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Chapter 12

Solids and Modern Materials

Educators

ES

Problem 1

Two solids are shown below. One is a semiconductor and one is an insulator. Which one is which? Explain your reasoning. ISections $12.1,12.7 ]$

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Problem 2

For each of the two-dimensional structures shown here (a) draw the unit cell, (b) determine the type of two-dimensional lattice (from Figure 12.4), and (c) determine how many of each type of circle (white or black) there are per unit cell. [ Section 12.2$]$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 3

Shown here are sketches of two processes. Which of the processes refers to the ductility of metals and which refers to malleability of metals? [ Section 12.3$]$

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Problem 4

Which arrangement of atoms in a lattice represents close-packing? (Section 12.3)

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 5

(a) What kind of packing arrangement is seen in the accompanying photo? (b) What is the coordination number of each cannonball in the interior of the stack? (c) What are the coordination numbers for the numbered cannon balls on the visible side of the stack? [Section 12.3$]$

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Problem 6

Which arrangement of cations (yellow) and anions (blue) in a lattice is the more stable? Explain your reasoning. [Section 12.5$]$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 7

Which of these molecular fragments would you expect to be more likely to give rise to electrical conductivity? Explain your reasoning. [Sections $12.6,12.8 ]$

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Problem 8

The electronic structure of a doped semiconductor is shown here. (a) Which band, A or B, is the valence band? (b) Which band is the conduction band? (c) Which region of the diagram represents the band gap? (d) Which band consists of bonding molecular orbitals? (e) Is this an example of an n-type or p-type semiconductor? (f) If the semi conductor is germanium, which of the following elements could be the dopant: Ga, Si, or P? [Section 12.7$]$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 9

Shown here are cartoons of two different polymers. Which of these polymers would you expect to be more crystalline? Which one would have the higher melting point? [Section 12.8$]$

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Problem 10

The accompanying image shows photoluminescence from four different samples of CdTe nanocrystals, each embedded in a polymer matrix. The photoluminescence occurs because the samples are being irradiated by a UV light source. The nanocrystals in each vial have different average sizes. The sizes are $4.0,3.5,3.2,$ and 2.8 $\mathrm{nm}$ . (a) Which vial contains the 4.0 -nm nanocrystals? (b) Which vial contains the 2.8 -nm nanocrystals? (c) Crystals of CaTe that have sizes that are larger than approximately 100 nm have a band gap of 1.5 eV. What would be the wavelength and frequency of light emitted from these crystals? What type of light is this?
[Sections 12.7 and 12.9$]$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 11

Covalent bonding occurs in both molecular and covalent network solids. Which of the following statements best explains why these two kinds of solids differ so greatly in their hardness and melting points?

$$
\begin{array}{l}{\text { (a) The molecules in molecular solids have stronger covalent bonding than covalent-network solids do. }} \\ {\text { (b) The molecules in molecular solids are held together by weak intermolecular interactions. }}\end{array}
$$ $$
\begin{array}{l}{\text { (c) The atoms in covalent-network solids are more polarizable than those in molecular solids. }} \\ {\text { (d) Molecular solids are denser than covalent-network solids. }}\end{array}
$$

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Problem 12

Silicon is the fundamental component of integrated circuits. Si has the same structure as diamond. (a) Is Si a molecular, metallic, ionic, or covalent-network solid? (b) Silicon readily reacts to form silicon dioxide, $\mathrm{SiO}_{2}$ , which is quite hard and is insoluble in water. Is $\mathrm{SiO}_{2}$ most likely a molecular, metallic, ionic, or covalent-network solid?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 13

What kinds of attractive forces exist between particles (atoms, molecules, or ions) in (a) molecular crystals, (b) covalent-network crystals, (c) ionic crystals, (d) and metallic crystals?

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Problem 14

Which type (or types) of crystalline solid is characterized by each of the following? (a) High mobility of electrons throughout the solid; (b) softness, relatively low melting point; (c) high melting point and poor electrical conductivity; ( $\mathbf{d} )$ network of covalent bonds.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 15

Indicate the type of solid (molecular, metallic, ionic, or covalent-network) for each compound: (a) $\mathrm{CaSO}_{4},(\mathbf{b}) \mathrm{Pd}$ , (c) $\mathrm{Ta}_{2} \mathrm{O}_{5}$ (melting point, $1872^{\circ} \mathrm{C} ),(\mathbf{d})$ caffeine $\left(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\right)$ (e) toluene $\left(\mathrm{C}_{7} \mathrm{H}_{8}\right),(\mathbf{f}) \mathrm{P}_{4}$

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Problem 16

Indicate the type of solid (molecular, metallic, ionic, or covalent-network) for each compound: (a) InAs, (b) MgO, $(\mathbf{c}) \mathrm{HgS},(\mathbf{d}) \mathrm{In},(\mathbf{e}) \mathrm{HBr}$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 17

You are given a gray substance that melts at $700^{\circ} \mathrm{C}$ ; the solid is a conductor of electricity and is insoluble in water. Which type of solid (molecular, metallic, covalent-network, or ionic) might this substance be?

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Problem 18

You are given a white substance that melts at $100^{\circ} \mathrm{C}$ . The substance is soluble in water. Neither the solid nor the solution is a conductor of electricity. Which type of solid (molecular, metallic, covalent-network, or ionic) might this substance be?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 19

(a) Draw a picture that represents a crystalline solid at the atomic level. (b) Now draw a picture that represents an amorphous solid at the atomic level.

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Problem 20

Amorphous silica, $\mathrm{SiO}_{2},$ has a density of about 2.2 $\mathrm{g} / \mathrm{cm}^{3}$ ,
whereas the density of crystalline quartz, another form of $\mathrm{SiO}_{2},$ is 2.65 $\mathrm{g} / \mathrm{cm}^{3} .$ Which of the following statements is the best explanation for the difference in density?

$$
\begin{array}{l}{\text { (a) Amorphous silica is a network-covalent solid, but quartz }} \\ {\text { is metallic. }} \\ {\text { (b) Amorphous silica crystallizes in a primitive cubic lattice. }} \\ {\text { (c) Quartz is harder than amorphous silica. }}\end{array}
$$ $$
\begin{array}{l}{\text { (d) Quartz must have a larger unit cell than amorphous }} \\ {\text { silica. }}\end{array}
$$ $$
\begin{array}{l}{\text { (e) The atoms in amorphous silica do not pack as efficiently }} \\ {\text { in three dimensions as compared to the atoms in quartz. }}\end{array}
$$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 21

Two patterns of packing for two different circles of the same size are shown here. For each structure (a) draw the two-dimensional unit cell; (b) determine the angle between the lattice vectors, $\gamma,$ and determine whether the lattice vectors are of the same length or of different lengths; and (c) determine the type of two-dimensional lattice (from Figure 12.4$)$ .

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Problem 22

Two patterns of packing two different circles of the same size are shown here. For each structure (a) draw the two-dimensional unit cell; (b) determine the angle between the lattice vectors, $\gamma,$ and determine whether the lattice vectors are of the same length or of different lengths; ( c) determine the type of two-dimensional lattice (from Figure 12.4$)$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 23

Imagine the primitive cubic lattice. Now imagine grabbing the top of it and stretching it straight up. All angles remain $90^{\circ} .$ What kind of primitive lattice have you made?

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Problem 24

Imagine the primitive cubic lattice. Now imagine grabbing opposite corners and stretching it along the body diagonal while keeping the edge lengths equal. The three angles between the lattice vectors remain equal but are no longer $90^{\circ}$ . What kind of primitive lattice have you made?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 25

Which of the three-dimensional primitive lattices has a unit cell where none of the internal angles is $90^{\circ}$ ? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (d) triclinic, (e) both rhombohedral and triclinic.

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Problem 26

Besides the cubic unit cell, which other unit cell(s) has edge lengths that are all equal to each other? (a) Orthorhombic, (b) hexagonal, (c) rhombohedral, (a) triclinic, (e) both rhombohedral and triclinic.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 27

What is the minimum number of atoms that could be contained in the unit cell of an element with a body-centered cubic lattice? (a) $1,(\mathbf{b}) 2,(\mathbf{c}) 3,(\mathbf{d}) 4,(\mathbf{e}) 5$

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Problem 28

The unit cell of nickel arsenide is shown here. (a) What type of lattice does this crystal possess? (b) What is the empirical formula?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 29

The unit cell of nickel arsenide is shown here. (a) What type of lattice does this crystal possess? (b) What is the empirical formula?

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Problem 30

The unit cell of a compound containing potassium, aluminum, and fluorine is shown here. (a) What type of lattice does this crystal possess (all three lattice vectors are mutually perpendicular)? (b) What is the empirical formula?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 31

The densities of the elements $\mathrm{K}, \mathrm{Ca}, \mathrm{Sc},$ and Ti are $0.86,1.5$ ,
$3.2,$ and 4.5 $\mathrm{g} / \mathrm{cm}^{3}$ , respectively. One of these elements crystallizes in a body-centered cubic structure; the other three crystallize in a face-centered cubic structure. Which one crystallizes in the body-centered cubic structure? Justify your answer.

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Problem 32

For each of these solids, state whether you would expect it to possess metallic properties: (a) TiCl_ $_{4},(\mathbf{b})$ NiCo alloy, $(\mathbf{c}) \mathrm{W}$ $(\mathbf{d}) \mathrm{Ge},(\mathbf{e}) \mathrm{ScN}$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 33

Consider the unit cells shown here for three different structures that are commonly observed for metallic elements.(a) Which structure(s) corresponds to the densest packing of atoms? (b) Which structure(s) corresponds to the leastdense packing of atoms?

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Problem 34

Sodium metal (atomic weight 22.99 $\mathrm{g} / \mathrm{mol}$ ) adopts a body-centered cubic structure with a density of 0.97 $\mathrm{g} / \mathrm{cm}^{3}$ . (a) Use this information and Avogadro's number $\left(N_{\mathrm{A}}=6.022 \times 10^{23} / \mathrm{mol}\right)$ to estimate the atomic radius of sodium. $(\mathbf{b})$ If sodium didn't react so vigorously, it could float on water. Use the answer from part (a) to estimate the density of Na if its structure were that of a cubic close packed metal. Would it still float on water?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 35

Iridium crystallizes in a face-centered cubic unit cell that has an edge length of 3.833 $\dot{A}$. (a) Calculate the atomic radius of an iridium atom. (b) Calculate the density of iridium metal.

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Problem 36

Calcium crystallizes in a body-centered cubic structure at $467^{\circ} \mathrm{C}$ (a) How many Ca atoms are contained in each unit cell? (b) How many nearest neighbors does each Ca atom possess? (c) Estimate the length of the unit cell edge, $a,$ from the atomic radius of calcium $(1.97$ A). (d) Estimate the density of Ca metal at this temperature.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 37

Calcium crystallizes in a face-centered cubic unit cellas room temperature that has an edge length of 5.588 (a) Calculate the atomic radius of a calcium atom. (b) Calculate the density of Ca metal at this temperature.

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Problem 38

Calculate the volume in $\hat{A}^{3}$ of each of the following types of cubic unit cells if it is composed of atoms with an atomic radius of 1.82 A. (a) primitive (b) face-centered cubic.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 39

Aluminum metal crystallizes in a face-centered cubic unit cell. (a) How many aluminum atoms are in a unit cell? (b) What is the coordination number of each aluminum atom? (c) Estimate the length of the unit cell edge, $a$ , from the atomic radius of aluminum $(1.43 \hat{\mathrm{A}}) .$ (d) Calculate the density of aluminum metal.

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Problem 40

An element crystallizes in a face-centered cubic lattice. The edge of the unit cell is 4.078$\hat{A}$ , and the density of the crystal is 19.30 $\mathrm{g} / \mathrm{cm}^{3} .$ Calculate the atomic weight of the element and identify the element.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 41

Which of these statements about alloys and intermetallic compounds is false? (a) Bronze is an example of an alloy. (b) "Alloy" is just another word for "a chemical compound of fixed composition that is made of two or more metals." (c) Intermetallics are compounds of two or more metals that have a definite composition and are not considered alloys. (d) If you mix two metals together and, at the atomic level, they separate into two or more different compositional phases, you have created a heterogeneous alloy.(e) Alloys can be formed even if the atoms that comprise them are rather different in size.

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Problem 42

Determine if each statement is true or false: (a) Substitutional alloys are solid solutions, but interstitial alloys are heterogenous alloys. (b) Substitutional alloys have "solute" atoms that replace "solvent" atoms in a lattice, but interstitial alloys have "solute" atoms that are in between the "solvent" atoms in a lattice. (c) The atomic radii of the atoms in a substitutional alloy are similar to each other, but in an interstitial alloy, the interstitial atoms are a lot smaller than the host lattice atoms.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 43

For each of the following alloy compositions, indicate whether you would expect it to be a substitutional alloy, an interstitial alloy, or an intermetallic compound:

$$
(a)\mathrm{Fe}_{0.97} \mathrm{Si}_{0.03}, \quad(\mathbf{b})\mathrm{Fe}_{0.60} \mathrm{Ni}_{0.40}, \quad(\mathbf{c}) \mathrm{Sm} \mathrm{Co}_{5}
$$

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Problem 44

For each of the following alloy compositions, indicate whether you would expect it to be a substitutional alloy, an interstitial alloy, or an intermetallic compound:

$$
(a)\mathrm{Cu}_{0.66} \mathrm{Zn}_{0.34}, \quad(\mathbf{b}) \mathrm{Ag}_{3} \mathrm{Sn}, \quad(\mathbf{c}) \mathrm{Ti}_{0.99} \mathrm{O}_{0.01}
$$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 45

Indicate whether each statement is true or false:

$$
\begin{array}{l}{\text { (a) Substitutional alloys tend to be more ductile than inter- }} \\ {\text { stitial alloys. }} \\ {\text { (b) Interstitial alloys tend to form between elements with }} \\ {\text { similar ionic radii. }} \\ {\text { (c) Nonmetallic elements are never found in alloys. }}\end{array}
$$

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Problem 46

Indicate whether each statement is true or false:

$$
\begin{array}{l}{\text { (a) Intermetallic compounds have a fixed composition. }} \\ {\text { (b) Copper is the majority component in both brass and }} \\ {\text { bronze. }} \\ {\text { (c) In stainless steel, the chromium atoms occupy interstitial }} \\ {\text { positions. }}\end{array}
$$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 47

Which element or elements are alloyed with gold to make the following types of "colored gold" used in the jewelry industry? For each type, also indicate what type of alloy is formed: (a) white gold, (b) rose gold, (c) green gold.

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Problem 48

An increase in temperature causes most metals to undergo thermal expansion, which means the volume of the metal increases upon heating. How does thermal expansion affect the unit cell length? What is the effect of an increase in temperature on the density of a metal?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 49

State whether each sentence is true or false:

$$
\begin{array}{l}{\text { (a) Metals have high electrical conductivities because the }} \\ {\text { electrons in the metal are delocalized. }} \\ {\text { (b) Metals have high electrical conductivities because they }} \\ {\text { are denser than other solids. }}\end{array}
$$ $$
\begin{array}{l}{\text { (c) Metals have large thermal conductivities because they }} \\ {\text { expand when heated. }} \\ {\text { (d) Metals have small thermal conductivities because the }} \\ {\text { delocalized electrons cannot easily transfer the kinetic }} \\ {\quad \text { energy imparted to the metal from heat. }}\end{array}
$$

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Problem 50

Imagine that you have a metal bar sitting half in the sun and half in the dark. On a sunny day, the part of the metal that has been sitting in the sun feels hot. If you touch the part of the metal bar that has been sitting in the dark, will it feel hot or cold? Justify your answer in terms of thermal conductivity.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 51

The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22 . Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: (a) How many molecular orbitals are there in the diagram? (b) How many nodes are in the lowest-energy molecular orbital? (c) How many nodes are in the highest energy molecular orbital? (d) How many nodes are in the highest-energy occupied molecular orbital (HOMO)? (e) How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)? (f) How does the HOMO-LUMO energy gap for this case compare to that of the four-atom case?

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Problem 52

Repeat Exercise 12.51 for a linear chain of eight lithium atoms.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 53

Which would you expect to be the more ductile element, (a) Ag or Mo, ( b) Zn or Si? In each case explain your reasoning.

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Problem 54

Which of the following statements does not follow from the fact that the alkali metals have relatively weak metal-metal bonding?

$$
\begin{array}{l}{\text { (a) The alkali metals are less dense than other metals. }} \\ {\text { (b) The alkali metals are soft enough to be cut with a knife. }} \\ {\text { (c) The alkali metals are more reactive than other metals. }} \\ {\text { (d) The alkali metals have higher melting points than }} \\ {\text { other metals. }} \\ {\text { (e) The alkali metals have lowization energies. }}\end{array}
$$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 55

Arrange the following metals in increasing order of expected melting point: Mo, Zr, Y, Nb. Explain this trend in melting points.

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Problem 56

For each of the following groups, which metal would you expect to have the highest melting point: (a) gold, rhenium, or cesium; (b) rubidium, molybdenum, or indium; (c) ruthenium, strontium, or cadmium?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 57

Tausonite, a mineral composed of Sr, O, and Ti, has the cubic unit cell shown in the drawing. (a) What is the empirical formula of this mineral? (b) How many oxygens are coordinated to titanium? (c) To see the full coordination environment of the other ions, we have to consider neighboring unit cells. How many oxygens are coordinated to strontium?

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Problem 58

The unit cell of a compound containing Co and O has a unit cell shown below. The Co atoms are on the corners, and the O atoms are completely within the unit cell. What is the empirical formula of this compound? What is the oxidation state of the metal?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 59

Alabandite is a mineral composed of manganese(II) sulfide (MnS). The mineral adopts the rock salt structure. The length of an edge of the MnS unit cell is 5.223 A at $25^{\circ} \mathrm{C}$ . Determine the density of Mns in $\mathrm{g} / \mathrm{cm}^{3} .$

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Problem 60

Clausthalite is a mineral composed of lead selenide (PbSe). The mineral adopts the rock salt structure. The density of PbSe at $25^{\circ} \mathrm{C}$ is 8.27 $\mathrm{g} / \mathrm{cm}^{3} .$ Calculate the length of an edge of the PbSe unit cell.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 61

A particular form of cinnabar (HgS) adopts the zinc blende structure. The length of the unit cell edge is 5.852 A. (a) Calculate the density of HgS in this form. (b) The mineral tiemannite (HgSe) also forms a solid phase with the zinc blende structure. The length of the unit cell edge in this mineral is 6.085 A. What accounts for the larger unit cell length in tiemmanite? (c) Which of the two substances has the higher density? How do you account for the difference in densities?

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Problem 62

At room temperature and pressure RbI crystallizes with the NaCl-type structure. (a) Use ionic radii to predict the length of the cubic unit cell edge. (b) Use this value to estimate the density. (c) At high pressure the structure transforms to one with a CsCl-type structure. (c) Use ionic radii to predict the length of the cubic unit cell edge for the high-pressure form of RbI. (d) Use this value to estimate the density. How does this density compare with the density you calculated in part (b)?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 63

CuI, CsI, and Nal each adopt a different type of structure. The three different structures are those shown in Figure $12.26 .$ (a) Use ionic radii, $\mathrm{Cs}^{+}(r=1.81 \mathrm{A})$ $\mathrm{Na}^{+}(r=1.16 \mathrm{A}), \mathrm{Cu}^{+}(r=0.74 \mathrm{A}),$ and, $\mathrm{I}^{-}(r=2.06 \mathrm{A}),$ to predict which compound will crystallize with structure. (b) What is the coordination number of iodide in each of these structures?

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Problem 64

The rutile and fluorite structures, shown here (anions are colored green), are two of the most common structure types of ionic compounds where the cation to anion ratio is $1 : 2$ . (a) For $\mathrm{CaF}_{2}$ and $\mathrm{ZnF}_{2}$ use ionic radii, $\mathrm{Ca}^{2+}(r=1.14 \hat{\mathrm{A}})$ $\mathrm{Zn}^{2+}(r=0.88 \mathrm{A}),$ and $\mathrm{F}^{-}(r=1.19 \mathrm{A}),$ to predict which compound is more likely to crystallize with the fluorite structure and which with the rutile structure. (b) What are the coordination numbers of the cations and anions in each
of these structures?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 65

The coordination number for $\mathrm{Mg}^{2+}$ ion is usually six. Assuming this assumption holds, determine the anion coordination number in the following compounds: (a) MgS, (b) $\mathrm{MgF}_{2},(\mathbf{c}) \mathrm{MgO}$

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Problem 66

The coordination number for the $\mathrm{Al}^{3+}$ ion is typically between four and six. Use the anion coordination number to determine the $\mathrm{Al}^{3+}$ coordination number in the following compounds: (a) AlF_ $_{3}$ where the fluoride ions are two coordinate, (b) $\mathrm{Al}_{2} \mathrm{O}_{3}$ where the oxygen ions are six coordinate, (c) AlN where the nitride ions are four coordinate.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 67

Classify each of the following statements as true or false:

$$
\begin{array}{l}{\text { (a) Although both molecular solids and covalent-network }} \\ {\text { solids have covalent bonds, the melting points of molec- }} \\ {\text { ular solids are much lower because their covalent bonds }} \\ {\text { are much weaker. }} \\ {\text { (b) Other factors being equal, highly symmetric molecules }} \\ {\text { tend to form solids with highly symmetric molecules }} \\ {\text { asymmetrically shaped molecules. }}\end{array}
$$

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Problem 68

Classify each of the following statements as true or false:

$$
\begin{array}{l}{\text { (a) For molecular solids, the melting point generally in- }} \\ {\text { creases as the strengths of the covalent bonds increase. }}\end{array}
$$ $$
\begin{array}{l}{\text { (b) For molecular solids, the melting point generally in- }} \\ {\text { creases as the strengths of the intermolecular forces }} \\ {\text { increase. }}\end{array}
$$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 69

Both covalent-network solids and ionic solids can have melting points well in excess of room temperature, and both can be poor conductors of electricity in their pure form.
However, in other ways their properties are quite different.

$$
\begin{array}{l}{\text { (a) Which type of solid is more likely to dissolve in water? }} \\ {\text { (b) Which type of solid can become a considerably better }} \\ {\text { conductor of electricity via chemical substitution? }}\end{array}
$$

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Problem 70

Which of the following properties are typical characteristics of a covalent-network solid, a metallic solid, or both: (a) ductility, (b) hardness, (c) high melting point?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 71

For each of the following pairs of semiconductors, which one will have the larger band gap: (a) CdS or CdTe, (b) GaN or InP, ( c) GaAs or InAs?

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Problem 72

For each of the following pairs of semiconductors, which one will have the larger band gap: (a) InP or InAs, $(\mathbf{b})$ Ge or AlP, (c) Agl or CdTe?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 73

If you want to dope GaAs to make an n-type semiconductor with an element to replace Ga, which element(s) would you pick?

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Problem 74

If you want to dope GaAs to make a p-type semiconductor with an element to replace As, which element(s) would you pick?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 75

Silicon has a band gap of 1.1 $\mathrm{eV}$ at room temperature. (a) What wavelength of light would a photon of this energy correspond to? (b) Draw a vertical line at this wavelength in the figure shown, which shows the light output of the Sun as a function of wavelength. Does silicon absorb all, none, or a portion of the visible light that comes from the Sun? (c) You can estimate the portion of the overall solar spectrum that silicon absorbs by considering the area under the curve. If you call the area under the entire curve $" 100 \%, "$ what approximate percentage of the area under the curve is absorbed by silicon?

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Problem 76

Cadmium telluride is an important material for solar cells. (a) What is the band gap of CdTe? (b) What wavelength of light would a photon of this energy correspond to? (c) Draw a vertical line at this wavelength in the figure shown in Exercise $12.75,$ which shows the light output of the sun as a function of wavelength. (d) With respect to silicon, does CdTe absorb a larger or smaller portion of the solar spectrum?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 77

The semiconductor CaSe has a band gap of 1.74 eV. What wavelength of light would be emitted from an LED made from CdSe? What region of the electromagnetic spectrum is this?

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Problem 78

The first LEDs were made from GaAs, which has a band gap of 1.43 eV. What wavelength of light would be emitted from an LED made from GaAs? What region of the electromagnetic spectrum does this light correspond to: ultraviolet, visible, or infrared?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 79

GaAs and GaP make solid solutions that have the same crystal structure as the parent materials, with As and Prandomly distributed throughout the crystal. GaP As $_{1-x}$ exists for any value of $x .$ If we assume that the band gap varies linearly with composition between $x=0$ and $x=1,$ estimate the band gap for GaP $_{0.5} \mathrm{As}_{0.5}$ . (GaAs and GaP band gaps are 1.43 $\mathrm{eV}$ and 2.26 $\mathrm{eV}$ , respectively.) What wavelength of light does this correspond to?

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Problem 80

Red light-emitting diodes are made from GaAs and GaP solid solutions, GaP $_{x} A s_{1-x}($ see Exercise 12.79$) .$ The original red LEDs emitted light with a wavelength of 660 nm. If we assume that the band gap varies linearly with composition between $x=0$ and $x=1,$ estimate the composition (the value of $x$ ) that is used in these LEDs.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 81

(a) What is a monomer? (b) Which of these molecules can be used as a monomer: ethanol, ethene (also called ethylene), methane?

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Problem 82

The molecular formula of $n$ -decane $\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{8} \mathrm{CH}_{3} . \mathrm{De}-$ cane is not considered a polymer, whereas polyethylene is. What is the distinction?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 83

State whether each of these numbers is a reasonable value for a polymer's molecular weight: 100 amu, $10,000$ amu, $100,000$ amu, $1,000,000$ amu?

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Problem 84

Indicate whether the following statement is true or false: For an addition polymerization, there are no by-products of the reaction (assuming 100$\%$ yield).

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 85

An ester is a compound formed by a condensation reaction between a carboxylic acid and an alcohol that eliminates a water molecule. Read the discussion of esters in Section 24.4 and then give. an example of a reaction forming an ester. How might this kind of reaction be extended to form a polymer (a polyester)?

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Problem 86

Write a balanced chemical equation for the formation of polymer via a condensation reaction from the monomers succinic acid (HOOCCH $_{2} \mathrm{CH}_{2} \mathrm{COOH}$ ) and ethylenediamine $\left(\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 87

An addition polymerization forms the polymer originally used as Saran" wrap. It has the following structure $+\mathrm{CCl}_{2}-\mathrm{CH}_{2} \mathrm{J}_{n} .$ Draw the structure of the monomer.

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Problem 88

Write the chemical equation that represents the formation of

$$
\begin{array}{l}{\text { (a) polychloroprene from chloroprene (polychloroprene is }} \\ {\text { used in highway-pavement seals, expansion joints, con- }} \\ {\text { veyor belts, and wire and cable jackets) }}\end{array}
$$ $$
\begin{array}{c}{\mathrm{CH}_{2}=\mathrm{CH}-\underset{\mathrm{C}}{\mathrm{C}=\mathrm{CH}_{2}}} \\ {\text { Chloroprene }}\end{array}
$$ $$
\begin{array}{l}{\text { (b) polyacrylonitrile from acrylonitrile (polyacrylonitrile }} \\ {\text { is used in home furnishings, craft yarns, clothing, and }} \\ {\text { many other items). }}\end{array}
$$ $$
\begin{array}{c}{\mathrm{CH}_{2}=\mathrm{CH}} \\ {\mathrm{I}} \\ {\text { Acrylonitrile }}\end{array}
$$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 89

The polymer Kevlar, a condensation polymer, is used as reinforcement in car tires, strings of archery bows, and as a component of bulletproof vests. Draw the structures of the two monomers that yield Kevlar.

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Problem 90

Proteins are naturally occurring polymers formed by condensation reactions of amino acids, which have the general structure In this structure, $-\mathrm{R}$ represents $-\mathrm{H},-\mathrm{CH}_{3},$ or another group of atoms; there are 20 different natural amino acids, and each has one of 20 different $\mathrm{R}$ groups. (a) Draw the general structure of a protein formed by condensation polymerization of the generic amino acid shown here. (b) When only a few amino acids react to make a chain, the product is called a "peptide" rather than a protein; only when there are 50 amino acids or more in the chain would the molecule be called a protein. For three amino acids (distinguished by having three different $\mathrm{R}$ groups, $\mathrm{R} 1, \mathrm{R} 2,$ and $\mathrm{R} 3$ , draw the peptide that results from their condensation reactions. (c) The order in which the $\mathrm{R}$ groups exist in a peptide or protein has a huge influence on
its biological activity. To distinguish different peptides and proteins, chemists call the first amino acid the one at the "N terminus" and the last one the one at the $^{4} \mathrm{C}$ terminus." From your drawing in part (b) you should be able to figure out what "N terminus" and "C terminus" mean. How many different peptides can be made from your three different amino acids?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 91

(a) What molecular features make a polymer flexible? (b) If you cross-link a polymer, is it more flexible or less flexible than it was before?

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Problem 92

What molecular structural features cause high-density polyethylene to be denser than low-density polyethylene?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 93

If you want to make a polymer for plastic wrap, should you strive to make a polymer that has a high or low degree of crystallinity?

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Problem 94

Indicate whether each statement is true or false:

$$
\begin{array}{l}{\text { (a) Elastomers are rubbery solids. }} \\ {\text { (b) Thermosets cannot be reshaped. }} \\ {\text { (c) Thermoplastic polymers can be recycled. }}\end{array}
$$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 95

Explain why "bands" may not be the most accurate description of bonding in a solid when the solid has nanoscale dimensions.

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Problem 96

CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy. (a) What color is the emitted light? (b) Would appropriately sized Cds quantum dots be able to emit blue light? (c) What about red light?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 97

Indicate whether each statement is true or false:

$$
\begin{array}{l}{\text { (a) The band gap of a semiconductor decreases as the parti- }} \\ {\text { cle size decreases in the } 1-10 \text { -nm range. }} \\ {\text { (b) The light that is emitted from a semiconductor, upon }} \\ {\text { external stimulation, becomes longer in wavelength as }} \\ {\text { the particle size of the semiconductor decreases. }}\end{array}
$$

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Problem 98

Indicate whether this statement is true or false: If you want a semiconductor that emits blue light, you could either use a material that has a band gap corresponding to the energy of a blue photon or you could use a material that has a smaller band gap but make an appropriately sized nanoparticle of the same material.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 99

Gold adopts a face-centered cubic structure with a unit cell edge of 4.08 A (Figure 12.11). How many gold atoms are there in a sphere that is 20 nm in diameter? Recall that the volume of a sphere is $\frac{4}{3} \pi r^{3}$ .

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Problem 100

An ideal quantum dot for use in TVs does not contain any cadmium due to concerns about disposal. One potential material for this purpose is InP, which adopts the zinc blende $(\mathrm{ZnS})$ structure (face-centered cubic). The unit cell edge length is 5.869 \&. (a) If the quantum dot is shaped like a cube, how many of each type of atom are there in a cubic crystal with an edge length of 3.00 $\mathrm{nm} ? 5.00 \mathrm{nm}$ ? (b) If one of the nanoparticles in part (a) emits blue light and the
other emits orange light, which color is emitted by the crystal with the 3.00 -nm edge length? With the 5.00 -nm edge length?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 101

Which statement correctly describes a difference between graphene and graphite?
(a) Graphene is a molecule but graphite is not. (b) Graphene is a single sheet of carbon atoms and graphite contains many, and larger, sheets of carbon atoms. (c) Graphene is an insulator but graphite is a metal. (d) Graphite is pure carbon but graphene is not. (e) The carbons are $s p^{2}$ hybridized in graphene but $s p^{3}$ hybridized in graphite.

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Problem 102

What evidence supports the notion that buckyballs are actual molecules and not extended materials?

$$
\begin{array}{l}{\text { (a) Buckyballs are made of carbon. }} \\ {\text { (b) Buckyballs have a well-defined atomic structure and }} \\ {\text { molecular weight. }} \\ {\text { (c) Buckyballs have a well-defined melting point. }} \\ {\text { (a) Buckyballs are semiconductors. }} \\ {\text { (e) More than one of the previous choices. }}\end{array}
$$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 103

Selected chlorides have the following melting points: NaCl $\left(801^{\circ} \mathrm{C}\right), \mathrm{MgCl}_{2}\left(714^{\circ} \mathrm{C}\right), \mathrm{PCl}_{3}\left(-94^{\circ} \mathrm{C}\right), \mathrm{SCl}_{2}\left(-121^{\circ} \mathrm{C}\right)$

$$
\begin{array}{l}{\text { (a) For each compound, indicate what type its solid }} \\ {\text { form is (molecular, metallic, ionic, or covalent-network). }} \\ {\text { (b) Predict which of the following compounds has a }} \\ {\text { higher melting point: } \mathrm{CaCl}_{2} \text { or } \mathrm{SiCl}_{4} \text { . }}\end{array}
$$

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Problem 104

A face-centered tetragonal lattice is not one of the 14 three-dimensional lattices. Show that a face-centered tetragonal unit cell can be redefined as a body-centered tetragonal lattice with a smaller unit cell.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 105

Imagine the primitive cubic lattice. Now imagine pushing on top of it, straight down. Next, stretch another face by pulling it to the right. All angles remain $90^{\circ} .$ What kind of primitive lattice have you made?

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Problem 106

Pure iron crystallizes in a body-centered cubic structure, but small amounts of impurities can stabilize a face-centered cubic structure. Which form of iron has a higher density?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 107

Introduction of carbon into a metallic lattice generally results in a harder, less ductile substance with lower electrical and thermal conductivities. Explain why this might be so.

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Problem 108

$\mathrm{Ni}_{3} \mathrm{Al}$ is used in the turbines of aircraft engines because of its strength and low density. Nickel metal has a cubic close-packed structure with a face-centered cubic unit cell.while $\mathrm{Ni}_{3}$ Al has the ordered cubic structure shown in Figure 12.17 . The length of the cubic unit cell cedge is 3.53 $\mathrm{A}$ for nickel and 3.56 $\mathrm{A}$ for $\mathrm{Ni}_{3}$ Al. Use these data to calculate and compare the densities of these two materials.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 109

For each of the intermetallic compounds shown in Figure 12.17 determine the number of each type of atom in the unit cell. Do your answers correspond to the ratios expected from the empirical formulas: $\mathrm{Ni}_{3} \mathrm{Al}, \mathrm{Nb}_{3} \mathrm{Sn},$ and $\mathrm{Sm} \mathrm{Co}_{5} ?$

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Problem 110

What type of lattice-primitive cubic, body-centered cubic, or face-centered cubic-does each of the following structure types possess: (a) CsCl, (b) Au, (c) NaCl, (d) Po, (e) Zns?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 111

Cinnabar (HgS) was utilized as a pigment known as ver-million. It has a band gap of 2.20 eV near room temperature for the bulk solid. What wavelength of light (in nm) would a photon of this energy correspond to?

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Problem 112

The electrical conductivity of aluminum is approximately $10^{9}$ times greater than that of its neighbor in the periodic table, silicon. Aluminum has a face-centered cubic structure, and silicon has the diamond structure. A classmate of yours tells you that density is the reason aluminum is a metal but silicon is not; therefore, if you were to put silicon under high pressure, it too would act like a metal. Discuss this idea with your classmates, looking up data about Al and Si as needed.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 113

Silicon carbide, $\mathrm{SiC}$ , has the three-dimensional structure
shown in the figure.
$$
\begin{array}{l}{\text { (a) Name another compound that has the same structure. }} \\ {\text { (b) Would you expect the bonding in SiC to be predomi- }} \\ {\text { nantly ionic, metallic, or covalent? (c) How do the bond- }} \\ {\text { ing and structure of SiC lead to its high thermal stability }} \\ {\text { (to } 2700^{\circ} \mathrm{C} \text { ) and exceptional hardness? }}\end{array}
$$

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Problem 114

Energy bands are considered continuous due to the large number of closely spaced energy levels. The range of energy levels in a crystal of copper is approximately $1 \times 10^{-19} \mathrm{J}$ . Assuming equal spacing between levels, the spacing between energy levels may be approximated by dividing the range of energies by the number of atoms in the crystal. (a) How many copper atoms are in a piece of copper metal in the shape of a cube with edge length 0.5 $\mathrm{mm} ?$ The density of copper is 8.96 $\mathrm{g} / \mathrm{cm}^{3} .$ (b) Determine the average spacing in J between energy levels in the copper metal in part (a).(c) Is this spacing larger, substantially smaller, or about the same as the 1 $\times 10^{-18}$ J separation between energy levels in a hydrogen atom?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 115

Unlike metals, semiconductors increase their conductivity as you heat them (up to a point). Suggest an explanation.

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Problem 116

Sodium oxide $\left(\mathrm{Na}_{2} \mathrm{O}\right)$ adopts a cubic structure with Na atoms represented by green spheres and O atoms by red spheres.

$$
\begin{array}{l}{\text { (a) How many atoms of each type are there in the unit cell? }} \\ {\text { (b) Determine the coordination number and describe the }} \\ {\text { shape of the coordination environment for the sodium }} \\ {\text { ion. }} \\ {\text { (c) The unit cell edge length is } 5.550 \text { A. Determine the den- }} \\ {\text { sity of } \mathrm{Na}_{2} \text { O. }}\end{array}
$$

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 117

Teflon is a polymer formed by the polymerization of $\mathrm{F}_{2} \mathrm{C}=\mathrm{CF}_{2}$ . (a) Draw the structure of a section of this polymer. (b) What type of polymerization reaction is required to form Teflon?

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Problem 118

Hydrogen bonding between polyamide chains plays an important role in determining the properties of a nylon such as nylon $6,6$ (Table 12.6$) .$ Draw the structural formulas for two adjacent chains of nylon $6,6$ and show where hydrogen-bonding interactions could occur between them.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 119

Explain why X rays can be used to measure atomic distances in crystals but visible light cannot be used for this purpose.

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Problem 120

In their study of X-ray diffraction, William and Lawrence Bragg determined that the relationship among the wavelength of the radiation $(\lambda),$ the angle at which the raveation is diffracted $(\theta),$ and the distance between planes of atoms in the crystal that cause the diffraction $(d)$ is given by $n \lambda=2 d \sin \theta . X$ rays from a copper $X$ -ray tube that have a wavelength of 1.54$\hat{\mathrm{A}}$ are diffracted at an angle of 14.22 degrees by crystalline silicon. Using the Bragg equation, calculate the distance between the planes of atoms responsible
for diffraction in this crystal, assuming $n=1$ (first-order diffraction).

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 121

Germanium has the same structure as silicon, but the unit cell size is different because Ge and Si atoms are not the same size. If you were to repeat the experiment described in the previous problem but replace the Si crystal with a Ge crystal, would you expect the X rays to be diffracted at a larger or smaller angle $\theta$ ?

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Problem 122

(a) The density of diamond is $3.5 \mathrm{g} / \mathrm{cm}^{3},$ and that of graphite is 2.3 $\mathrm{g} / \mathrm{cm}^{3} .$ Based on the structure of buckminsterfullerene, what would you expect its density to be relative to these other forms of carbon? (b) X-ray diffraction studies of buckminsterfullerene show that it has a face-centered cubic lattice of $\mathrm{C}_{60}$ molecules. The length of an edge of the unit cell is 14.2$\hat{\mathrm{A}}$ . Calculate the density of
buckminsterfullerene.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 123

When you shine light of band gap energy or higher on a semiconductor and promote electrons from the valence band to the conduction band, do you expect the conductivity of the semiconductor to (a) remain unchanged, (b) increase, or (c) decrease?

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Problem 124

The karat scale used to describe gold alloys is based on mass percentages. (a) If an alloy is formed that is 50 $\mathrm{mol} \%$ silver and 50 $\mathrm{mol} \%$ gold, what is the karat number of the alloy? Use Figure 12.18 to estimate the color of this alloy. (b) If an alloy is formed that is 50 $\mathrm{mol} \%$ copper and 50 $\mathrm{mol} \%$ gold, what is the karat number of the alloy? What is the color of this alloy?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 125

Spinel is a mineral that contains 37.9$\%$ Al, 17.1$\%$ Mg, and 45.0$\%$ O, by mass, and has a density of 3.57 $\mathrm{g} / \mathrm{cm}^{3} .$ The unit cell is cubic with an edge length of 8.09 A. How many atoms of each type are in the unit cell?

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Problem 126

(a) What are the $\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}$ bond angles in diamond? (b) What are they in graphite (in one sheet)? (c) What atomic orbitals are involved in the stacking of graphite sheets with each other?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 127

Employing the bond enthalpy values listed in Table 8.4 , estimate the molar enthalpy change occurring upon (a) polymerization of ethylene, (b) formation of nylon $6,6$ , (c) formation of polyethylene terephthalate (PET).

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Problem 128

Although polyethylene can twist and turn in random ways, the most stable form is a linear one with the carbon back-bone oriented as shown in the following figure: The solid wedges in the figure indicate bonds from carbon that come out of the plane of the page; the dashed wedges indicate bonds that lie behind the plane of the page.

(a) What is the hybridization of orbitals at each carbon atom? What angles do you expect between the bonds?

(b) Now imagine that the polymer is polypropylene rather than polyethylene. Draw structures for polypropylene in which (i) the CH $_{3}$ groups all lie on the
same side of the plane of the paper (this form is called isotactic polypropylene), (ii) the $\mathrm{CH}_{3}$ groups lie on alternating sides of the plane (syndiotactic polypropylene), or (iii) the $\mathrm{CH}_{3}$ groups are randomly distributed
on either side (atactic polypropylene). Which of these forms would you expect to have the highest crystallinity and melting point, and which the lowest? Explain
in terms of intermolecular interactions and molecular shapes.

(c) Polypropylene fibers have been employed in athletic wear. The product is said to be superior to cotton or polyester clothing in wicking moisture away from the
body through the fabric to the outside. Explain the difference between polypropylene and polyester or cotton (which has many $-\mathrm{OH}$ groups along the molecular chain) in terms of intermolecular interactions with water.

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 129

(a) In polyvinyl chloride shown in Table $12.6,$ which bonds have the lowest average bond enthalpy?
(b) When subjected to high pressure and heated, polyvinyl chloride converts to diamond. During this transformation which bonds are most likely to break first? (c) Employing the values ore average bond enthalpy in Table $8.3,$ estimate the overall enthalpy change for converting PVC to diamond.

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Problem 130

Silicon has the diamond structure with a unit cell edge length of 5.43 \& and eight atoms per unit cell. (a) How many silicon atoms are there in 1 $\mathrm{cm}^{3}$ of material? (b) Suppose you dope that 1 $\mathrm{cm}^{3}$ sample of silicon with 1 ppm of phosphorus that will increase the conductivity by a factor of a million. How many milligrams of phosphorus are required?

ES
Eugene S.
University of Minnesota - Twin Cities

Problem 131

One method to synthesize ionic solids is by the heating of two reactants at high temperatures. Consider the reaction of FeO with $\mathrm{TiO}_{2}$ to form FeTiO $_{3} .$ Determine the amount of each of the two reactants to prepare 2.500 $\mathrm{g}$ FeTiO $_{3},$ assuming the reaction goes to completion.

(a) Write a balanced chemical reaction.
(b) Calculate the formula weight of FeTiO_{3} .
(c) Determine the moles of FeTiO_{3} .
(d) Determine moles and mass (g) of FeO required.
(e) Determine moles and mass (g) of TiO_ $_{2}$ required.

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Problem 132

Look up the diameter of a silicon atom, in $\hat{A} .$ The latest semiconductor chips have fabricated lines as small as 14 nm. How many silicon atoms does this correspond to?

ES
Eugene S.
University of Minnesota - Twin Cities