Chem 123 (S06)
Assignment 1 Due: Friday May 26
1.
Consider a simple cubic lattice of identical hard spheres of radius
R
.
a)
How many spheres are contained
within
one unit cell?
What is the coordination number of each sphere?
b)
Show that the edge length
a
of the unit cell is
a
= 2
R
.
c)
Calculate the packing efficiency (
V
spheres /
V
cell) for the simple cubic lattice. (i.e. What fraction of unit cell volume is
occupied by the spheres?
2.
Show that the following data are consistent with the fact that silver metal crystallizes in a facecentred cubic lattice:
Edge length of unit cell,
a
= 408 pm
Density of silver, 10.6 g cm
−
3
Atomic weight of silver, 107.9 g mol
−
1
Avogadro’s number,
N
A = 6.022 × 10
23
(Use any three quantities to calculate the fourth. Compare the calculated value with the given value.)
3.
A tetrahedral site can be generated by placing four spheres of radius
R
at alternate corners of a cube. Let
r
t
be the radius
of the sphere that just fits into the tetrahedral site. Show that
r = ½
2)
R
. (Hint: Since the spheres are in contact
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 Winter '08
 Oakley
 pH, Cubic crystal system, Crystal system, cubic lattice

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