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 (). (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?
%