39 Calculate the radius of a palladium (Pd) atom, • given that Pu has an FCC crystal structure, a density of 12.0 g/em', and an atomic weight of 106.4 g'mol.
39 Calculate the radius of a palladium (Pd) atom, • given that Pu has an FCC crystal structure, a density of 12.0 g/em', and an atomic weight of 106.4 g'mol.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
I want
3.9
3.10
3.23
Thx
![5:19 1
Done
n u a un II
3.6 Show that the atomic packing factor for HCP is 0.74.
98 · Chapter 3 I The Structure of Crystalline Solids
Density Computations
Atomic
Atomic
Radius
3.7 Molybdenum (Mo) has a BCC erystal structure,
O an atomic radius of 0.1363 nm, and an atomic
weight of 95.94 g/mol. Compute and compare its
theoretical density with the experimental value
found inside the front cover of the book.
Weight
(g/mol)
Density
(g/cm'y
Alloy
(nm)
A
43.1
6.40
0.122
184,4
12.30
0,146
91.6
9.60
0.137
3.8 Strontium (Sr) has an FCC erystal structure, an
e atomic radius of 0.215 nm, and an atomic weight 3.17 The unit cell for uranium (U) has orthorhombic
of 87.62 g/mol. Calculate the theoretical density e symmetry, with a, b, and e lattice parameters of
for Sr
r.
3.9 Calculate the radius of a palladium (Pd) atom,
O given that Pd has an FCC crystal structure, a
density of 12.0 g/em', and an atomic weight of
106.4 g/mol.
0.286, 0.587, and 0.495 nm, respectively. If its den-
sity, atomic weight, and atomic radius are 19.05
giem', 238.03 g/mol, and 0.1385 nm, respectively.
compute the atomie packing factor.
3.18 Indium (In) has a tetragonal unit eell for which
3.10 Calculate the radius of a tantalum (Ta) atom, e the a and e lattice parameters are 0459 and 0.495
O given that Ta has a BCC crystal structure. a
density of 16.6 g/em', and an atomic weight of
180.9 g/mol.
3.11 A hypothetical metal has the simple cubic crystal
O structure shown in Figure 3.3. If its atomic weight
is 74.5 g/mol and the atomic radius is 0,145 nm.
compute its density.
3.12 Titanium (Ti) has an HCP erystal structure and a e the ratio of the lattice parameters cla is 1.568. If
nm, respectively.
(a) If the atomic packing factor and atomic radius
are 0.693 and 0.1625 nm, respectively, determine
the number of atoms in each unit celi.
(b) The atomic weight of In is 114.82 g/mol; com-
pute its theoretical density.
3.12 Titanium (Ti) has an HCP erystal structure and a 19 Beryllium (Be) has an HCP unit cell for which
O density of 4.51 g/em".
the radius of the Be atom is 0.1143 nm, (a) deter-
mine the unit cell volume, and (b) calculate the
theoretical density of Be and compare it with the
literature value.
(a) What is the volume of its unit cell in cubic
meters?
(b) If the cla ratio is 1.58, compute the values of c
and a.
3.13 Magnesium (Mg) has an HCP crystal structure
and a density of 1.74 g/em'.
3.20 Magnesium (Mg) has an HCP crystal structure,
O a cla ratio of 1.624, and a density of 1.74 g/em.
Compute the atomic radius for Mg.
(u) What is the volume of its unit cell in cubic 3.21 Cobalt (Co) has an HCP crystal structure, an
atomic radius of 0.1253 nm. and a cla ratio of
1.623. Compute the volume of the unit cell for Co.
centimeters?
(b) If the cla ratio is 1.624, compute the values of
c and a.
Polymorphism and Allotropy
3.14 Using atomic weight, crystal structure, and 3.22 Iron (Fe) undergoes an allotropic transformation
atomic radius data tabulated inside the front e at 912 C: upon heating from a BCC (a phase) to an
FCC (y phase). Accompanying this transformation
is a change in the atomic radius of Fe-from Ruce =
0.12584 nm to Ryrce = 0.12894 nm-and, in addition.
a change in density (and volume). Compute the per-
.
cover of the book, compute the theoretical densi-
ties of aluminum (Al), nickel (Ni), magnesium
(Mg), and tungsten (W), and then compare these
values with the measured densities listed in this
same table. The cla ratio for Mg is 1.624.
centage volume change associated with this reaction.
Does the volume increase or decrease?
3.15 Niobium (Nb) has an atomic radius of 0.1430 nm
O and a density of 8.57 g/em'. Determine whether it Crystal Syitems
has an FCC or a BCC crystal structure.
3.16 The atomic weight, density, and atomic radius e .
O for three hypothetical alloys are listed in the fol-
lowing table. For each, determine whether its
crystal structure is FCC, BCC, or simple cubie and
then justify your determination.
3.23 The accompanying figure shows a unit cell for a
• hypothetical metal.
(a) To which erystal system does this unit cell
belong?
(b) What would this crystal structure be called?
Questions and Problems· 99
(e) Calculate the density of the material, given Crystallographic Directions
that its atomic weight is 141 g/mol.
3,31 Draw an orthorhombie unit cell, and within that
cell, a [211] direction.
3.32 Sketch a monoclinic unit cell, and within that
cell, a [101] direction.
3.33 What are the indices for the directions indicated
by the two vectors in the following sketch?
0.45 rm
035 m
-0.35 nm
04 emDirectien 2
3.24 Sketch a unit cell for the face-centered orthorhom-
bic erystal structure.
-----O .
0.3 nm
Point Coordinates
3.25 List the point coordinates for all atoms that are
O associated with the FCC
126 Lid iha noint cgardinntar
the codium](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9715461-f5a2-4dc1-935c-0b02c448b3b6%2F819a5318-697b-4b8e-a09a-7668ad993efa%2Fxzxqd37_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5:19 1
Done
n u a un II
3.6 Show that the atomic packing factor for HCP is 0.74.
98 · Chapter 3 I The Structure of Crystalline Solids
Density Computations
Atomic
Atomic
Radius
3.7 Molybdenum (Mo) has a BCC erystal structure,
O an atomic radius of 0.1363 nm, and an atomic
weight of 95.94 g/mol. Compute and compare its
theoretical density with the experimental value
found inside the front cover of the book.
Weight
(g/mol)
Density
(g/cm'y
Alloy
(nm)
A
43.1
6.40
0.122
184,4
12.30
0,146
91.6
9.60
0.137
3.8 Strontium (Sr) has an FCC erystal structure, an
e atomic radius of 0.215 nm, and an atomic weight 3.17 The unit cell for uranium (U) has orthorhombic
of 87.62 g/mol. Calculate the theoretical density e symmetry, with a, b, and e lattice parameters of
for Sr
r.
3.9 Calculate the radius of a palladium (Pd) atom,
O given that Pd has an FCC crystal structure, a
density of 12.0 g/em', and an atomic weight of
106.4 g/mol.
0.286, 0.587, and 0.495 nm, respectively. If its den-
sity, atomic weight, and atomic radius are 19.05
giem', 238.03 g/mol, and 0.1385 nm, respectively.
compute the atomie packing factor.
3.18 Indium (In) has a tetragonal unit eell for which
3.10 Calculate the radius of a tantalum (Ta) atom, e the a and e lattice parameters are 0459 and 0.495
O given that Ta has a BCC crystal structure. a
density of 16.6 g/em', and an atomic weight of
180.9 g/mol.
3.11 A hypothetical metal has the simple cubic crystal
O structure shown in Figure 3.3. If its atomic weight
is 74.5 g/mol and the atomic radius is 0,145 nm.
compute its density.
3.12 Titanium (Ti) has an HCP erystal structure and a e the ratio of the lattice parameters cla is 1.568. If
nm, respectively.
(a) If the atomic packing factor and atomic radius
are 0.693 and 0.1625 nm, respectively, determine
the number of atoms in each unit celi.
(b) The atomic weight of In is 114.82 g/mol; com-
pute its theoretical density.
3.12 Titanium (Ti) has an HCP erystal structure and a 19 Beryllium (Be) has an HCP unit cell for which
O density of 4.51 g/em".
the radius of the Be atom is 0.1143 nm, (a) deter-
mine the unit cell volume, and (b) calculate the
theoretical density of Be and compare it with the
literature value.
(a) What is the volume of its unit cell in cubic
meters?
(b) If the cla ratio is 1.58, compute the values of c
and a.
3.13 Magnesium (Mg) has an HCP crystal structure
and a density of 1.74 g/em'.
3.20 Magnesium (Mg) has an HCP crystal structure,
O a cla ratio of 1.624, and a density of 1.74 g/em.
Compute the atomic radius for Mg.
(u) What is the volume of its unit cell in cubic 3.21 Cobalt (Co) has an HCP crystal structure, an
atomic radius of 0.1253 nm. and a cla ratio of
1.623. Compute the volume of the unit cell for Co.
centimeters?
(b) If the cla ratio is 1.624, compute the values of
c and a.
Polymorphism and Allotropy
3.14 Using atomic weight, crystal structure, and 3.22 Iron (Fe) undergoes an allotropic transformation
atomic radius data tabulated inside the front e at 912 C: upon heating from a BCC (a phase) to an
FCC (y phase). Accompanying this transformation
is a change in the atomic radius of Fe-from Ruce =
0.12584 nm to Ryrce = 0.12894 nm-and, in addition.
a change in density (and volume). Compute the per-
.
cover of the book, compute the theoretical densi-
ties of aluminum (Al), nickel (Ni), magnesium
(Mg), and tungsten (W), and then compare these
values with the measured densities listed in this
same table. The cla ratio for Mg is 1.624.
centage volume change associated with this reaction.
Does the volume increase or decrease?
3.15 Niobium (Nb) has an atomic radius of 0.1430 nm
O and a density of 8.57 g/em'. Determine whether it Crystal Syitems
has an FCC or a BCC crystal structure.
3.16 The atomic weight, density, and atomic radius e .
O for three hypothetical alloys are listed in the fol-
lowing table. For each, determine whether its
crystal structure is FCC, BCC, or simple cubie and
then justify your determination.
3.23 The accompanying figure shows a unit cell for a
• hypothetical metal.
(a) To which erystal system does this unit cell
belong?
(b) What would this crystal structure be called?
Questions and Problems· 99
(e) Calculate the density of the material, given Crystallographic Directions
that its atomic weight is 141 g/mol.
3,31 Draw an orthorhombie unit cell, and within that
cell, a [211] direction.
3.32 Sketch a monoclinic unit cell, and within that
cell, a [101] direction.
3.33 What are the indices for the directions indicated
by the two vectors in the following sketch?
0.45 rm
035 m
-0.35 nm
04 emDirectien 2
3.24 Sketch a unit cell for the face-centered orthorhom-
bic erystal structure.
-----O .
0.3 nm
Point Coordinates
3.25 List the point coordinates for all atoms that are
O associated with the FCC
126 Lid iha noint cgardinntar
the codium
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