o In modeling solid-state structures, atoms and ions are most often modeled as s
ID: 227978 • Letter: O
Question
o In modeling solid-state structures, atoms and ions are most often modeled as sphere. A structure built using spheres will have some empty, or void, space in it. A measure 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 3.33 A on each side, answer questions (a)-(e). (1 A = 1.x 1010 m.) (a) How many total atoms are there in each unit cell? atom(s) (b) What is the volume of one unit cell in A3 A3 (e) Assuming that the atoms are spheres and the radius of each sphere is 1.44 A, what is the volume of one atom in A3 (Vsphere 4/3) A3 (d) Therefore, what volume of atoms are in one unit cell? A3 (e) Based on your results from parts (b) and (d), what is the packing efficiency of the solid expressed as a percentage?Explanation / Answer
ans a ) In bcc unit cell, total number of atoms
= the number of atoms contributed from the corners of the unit cell + the number of atoms contributed from the body of unit cell
= 8 corners X 1/8 atom per corner + 1 body center atom X 1
=1/8x8 +1X1
= 2 atoms
b)volume = a3 = 36.92 A3
c)volume of sphere/atom = 12.51 A3
d) volume of atoms in one unit cell = number of atoms in unit cell * volume of one atom =2*12.51
=25.02 A3
e) packing efficiency = volume occupied by atoms/ volume of unit cell *100
= 25.02/36.92 *100 = 67.7 %
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