What is the space lattice of a metal called if it has 9 atoms with 1 in the center and the rest on the corners?

What is the space lattice of a metal called if it has 9 atoms with 1 in the center and the rest on the corners?

• A. Body-centered cubic structure
• B. Face-centered cubic structure
• C. Simple cubic structure
• D. Hexagonal close-packed structure

Answer: (A)

Having an atom at the center of the cube with atoms at all eight corners defines a body-centered cubic lattice. In this arrangement the center atom sits inside the cube, while the corner atoms are shared with neighboring cubes, so the corners collectively contribute one atom to the unit cell and the center adds one more, giving a total of two atoms per conventional unit cell. The mention of nine atoms isn’t how the atom count is ordinarily described for a single unit cell, but the pattern described—one center atom plus corner atoms—is characteristic of the body-centered cubic structure. The other structures don’t fit: a simple cubic lattice has only corner atoms, a face-centered cubic lattice has atoms on the faces (not a central atom), and hexagonal close-packed is a different, hexagonal arrangement entirely.

Having an atom at the center of the cube with atoms at all eight corners defines a body-centered cubic lattice. In this arrangement the center atom sits inside the cube, while the corner atoms are shared with neighboring cubes, so the corners collectively contribute one atom to the unit cell and the center adds one more, giving a total of two atoms per conventional unit cell. The mention of nine atoms isn’t how the atom count is ordinarily described for a single unit cell, but the pattern described—one center atom plus corner atoms—is characteristic of the body-centered cubic structure. The other structures don’t fit: a simple cubic lattice has only corner atoms, a face-centered cubic lattice has atoms on the faces (not a central atom), and hexagonal close-packed is a different, hexagonal arrangement entirely.