Ch.12 - Solids and Solid-State Materials
Back
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.
- The following diagram represents the electron population of the bands of MO energy levels for elemental silicon:
Problem 23
(a) Identify the valence band, conduction band, and band gap.
- 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
- 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 38
- 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
- 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 42
- 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
- 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 48
- 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 50
- 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
- State whether each of the following compounds is likely to have a liquid crystalline phase. Explain your reasoning. (a)
Problem 68
- Draw an MO energy-level diagram for beryllium metal, and show the population of the MOs for the following two cases. (a) The 2s and 2p bands are well separated in energy. (b) The 2s and 2p bands overlap in energy. Which diagram agrees with the fact that beryllium has a high electrical conductivity? Explain.
Problem 70
- 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
- Explain why the enthalpy of vaporization of vanadium (460 kJ/mol) is much larger than that of zinc (114 kJ/mol).
Problem 75
- Tell what is meant by each of the following terms. (c) Band gap
Problem 77
- Draw the bands of MO energy levels and the electron population for: (a) A semiconductor (b) An electrical insulator Explain why a semiconductor has the higher electrical conductivity.
Problem 78
