Ch.12 - Solids and Solid-State Materials
Back
- 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 pm
Problem 2
- Niobium oxide crystallizes in the following cubic unit cell:
Problem 5
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
- The following diagrams represent the electron population of the composite s–d band for three metals—Ag, Mo, and Y:
Problem 6
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
- 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 7
- 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)
Problem 9
(a) n-type, As (b) n-type, Ga (c) p-type, As (d) p-type, Ga
- 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 nm
Problem 11
- 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)
Problem 13
(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)
- Titanium oxide crystallizes in the following cubic unit cell:
Problem 20
(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.
- 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)
Problem 25
(2)
- List the four main classes of crystalline solids, and give a specific example of each.
Problem 26
- 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 solid
Problem 28
- 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 36
- 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 39
- 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 41
- 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 44
- 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 45
- 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 46
- 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 51
- 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.)
Problem 52
- Silicon carbide, SiC, is a covalent network solid with a structure similar to that of diamond. Sketch a small portion of the SiC structure.
Problem 54
- Carbon and oxygen combine to form the molecular compound CO2, while silicon and oxygen combine to form a covalent network solid with the formula unit SiO2. Explain the difference in bonding between the two group 4A elements and oxygen.
Problem 57
- Potassium metal crystallizes in a body-centered cubic structure. Draw one unit cell, and try to draw an electron-dot structure for bonding of the central K atom to its nearestneighbor K atoms. What is the problem?
Problem 58
- The melting point of sodium metal is 97.8 °C, and the melting point of sodium chloride is 801 °C. What can you infer about the relative strength of metallic and ionic bonding from these melting points?
Problem 62
- Sodium melts at 98 °C, and magnesium melts at 650 °C. Account for the higher melting point of magnesium using the electron-sea model.
Problem 65
- Draw an MO energy-level diagram that shows the population of the 4s band for potassium metal.
Problem 67
- The melting points for the second-series transition elements increase from 1522 °C for yttrium to 2623 °C for molybdenum and then decrease to 321 °C for cadmium. Account for the trend using band theory.
Problem 72
- Tungsten is hard and has a very high melting point (3422 °C), and gold is soft and has a relatively low melting point (1064 °C). Are these facts in better agreement with the electron-sea model or the MO model (band theory)? Explain.
Problem 74
