Chapter 13

What is graphene? Why is graphene unique?

Explain the basic principles involved in X-ray crystallography. Include Bragg's law in your explanation.

What is a crystalline lattice? How is the lattice represented with the unit cell?

What is the difference between hexagonal closest packing and cubic closest packing? What are the unit cells for each of these structures?

What are the three basic types of solids and the composite units of each? What types of forces hold each type of solid together?

What are the three categories of atomic solids?

What kinds of forces hold each of the three basic categories of atomic solids together?

Show how the cesium chloride, sodium chloride, and zinc blende unit cells each contain a cation-to-anion ratio of \(1: 1 .\)

Show how the fluorite structure accommodates a cation-to-anion ratio of 1: 2 .

Name and describe the different allotropes of carbon.

What are silicates? What is quartz?

What is the definition of a ceramic? What are the three categories of ceramics?

List the major and minor components of Portland cement. What is the difference between the hardening process of Portland cement and the hardening process of clays?

Describe the difference between vitreous silica and soda-lime glass. What are some advantages and disadvantages of each of these types of glass?

In band theory of bonding for solids, what is a band? What is the difference between the valence band and the conduction band?

In band theory of bonding for solids, what is a band gap? How does the band gap differ in metals, semiconductors, and insulators?

Explain how doping can increase the conductivity of a semiconductor. What is the difference between an n-type semiconductor and a p-type semiconductor?

What is a polymer? What is the difference between a polymer and a copolymer?

How do an addition polymer and a condensation polymer differ from each other?

An X-ray beam with \(\lambda=154 \mathrm{pm}\) incident on the surface of a crystal produced a maximum reflection at an angle of \(\theta=28.3^{\circ}\) Assuming \(n=1,\) calculate the separation between layers of atoms in the crystal.

An X-ray beam of unknown wavelength is diffracted from a NaCl surface. If the interplanar distance in the crystal is \(286 \mathrm{pm}\), and the angle of maximum reflection is found to be \(7.23^{\circ},\) what is the wavelength of the X-ray beam? (Assume \(n=1 .\) )

Calculate the packing efficiency of the body-centered cubic unit cell. Show your work.

Calculate the packing efficiency of the face-centered cubic unit cell. Show your work.

Platinum crystallizes with the face-centered cubic unit cell. The radius of a platinum atom is \(139 \mathrm{pm}\). Calculate the edge length of the unit cell and the density of platinum in \(\mathrm{g} / \mathrm{cm}^{3}\).

Palladium crystallizes with a face-centered cubic structure. It has a density of \(12.0 \mathrm{~g} / \mathrm{cm}^{3}\), a radius of \(138 \mathrm{pm}\), and a molar mass of \(106.42 \mathrm{~g} / \mathrm{mol} .\) Use these data to calculate Avogadro's number.

Classify each of the following as a component of a silicate ceramic, an oxide ceramic, or a nonoxide ceramic. a. \(\mathrm{B}_{4} \mathrm{C}\) b. \(\mathrm{Mg}_{2} \mathrm{SiO}_{4}\) c. \(\mathrm{MoSi}_{2}\)

Classify each of the following as a component of a silicate ceramic, an oxide ceramic, or a nonoxide ceramic. a. \(\mathrm{TiB}_{2}\) b. \(\mathrm{ZrO}_{2}\) c. \(\mathrm{NaAlSi}_{3} \mathrm{O}_{8}\)

What are the name and formula of the compound commonly used in the manufacture of glass to reduce its tendency to crack or shatter under thermal shock?

One of the key components in the manufacture of Portland cement is \(\mathrm{Ca}_{3} \mathrm{SiO}_{5}\), a compound that is obtained by firing the reactants in a kiln at \(1400-1500^{\circ} \mathrm{C}\). Assign an oxidation state to each element in this compound.

Replacement of aluminum ions in kaolinite with magnesium ions yields a compound with the formula \(\mathrm{Mg}_{3} \mathrm{Si}_{2} \mathrm{O}_{5}(\mathrm{OH})_{4}\). Assign an oxidation state to each element in this compound.

Which solid would you expect to have the largest band gap? a. \(\operatorname{As}(s)\) b. \(\mathrm{Sb}(s)\) c. \(\mathrm{Bi}(s)\)

A substance has a band gap of \(6.9 \mathrm{eV}\) at \(273 \mathrm{~K}\). Is this substance best classified as an insulator, a semiconductor, or a metal?

Indicate if each solid forms an n-type or a p-type semiconductor. a. germanium doped with gallium b. silicon doped with arsenic

Indicate if each solid forms an n-type or a p-type semiconductor. a. silicon doped with gallium b. germanium doped with antimony

Which wavelength of light (in \(\mathrm{nm}\) ) is emitted if an electron moves from the conduction band to the valence band in a sample of diamond (diamond has a band gap of \(5.5 \mathrm{eV}\) )?

One kind of polyester is a condensation copolymer formed from terephthalic acid and ethylene glycol. Draw the structure of the dimer. [Hint: Water (circled) is eliminated when the bond between the monomers forms.]

Nomex, a condensation copolymer used by firefighters because of its flame- resistant properties, forms from isophthalic acid and \(m\) -aminoaniline. Draw the structure of the dimer. (Hint: Water is eliminated when the bond between the monomers forms.)

Consider the body-centered cubic structure shown here: a. What is the length of the line (labeled \(c\) ) that runs from one corner of the cube diagonally through the center of the cube to the other corner in terms of \(r\) (the atomic radius)? b. Use the Pythagorean theorem to derive an expression for the length of the line (labeled \(b\) ) that runs diagonally across one of the faces of the cube in terms of the edge length \((I) .\) c. Use the answer to parts a and \(\mathrm{b}\) along with the Pythagorean theorem to derive the expression for the edge length \((I)\) in terms of \(r\)

The density of an unknown metal is \(12.3 \mathrm{~g} / \mathrm{cm}^{3}\), and its atomic radius is \(0.134 \mathrm{nm} .\) It has a face-centered cubic lattice. Find the atomic mass of this metal.

An unknown metal is found to have a density of \(7.8748 \mathrm{~g} / \mathrm{cm}^{3}\) and to crystallize in a body-centered cubic lattice. The edge of the unit cell is \(0.28664 \mathrm{nm}\). Calculate the atomic mass of the metal.

When spheres of radius \(r\) are packed in a body-centered cubic arrangement, they occupy \(68.0 \%\) of the available volume. Use the fraction of occupied volume to calculate the value of \(a,\) the length of the edge of the cube, in terms of \(r\).

A tetrahedral site in a closest-packed lattice is formed by four spheres at the corners of a regular tetrahedron. This is equivalent to placing the spheres at alternate corners of a cube. In such a closest-packed arrangement the spheres are in contact, and if the spheres have a radius \(r\), the diagonal of the face of the cube is \(2 r\). The tetrahedral hole is inside the middle of the cube. Find the length of the body diagonal of this cube and then find the radius of the tetrahedral hole.

Why are X-rays used for crystallography? Why not use some other, more accessible type of electromagnetic radiation such as ultraviolet light?

Which is not likely to lead to an increase in electrical conductivity? a. Increasing the temperature of a semiconductor b. Choosing a semiconductor with a smaller band gap c. Doping the semiconductor d. All of the above would likely lead to an increase in electrical conductivity.

Make a list of questions you would need to ask in order to classify a solid into one of the categories of crystalline solids (molecular solid, ionic solid, nonbonded solid, metallic solid, and network covalent solid). Determine a good order to ask them. (You may need a branching decision tree.) Once you have agreed on a good set of questions, have each group member choose a substance from the chapter and then have the other group members ask the questions in turn until the correct classification is reached. You may agree to edit your questions if you discover ways to improve them when you are using your decision tree.

Have each group member select and study a material from the section on ceramics, cement, and glass. Take turns describing your material to the group, and see if they can identify the type of material based on your description (without consulting the text).

Describe how a common object or toy (e.g., a train, building blocks, or beads on a string) could represent the structure of a polymer. Describe how the following terms would be represented using your model: monomer, dimer, addition polymer, condensation polymer, branching.