1. Which of the following schemes for the repeating pattern of close-packed planes are not ways of generating close-packed lattices? (a) ABCABC ...; (b) ABAC ...; (c) ABBA ...; (d) ABCBC ...; (e) ABABC...; (f) ABCCB ... .
2. In the structure of MoS2, the S atoms are arranged in close-paced layers that repeat themselves in the sequence AAA... . The Mo Atoms occupy holes with C.N. = 6. Show that each Mo atom is surrounded by a trigonal prism of S atoms.
3. The Coulombic attraction of nearest-neighbor cations and anions accounts for the bulk of the lattice enthalpy of an ionic compound. With this fact in mind, estimate the order of increasing lattice enthalpy of (a) MgO, (b) NaCl, (c) AlN, all of which crystallize in the rock-salt structure. Give your reasoning.
4. Depending upon the temperature, RbCl can exist in either the rock-salt or cesium-chloride structure. (a) What is the coordination number of the anion and cation in each of these structures? (b) In which of these structures will Rb have the higher apparent radius?
5. The ReO3 structure is cubic with Re at each corner of the unit cell and one O atom on each unit cell edge midway between the Re atoms. Sketch this unit cell and determine (a) the coordination number of the cation and anion and (b) the identity of the structure type that would be generated if a cation were inserted in the center of the ReO3 structure.
6. Given the following data for the length of a side of the unit cell for compounds that crystallize in the rock-salt structure, determine the cation radii: MgSe (545 pm), CaSe (591 pm), SrSe (623 pm), BaSe (662 pm). (Hint: To determine the Se2– radius, assume that the Se2– ions are in contact in MgSe.)
7. Confirm that in rutile (TiO2) the stoichiometry is consistent with the structure.
8. Estimate the lattice energy for magnesium chloride using both the Born-Landé equation and using a Born-Haber cycle. The heat of formation for magnesium chloride is –641.3 kJ/mole and the other thermodynamic data can be found in your textbook. In the Born-Landé equation, assume a fluorite structure, n= 8, and an interion distance of 2.4 Å. Compare the two values and comment about the agreement or disagreement.
9. Calculate the lattice energy (in units of kJ/mol) for ZnO in the wurtzite structure using the Born-Landé equation and using a Born-Haber cycle. Compare the two answers and comment on any differences. Useful data: the Born exponent, n, = 8; the sublimation energy of zinc = 130.4 kJ/mol; and the standard heat of formation of zinc(II) oxide = –350.5 kJ/mol. Other data can be found in the textbook.
10. LiI is found to have the same structure as NaCl. Given this information, estimate the lattice energy for LiI using the Born-Mayer equation and d* = 34.5 pm. Radius ratio rules suggest that the the observed LiI structure is anomalous; explain why.
11. In the context of band theory, explain why Mg is a metal, despite the fact that it has a filled s2 electron configuration.
12. Look up the metallic radius for the first row transition metal elements (Sc to Zn) and explain the trend in terms of metallic bonding.
13. Gallium arsenide is a semiconductor that is widely used for the construction of the red-light-emitting displays and is under development for advanced central processor chips in supercomputers. If gallium arsenide (GaAs) is doped with selenium (on the As site), is it n-doped or p-doped?
14. The promotion of an electron from the valence band into the conduction band in pure titanium(IV) oxide by light absorption requires a wavelength of less than 350 nm. Calculate the energy gap in electronvolts between the valence and conduction bands.
15. When titanium(IV) oxide is heated in hydrogen, a blue color develops, indicating light absorption in the red. Does reduction of Ti(IV) to Ti(III) correspond to n-doping or p-doping?