The most space efficient arrangement of spheres is found in which type of unit cell
A) face-centered cubic
B) body-centered cubic
C) simple cubic
D) face-centered cubic and body-centered cubic
E) body-centered cubic and simple cubic

Question

Quizplus · Accepted Answer

In a face-centered cubic (FCC) unit cell, each corner is occupied by a sphere and there is a sphere at the center of each face. This means there are a total of 4 spheres per unit cell. This arrangement provides the most efficient packing of spheres, with 74% of the space in the cell being occupied by the spheres. In comparison, a body-centered cubic (BCC) unit cell has only one sphere at the center and eight at the corners, giving a total of 2 spheres per unit cell and an efficiency of 68%. A simple cubic (SC) unit cell has only one sphere at each corner, giving a total of 8 spheres per unit cell and an efficiency of 52%. Therefore, the most space-efficient arrangement of spheres is found in the FCC unit cell.

The Most Space Efficient Arrangement of Spheres Is Found in Which