Question

# 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 face centered cubic structure that is 5.09 Å 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 Å^{3}?

(c) Assuming that the atoms are spheres and the radius of each sphere is 1.80 Å, what is the volume of one atom in Å^{3}? (*V*_{sphere} = 4/3*πr*^{3}.)

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

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

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(a) How many total atoms are there in each unit cell? 4 atoms per unit cell (face centered cubicstructure) (b) What is the... View the full answer