Ch.12 - Solids and Solid-State Materials
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Problem 2
Diffraction of X rays with l = 131.5 pm occurred at an angle of 25.5 degrees by a crystal of aluminum. Assuming first-order diffraction, what is the interplanar spacing in aluminum? (LO 12.2) (a) 76.4 pm (b) 183.1 pm (c) 305.5 pm (d) 152.7 pmProblem 5
Niobium oxide crystallizes in the following cubic unit cell:
What is the formula of niobium oxide, and what is the oxidation state of niobium? (LO 12.5) (a) NbO, Nb = +2 (b) Nb2O, Nb = +2 (c) NbO2, Nb = +4 (d) Nb2O3, Nb = +3
Problem 6
The following diagrams represent the electron population of the composite s–d band for three metals—Ag, Mo, and Y:
Which diagram corresponds to which metal? (LO 12.7) (a) Ag = 3, Mo = 1, Y = 2 (b) Ag = 2, Mo = 1, Y = 3 (c) Ag = 2, Mo = 3, Y = 1 (d) Ag = 1, Mo = 2, Y = 3
Problem 7
Examine diagrams for the electron population of the composite s–d band for three metals in question 6. Which metal has the highest melting point? (LO 12.7) (a) Metal 1 (b) Metal 2 (c) Metal 3
Problem 8
The following diagrams represent the electron population of molecular orbitals for different substances. What diagram corresponds to magnesium oxide, germanium, and tin? (LO 12.8)
(a) Diagram 1 = tin, diagram 2 = magnesium oxide, diagram 3 = germanium (b) Diagram 1 = germanium, diagram 2 = magnesium oxide, diagram 3 = tin (c) Diagram 1 = germanium, diagram 2 = tin, diagram 3 = magnesium oxide (d) Diagram 1 = magnesium oxide, diagram 2 = tin, diagram 3 = germanium
Problem 9
The molecular orbital diagram of a doped semiconductor is shown below. If the semiconductor is silicon, does the diagram represent n-type or p-type doping and which of the following elements could be dopant? (LO 12.9)
(a) n-type, As (b) n-type, Ga (c) p-type, As (d) p-type, Ga
Problem 11
If the band-gap energy of a gallium phosphide (GaP) semiconductor is 222 kJ/mol, calculate the wavelength of light emitted in a GaP light-emitting diode (LED). (LO 12.11) (a) 186 nm (b) 245 nm (c) 539 nm (d) 854 nmProblem 13
A superconductor is a material that loses all electrical resistance below a characteristic temperature called the superconducting transition temperature. Which graph represents the behavior of a superconductor? (LO 12.13) (a)
(b)
(c)
(d)Problem 18b
Identify each of the following kinds of packing: (b)
Problem 18d
Identify each of the following kinds of packing: (d)
Problem 19
The following compound undergoes a phase transition from the solid to the smectic liquid crystal phase at 121 °C. Upon further heating, the compound undergoes another transition to liquid phase at 131 °C.
(b) Which image represents the arrangement of molecules at 135 °C?
Problem 20
Titanium oxide crystallizes in the following cubic unit cell:
(b) What is the formula of titanium oxide?
Problem 22a
The following diagrams show the electron populations of the bands of MO energy levels for four different materials: (a) Classify each material as an insulator, a semiconductor, or a conducting metal.
Problem 22c
The following diagrams show the electron populations of the bands of MO energy levels for four different materials:
. (c) Tell whether the conductivity of each material increases or decreases when the temperature increases.
Problem 23
The following diagram represents the electron population of the bands of MO energy levels for elemental silicon:
(a) Identify the valence band, conduction band, and band gap.
Problem 25
Diagrams (1) and (2) are energy-level diagrams for two different LEDs. One LED emits red light, and the other emits blue light. Which one emits red, and which blue? Explain. (1)
(2)
Problem 26
List the four main classes of crystalline solids, and give a specific example of each.Problem 28
Which of the substances Na3PO4, CBr4, rubber, Au, and quartz best fits each of the following descriptions? (a) Amorphous solid (b) Ionic solid (c) Molecular solid (d) Covalent network solid (e) Metallic solidProblem 36
Copper crystallizes in a face-centered cubic unit cell with an edge length of 362 pm. What is the radius of a copper atom in picometers? What is the density of copper in g>cm3?Problem 38
Aluminum has a density of 2.699 g>cm3 and crystallizes with a face-centered cubic unit cell. What is the edge length of a unit cell in picometers?Problem 39
Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 317 pm. What is the length in picometers of a unit-cell diagonal that passes through the center atom?Problem 41
Sodium has a density of 0.971 g>cm3 and crystallizes with a body-centered cubic unit cell. What is the radius of a sodium atom, and what is the edge length of the cell in picometers?Problem 42
Titanium metal has a density of 4.506 g>cm3 and an atomic radius of 144.8 pm. In what cubic unit cell does titanium crystallize?Problem 44
The atomic radius of Pb is 175 pm, and the density is 11.34 g>cm3. Does lead have a primitive cubic structure or a face-centered cubic structure?Problem 45
The density of a sample of metal was measured to be 6.84 g>cm3. An X-ray diffraction experiment measures the edge of a face-centered cubic cell as 350.7 pm. What is the atomic weight, atomic radius, and identity of the metal?Problem 46
If a protein can be induced to crystallize, its molecular structure can be determined by X-ray crystallography. Protein crystals, though solid, contain a large amount of water molecules along with the protein. The protein chicken egg-white lysozyme, for instance, crystallizes with a unit cell having angles of 90° and with edge lengths of 7.9 * 103 pm, 7.9 * 103 pm, and 3.8 * 103 pm. There are eight molecules in the unit cell. If the lysozyme molecule has a molecular weight of 1.44 * 104 and a density of 1.35 g>cm3, what percent of the unit cell is occupied by the protein?Problem 48
Iron crystallizes in a body-centered cubic unit cell with an edge length of 287 pm. Iron metal has a density of 7.86 g>cm3 and a molar mass of 55.85 g. Calculate a value for Avogadro's number.Problem 50
Sodium hydride, NaH, crystallizes in a face-centered cubic unit cell similar to that of NaCl (Figure 12.11). How many Na+ ions touch each H- ion, and how many H- ions touch each Na+ ion?Problem 51
Cesium chloride crystallizes in a cubic unit cell with Cl- ions at the corners and a Cs+ ion in the center. Count the numbers of + and - charges, and show that the unit cell is electrically neutral.Problem 52
If the edge length of an NaH unit cell is 488 pm, what is the length in picometers of an Na¬H bond? (See Problem 12.50.)
