Question

Metallic iron crystallizes in a cubic lattice. The unit cell edge length is 287 pm. The density of iron is 7.87 g/cm³. How many iron atoms are within a unit cell?

A. 1 atom/cell
B. 2 atoms/cell
C. 4 atoms/cell
D. 8 atoms/cell

Answer 1

Metallic iron crystallizes in a body-centered cubic structure, where there is one atom at the center and one-eighth of an atom at each of the cube's eight corners, accounting for a total of 2 atoms per unit cell.

Step-by-step explanation:

The question asks how many iron atoms are within a unit cell, given that metallic iron crystallizes in a cubic lattice and the unit cell edge length is 287 pm. Iron has a density of 7.87 g/cm³.

Iron crystallizes in a body-centered cubic (BCC) structure at temperatures below 910 °C. This means that the lattice points of the cubic unit cell are occupied in a specific manner: there is one atom at the center of the cube and one-eighth of an atom at each of the cube's eight corners. To find the number of iron atoms per unit cell, we add the contribution from the corners (8 × ⅛ = 1 atom) and the center atom (1 × 1 = 1 atom). Therefore, the cumulative number of iron atoms per unit cell is 2.