cle is 0.3 m, and the corners ot the cube le directly on the ecge of the clfcle,
ID: 1355843 • Letter: C
Question
cle is 0.3 m, and the corners ot the cube le directly on the ecge of the clfcle, Whatis the length of a side of the cube? Perspective View 2. Solids consist of a crystalline lattice of atoms - a unit cell that has a certain configuration of atoms that is repeated over and over. The picture to the right of stacked metal spheres represents a lattice configuration called face-centered-cubic (fcc). Calculate the packing fraction for this case, e.g. the amount of the volume occupied by the metal spheres divid ed by the total volume of the pyramid structure.Explanation / Answer
The FCC unit cell is formed by 4 atoms:
- 8 times one eighth of an atom at the corners of the cube
- 4 times a half of an atom at the center of the of the faces.
At the faces the atoms at the corners and the center atom touch, so that the perfectly fill the face. Hence the length of the face diagonal is
D = R + 2R + R = 4R
From Pythagorean theorem you get
A² + A² = D²
=>
A = 8 · R = 2 · 2·R
The volume of the cube cell is
Vc = A³ = 2 · 16·R
The volume of the atoms in the cell is
Va = 4 · (4··R³ /3) = 16··R³ /3
The packing density is
p = Va / Vc
= (16··R³ /3) / (2 · 16·R)
= / (3·2)
= 0.74
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