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 3.30Å on each side, answer questions (a)-(e). (1 Å = 1. 10-10 m.)(a) How many total atoms are there in each unit cell?
(b) What is the volume of one unit cell in Å3?
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(c) Assuming that the atoms are spheres and the radius of each sphere is 1.43 Å, what is the volume of one atom in Å3? (Vsphere = 4/3πr3.)
(d) Therefore, what volume of atoms are in one unit cell?
(e) Based on your results from parts (b) and (d), what is the packing efficiency of the solid expressed as a percentage?
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