ENMA 300
Homework 2 Solutions
Fall 2011
1. Callister 3.3
Molybdenum has a BCC crystal structure, an atomic radius of 0.1363 nm, and an atomic weight
of 95.94 g/mol.
Compute its theoretical density and compare it with the experimental value
found inside the front cover.
Solution
This problem calls for a computation of the density of molybdenum.
According to Equation 3.5
For BCC,
n
= 2 atoms/unit cell, and realizing that
V
C
=
a
3
,
and using Equation 3.3
Thus,
= 10.22 g/cm
3
The value given inside the front cover is 10.22 g/cm
3
.
This is excellent agreement.
Agreement is often not this
good because atomic and ionic radii are averages based on a variety of alloys or compounds.
2.
Callister 3.7
Below are listed the atomic weight, density and atomic radius for three hypothetical metals.
For
each determine whether its crystal structure is FCC, BCC or simple cubic and then justify your
determination.
A simple cubic unit cell is shown in Figure 3.42.
Alloy
Atomic Weight
(g/mol)
Density (g/cm
3
)
Atomic Radius (nm)
A
43.1
6.40
0.122
B
184.4
12.30
0.146
C
91.6
9.60
0.137
1
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View Full DocumentSolution
This is a problem where there is more than one approach to determine the solution.
The book’s solution follows.
For each of these three alloys we need, by trial and error, to calculate the density using Equation 3.5, and
compare it to the value cited in the problem.
For SC, BCC, and FCC crystal structures, the respective values of
n
are 1, 2, and 4, whereas the respective expressions for
a
(since
V
C
=
a
3
) are 2
R
, , and .
For alloy A, let us calculate
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 Spring '12
 Christou
 Ion

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