In a simple cubic unit cell, how many whole atoms are contained within the cell?

In a simple cubic unit cell, how many whole atoms are contained within the cell?

• A. 2
• B. 1
• C. 3
• D. 4

Answer: (B)

Counting atoms in a unit cell requires accounting for how atoms at the lattice points are shared among neighboring cells. In a simple cubic arrangement, there is an atom at each of the eight corners of the cube. Each corner atom is shared by eight adjacent unit cells, so only one-eighth of each corner atom belongs to a given cell. With eight corners, the total contribution is 8 × (1/8) = 1 atom per cell. If you’re thinking about atoms that lie completely inside the cell with no part on a boundary, that would be zero. But in crystal counting, we sum fractional contributions from boundary atoms to get the effective number of atoms associated with the cell, which for a simple cubic is one. So the correct result is one atom per cell.

Counting atoms in a unit cell requires accounting for how atoms at the lattice points are shared among neighboring cells. In a simple cubic arrangement, there is an atom at each of the eight corners of the cube. Each corner atom is shared by eight adjacent unit cells, so only one-eighth of each corner atom belongs to a given cell. With eight corners, the total contribution is 8 × (1/8) = 1 atom per cell.

If you’re thinking about atoms that lie completely inside the cell with no part on a boundary, that would be zero. But in crystal counting, we sum fractional contributions from boundary atoms to get the effective number of atoms associated with the cell, which for a simple cubic is one. So the correct result is one atom per cell.