Chapter 12

Covalent bonding occurs in both molecular and covalent network solids. Why do these two kinds of solids differ so greatly in their hardness and melting points?

Silicon is the fundamental component of integrated circuits. Si has the same structure as diamond. Is Si a molecular, metallic, ionic, or covalent-network solid?

What kinds of attractive forces exist between particles in (a) molecular crystals, (b) covalent-network crystals, (c) ionic crystals, (d) 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 crystal (molecular, metallic, ionic, or covalent-network) each of the following would form upon solidification: (a) \(\mathrm{CaCO}_{3},\) (b) \(\mathrm{Pt},\) (c) \(\mathrm{ZrO}_{2} \quad\) (melting point, \(\left.2677{ }^{\circ} \mathrm{C}\right),\) (d) table sugar \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) (e) benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right),(\mathrm{f}) \mathrm{I}_{2}\)

Indicate the type of crystal (molecular, metallic, ionic, or covalent-network) each of the following would form upon solidification: (a) InAs, (b) \(\mathrm{MgO},\) (c) \(\mathrm{HgS},\) (d) \(\mathrm{In},\) (e) \(\mathrm{HBr}\).

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?

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?

(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.

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

Of the seven three-dimensional primitive lattices, (a) which one has a unit cell where the \(a\) and \(b\) lattice vectors form a rectangular base, while the \(c\) lattice vector is perpendicular to the other two and of a different length? (b) What is the lattice if the \(a\) and \(b\) lattice vectors form a square base and the \(c\) lattice vector is perpendicular to the other two and of a different length?

Of the seven three-dimensional primitive lattices, (a) which one has a unit cell where the \(a\) and \(b\) lattice vectors form a base that is an arbitrary parallelogram (like the unit cell of a two-dimensional oblique lattice), while the \(c\) lattice vector is perpendicular to the other two? (b) What is the lattice if the \(a\) and \(b\) lattice vectors form a base that corresponds to the two-dimensional hexagonal unit cell and the \(c\) lattice vector is perpendicular to the other two?

Of the seven three-dimensional primitive lattices, which ones have a unit cell where no two lattice vectors are perpendicular to each other?

Of the seven three-dimensional primitive lattices, which ones have a unit cell where all three lattice vectors are of the same length?

What is the minimum number of atoms that could be contained in the unit cell of an element with a body-centered cubic lattice?

What is the minimum number of atoms that could be contained in the unit cell of an element with a face-centered cubic lattice?

Which of the following substances would you expect to possess metallic properties: (a) \(\mathrm{TiCl}_{4}\), (b) NiCo alloy, (c) \(\mathrm{W},(\mathrm{d})\) Ge, (e) \(\mathrm{ScN}\) ?

Sodium metal (atomic weight \(22.99 \mathrm{~g} / \mathrm{cm}^{3}\) ) adopts a bodycentered cubic structure with a density of \(0.97 \mathrm{~g} / \mathrm{cm}^{3}\). (a) Use this information and Avogadro's number \(\left(N_{\mathrm{A}}=6.022 \times 10^{23}\right)\) to estimate the atomic radius of sodium. (b) If it didn't react so vigorously, sodium 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 with 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 cubic close-packed structure [face-centered cubic cell, Figure \(12.14(\mathrm{a})] .(\mathrm{a})\) 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 \((1.43 \AA) .\) (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.

Define the term alloy. Distinguish among solid solution alloys, heterogeneous alloys, and intermetallic compounds.

Distinguish between substitutional and interstitial alloys. What conditions favor formation of substitutional alloys?

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) \(\mathrm{Fe}_{0.97} \mathrm{Si}_{0.03}\), (b) \(\mathrm{Fe}_{0.60} \mathrm{Ni}_{0.40}\), (c) \(\mathrm{SmCo}_{5}\).

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) \(\mathrm{Ti}_{0.99} \mathrm{O}_{0.01}\)

Classify each of the following statements as 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.

Classify each of the following statements as 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 indicate what type of alloy is formed: (a) white gold, (b) rose gold, (c) blue gold, (d) green gold.

Explain how the electron-sea model accounts for the high electrical and thermal conductivity of metals.

(a) Compare the electronic structures of atomic chromium and atomic selenium. In what respects are they similar, and in what respects do they differ? (b) Chromium is a metal, and selenium is a nonmetal. What factors are important in determining this difference in properties?

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

How do you account for the observation that the alkali metals, like sodium and potassium, are soft enough to be cut with a knife?

For each of the following groups which metal would you expect to have the highest melting point; (a) gold (Au), rhenium (Re), or cesium (Cs); (b) rubidium (Rb), molybdenum (Mo), or indium (In); (c) ruthenium (Ru), strontium (Sr), or cadmium (Cd)?

For each of the following groups which metal would you expect to have the highest melting point; (a) gold (Au), rhenium (Re), or cesium (Cs); (b) rubidium (Rb), molybdenum (Mo), or indium (In); (c) ruthenium (Ru), strontium (Sr), or cadmium (Cd)?

NaF has the same structure as 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 \(\mathrm{NaF}\)

A particular form of cinnabar (HgS) adopts the zinc blende structure, Figure \(12.26 .\) 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 (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 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)?

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

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) \(\mathrm{AlF}_{3}\) 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.

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) CdS or CdTe, (b) GaN or InP, (c) GaAs or InAs?

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

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

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

The semiconductor GaP has a band gap of \(2.2 \mathrm{eV}\). Green LEDs are made from pure GaP. What wavelength of light would be emitted from an LED made from GaP?

The first LEDs were made from GaAs, which has a band gap of \(1.43 \mathrm{eV}\). What wavelength of light would be emitted from an LED made from GaAs? What region of the electromagnetic spectrum does this light correspond to: UV, visible, or IR?