Chapter 12

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 CdTe that have sizes that are larger than approximately \(100 \mathrm{~nm}\) have a band gap of \(1.5 \mathrm{eV}\). 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]

Covalent bonding occurs in both molecular and covalentnetwork solids. Which of the following statements best explains why these two kinds of solids differ so greatly in their hardness and melting points? (a) The molecules in molecular solids have stronger covalent bonding than covalent-network solids do. (b) The molecules in molecular solids are held together by weak intermolecular interactions. (c) The atoms in covalent-network solids are more polarizable than those in molecular solids. (d) Molecular solids are denser than covalent-network solids.

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?

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

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; (d) network of covalent bonds.

Indicate the type of solid (molecular, metallic, ionic, or covalent-network) for each compound: (a) \(\mathrm{CaCO}_{3}\), (b) \(\mathrm{Pt}\), (c) \(\mathrm{ZrO}_{2}\) (melting point, \(\left.2677^{\circ} \mathrm{C}\right)\), (d) table sugar \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\), (e) benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\), (f) \(\mathrm{I}_{2}\).

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

A white substance melts with some decomposition at \(730^{\circ} \mathrm{C}\). As a solid, it does not conduct electricity, but it dissolves in water to form a conducting solution. Which type of solid (molecular, metallic, covalent- network, or ionic) might the substance be?

You are given a white substance that sublimes at \(3000^{\circ} \mathrm{C}\); the solid is a nonconductor of electricity and is insoluble in water. Which type of solid (molecular, metallic, covalent-network, or ionic) might this substance be?

(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.

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

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?

Imagine the primitive cubic lattice. Now imagine pushing on top of it, straight down. All angles remain \(90^{\circ}\). What kind of primitive lattice have you made?

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.

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, (d) triclinic, (e) both rhombohedral and triclinic.

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, (b) 2, (c) 3, (d) 4, (e) 5 .

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

The densities of the elements \(\mathrm{K}, \mathrm{Ca}, \mathrm{Sc}\), and \(\mathrm{Ti}\) 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.

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

Sodium metal (atomic weight \(22.99 \mathrm{~g} / \mathrm{mol}\) ) adopts a bodycentered cubic structure with a density of \(0.97 \mathrm{~g} / \mathrm{cm}^{3}\). (a) Use this information and Avogadro's number \(\left(N_{A}=6.022 \times 10^{23} / \mathrm{mol}\right)\) to estimate the atomic radius of sodium. (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?

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

Calcium crystallizes in a body-centered cubic structure. (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 \(\AA\) ). (d) Estimate the density of Ca metal.

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 ?). (d) Calculate the density of aluminum metal.

An element crystallizes in a body-centered cubic lattice. The edge of the unit cell is \(2.86 \AA\), and the density of the crystal is \(7.92 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the atomic weight of the element.

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.

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.\(12.32\) Sodium metal (atomic weight \(22.99 \mathrm{~g} / \mathrm{mol}\) ) adopts a bodycentered cubic structure with a density of \(0.97 \mathrm{~g} / \mathrm{cm}^{3}\). (a) Use this information and Avogadro's number \(\left(N_{A}=6.022 \times 10^{23} / \mathrm{mol}\right)\) to estimate the atomic radius of sodium. (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?

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) \(\mathrm{Fe}_{0.97} \mathrm{Si}_{0.03 \text {, }}\) (b) \(\mathrm{Fe}_{0.60} \mathrm{Ni}_{0.40}\) (c) \(\mathrm{SmCo}_{s}\).

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

Indicate whether each statement is true or false: (a) Substitutional alloys tend to be more ductile than interstitial alloys. (b) Interstitial alloys tend to form between elements with similar ionic radii. (c) Nonmetallic elements are never found in alloys.

Indicate whether each statement is true or false: (a) Intermetallic compounds have a fixed composition. (b) Copper is the majority component in both brass and bronze. (c) In stainless steel, the chromium atoms occupy interstitial positions.

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.

State whether each sentence is true or false: (a) Metals have high electrical conductivities because the electrons in the metal are delocalized. (b) Metals have high electrical conductivities because they are denser than other solids. (c) Metals have large thermal conductivities because they expand when heated. (d) Metals have small thermal conductivities because the delocalized electrons cannot easily transfer the kinetic energy imparted to the metal from heat.

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.

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

Which of the following statements does not follow from the fact that the alkali metals have relatively weak metal-metal bonding? (a) The alkali metals are less dense than other metals. (b) The alkali metals are soft enough to be cut with a knife. (c) The alkali metals are more reactive than other metals. (d) The alkali metals have higher melting points than other metals. (e) The alkali metals have low ionization energies.

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?

\(\mathrm{NaF}\) has the same structure as \(\mathrm{NaCl}\). (a) Use ionic radii from Chapter 7 to estimate the length of the unit cell edge for NaF. (b) Use the unit cell size calculated in part (a) to estimate the density of NaF.

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.

A particular form of cinnabar (HgS) adopts the zinc blende structure. The length of the unit cell edge is \(5.852 \AA\). (a) Calculate the density of \(\mathrm{HgS}\) in this form. (b) The mineral tiemmanite ( \(\mathrm{HgSe}\) ) also forms a solid phase with the zinc blende structure. The length of the unit cell edge in this mineral is \(6.085 \AA\). 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?

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 highpressure form of RbI. (d) Use this value to estimate the density. How does this density compare with the density you calculated in part (b)?

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, \(\mathrm{Ca}^{2+}(r=1.14 \mathrm{~A}), \mathrm{Zn}^{2+}(r=0.88 \mathrm{~A})\), 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?

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) \(\mathrm{MgS}_{\text {, }}\) (b) \(\mathrm{MgF}_{2}\), (c) \(\mathrm{MgO}\).

Classify each of the following statements as true or false: (a) Although both molecular solids and covalent-network solids have covalent bonds, the melting points of molecular solids are much lower because their covalent bonds are much weaker. (b) Other factors being equal, highly symmetric molecules tend to form solids with higher melting points than asymmetrically shaped molecules.

Classify each of the following statements as true or false: (a) For molecular solids, the melting point generally increases as the strengths of the covalent bonds increase. (b) For molecular solids, the melting point generally increases as the strengths of the intermolecular forces increase.

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. (a) Which type of solid is more likely to dissolve in water? (b) Which type of solid can become an electrical conductor via chemical substitution?

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?

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

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

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

The semiconductor GaP has a band gap of \(2.26 \mathrm{eV}\). What wavelength of light would be emitted from an LED made from GaP? What color is this?