In modeling solid-state structures, atoms and ions are most often modeled as spheres. A structure built using spheres will have some empty, or void, space in it. A measure of void space in a particular structure is the packing efficiency, defined as the volume occupied by the spheres divided by the total volume of the structure.

Given that a solid crystallizes in a body centered cubic structure that is 3.09 ? on each side, answer questions (a)-(e). (1 ? = 1. In modeling solid-state structures, atoms and ions 10-10 m.)

(a) How many total atoms are there in each unit cell?
atom(s)

(b) What is the volume of one unit cell in ?3?
?3

(c) Assuming that the atoms are spheres and the radius of each sphere is 1.34 ?, what is the volume of one atom in ?3? (Vsphere = 4/3?r3.)
?3

(d) Therefore, what volume of atoms are in one unit cell?
?3

(e) Based on your results from parts (b) and (d), what is the packing efficiency of the solid expressed as a percentage?
%