21.46.Compare the two-particle coulombic energy of at-
traction with the more precise calculation of the lattice energy
for (a)cesium chloride, CsCl (0.331 Å); (b)zincblende,
ZnS (0.289 Å); and (c)rutile, TiO 2 (0.250). Are there
any trends in the discrepancies? Use data from Tables 21.4
and 21.6.
21.47.The lattice energy for potassium iodide, KI, is
627.2 kJ/mol. If the ionic separation is 3.533 Å, what is the re-
pulsive range parameter for KI? You will have to determine
which Madelung constant to use.
21.48.The concept of charge densityinvolves the total charge
of an ion divided by the space that the ion occupies. Using
Table 21.5, determine a trend between charge density of an
ion and the lattice energy of similar ionic crystals. Can you jus-
tify this trend on physical principles?
21.49.Lattice energies can also be defined for atomic ele-
ments like the gases He, Ne, and Ar. (a)Explain why equation
21.13 is not applicable to such crystals. (b)How would a sci-
entist measure the lattice energy of He, Ne, Ar, and so on?
Consider Chapters 1–8 in developing your answer.
21.50.Studies of crystals of He, Ne, Ar, and so on must be
performed in vacuum systems that have an apparatus that can
reach low temperatures so these elements are solids. These
vacuum systems should not have hydrocarbons in them that
might decompose to give off H atoms or H 2 molecules into
the vacuum system. Why?
21.51.Solid palladium metal is known to actually absorb hy-
drogen gas, and no other. This behavior is used to make ultra,
ultra-pure hydrogen. (In fact, because of this, hydrogen can
be obtained in purer form than any other element.) What kind
of defect are the hydrogen molecules probably making in the
solid Pd metal? On the basis of your answer, can you ratio-
nalize why hydrogen is absorbed by Pd and no other gas?
21.52.Gallium arsenide (GaAs) can also serve as a basis for a
semiconductor. It has a structure similar to that of elemental
silicon, but with alternating gallium and arsenic atoms. Draw
an electron-dot type of diagram of a unit cell of GaAs as well
as n-type and p-type substitutions for a semiconducting ma-
terial based on GaAs. What can be substituted for Ga for each
type of semiconductor? What can be substituted for As for
each type of semiconductor?
21.53.Suggest dopants for GaAs that would yield (a)a p-
type semiconductor, and (b)an n-type semiconductor.
21.54.Explain how holes conduct electricity.21.55.Calculate the volume of the unit cells for the com-
pounds in Table 21.7.
21.56.Set up a program or formula to calculate the angles
of diffraction for a cubic crystal in terms of the h, k, and val-
ues. (a)Calculate these angles for incoming X radiation of
1.5418 Å and a simple cubic lattice having a lattice parame-
ter of 6.46 Å. (b)Use Table 21.3 to determine which diffrac-
tions would be absent if the crystal were body-centered cubic
or face-centered cubic.764 Exercises for Chapter 21
Table 21.7 Parameters for several unit cellsa
Name Lattice abc
Coloradoite, HgTe Cubic 6.46 90 90 90
Ice, H 2 O Hexagonal 4.5212 7.366
Hafnia, HfO 2 Monoclinic 5.1156 5.17 5.2948 99.18
Turquoise, CuAl 6 (PO 4 ) 4 (OH) 8 4H 2 O Triclinic 7.424 7.62 9.910 68.61 69.71 65.08
aLengths a,b,care in units of Å. Angles , , are in degrees.Symbolic Math Exercises