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Problem 51a
The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: (a) How many molecular orbitals are there in the diagram?
Problem 51c
The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: (c) How many nodes are in the highest-energy molecular orbital?
Problem 51e
The molecular-orbital diagrams for two- and four-atom linear chains of lithium atoms are shown in Figure 12.22. Construct a molecular-orbital diagram for a chain containing six lithium atoms and use it to answer the following questions: (e) How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)?
Problem 52b,c,d,e
Repeat Exercise 12.51 for a linear chain of eight lithium atoms. (b) How many nodes are in the lowest-energy molecular orbital? (c) How many nodes are in the highestenergy molecular orbital? (d) How many nodes are in the highest-energy occupied molecular orbital (HOMO)? (e) How many nodes are in the lowest-energy unoccupied molecular orbital (LUMO)?
Problem 52f
Repeat Exercise 12.51 for a linear chain of eight lithium atoms. (f) How does the HOMO–LUMO energy gap for this case compare to that of the four-atom case?
Problem 53
Which would you expect to be the more ductile element, (a) Ag or Mo? (b) Zn or Si? In each case explain your reasoning.
Problem 54
Which of the following statements does not follow from the fact that the alkali metals have relatively weak metal–metal bonding? (a) The alkali metals are less dense than other metals. (b) The alkali metals are soft enough to be cut with a knife. (c) The alkali metals are more reactive than other metals. (d) The alkali metals have higher melting points than other metals. (e) The alkali metals have low ionization energies.
- Arrange the following metals in increasing order of expected melting points: Mo, Zr, Y, Nb. Explain this trend in melting points.
Problem 55
- For each of the following groups, which metal would you expect to have the highest melting point: (b) rubidium, molybdenum, or indium?
Problem 56
Problem 57a
Tausonite, a mineral composed of Sr, O, and Ti, has the cubic unit cell shown in the drawing. (a) What is the empirical formula of this mineral?
- The unit cell of a compound containing Co and O has a unit cell shown below. The Co atoms are on the corners, and the O atoms are completely within the unit cell. What is the empirical formula of this compound? What is the oxidation state of the metal?
Problem 58
- Alabandite is a mineral composed of manganese(II) sulfide (MnS). The mineral adopts the rock salt structure. The length of an edge of the MnS unit cell is 5.223 Å at 25 °C. Determine the density of MnS in g/cm³.
Problem 59
Problem 61a,c
A particular form of cinnabar (HgS) adopts the zinc blende structure. The length of the unit cell edge is 5.852 Å. (a) Calculate the density of HgS in this form. (c) Which of the two substances has the higher density? How do you account for the difference in densities?
Problem 61b
A particular form of cinnabar (HgS) adopts the zinc blende structure. The length of the unit cell edge is 5.852 Å. (b) The mineral tiemannite (HgSe) also forms a solid phase with the zinc blende structure. The length of the unit cell edge in this mineral is 6.085 Å. What accounts for the larger unit cell length in tiemmanite?
- 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. 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)?
Problem 62
Problem 63a
CuI, CsI, and NaI each adopt a different type of structure. The three different structures are those shown in Figure 12.26. (a) Use ionic radii, Cs+ 1r = 1.81 A 2, Na+ 1r = 1.16 A 2, Cu+ 1r = 0.74 A 2, and, I- 1r = 2.06 A 2, to predict which compound will crystallize with which structure.
- The coordination number for Mg2+ ion is usually six. Assuming this holds, determine the anion coordination number in the following compounds: (a) MgS, (b) MgF2, (c) MgO.
Problem 65
Problem 66a
The coordination number for the Al3+ ion is typically between four and six. Use the anion coordination number to determine the Al3 + coordination number in the following compounds: (a) AlF3 where the fluoride ions are two coordinate.
Problem 66b
The coordination number for the Al3+ ion is typically between four and six. Use the anion coordination number to determine the Al3 + coordination number in the following compounds: (b) Al2O3 where the oxygen ions are six coordinate.
Problem 66c
The coordination number for the Al3+ ion is typically between four and six. Use the anion coordination number to determine the Al3 + coordination number in the following compounds: (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.
Problem 67
- 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.
Problem 68
- Which type of solid can become a considerably better conductor of electricity via chemical substitution?
Problem 69
Problem 69a
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?
Problem 71
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?
- The smectic liquid crystalline phase can be said to be more highly ordered than the nematic phase. In what sense is this true?
Problem 72
Problem 73
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?
Problem 74
Problem 76b
Cadmium telluride is an important material for solar cells. (b) What wavelength of light would a photon of this energy correspond to?
Problem 76d
Cadmium telluride is an important material for solar cells. (d) With respect to silicon, does CdTe absorb a larger or smaller portion of the solar spectrum?