = (4/3)π(a/2)^3 / a^3 = π/6 ≈ 0.524. If you tried N = 0, 2, or 3, that would miscount the atoms per cell and wouldn’t match the actual corner-sharing arrangement of a simple cubic lattice (those other counts relate to different lattice types like body-centered or face-centered).