Page 580 - Chemistry--atom first
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570 Chapter 10 | Liquids and Solids
Ca atomic radii:
Solving this gives
(b) Density is given by The density of calcium can be found by determining the density
of its unit cell: for example, the mass contained within a unit cell divided by the volume of the unit cell. A face-centered Ca unit cell has one-eighth of an atom at each of the eight corners atom) and
one-half of an atom on each of the six faces atoms), for a total of four atoms in the unit cell. The mass of the unit cell can be found by:
The volume of a Ca unit cell can be found by:
(Note that the edge length was converted from pm to cm to get the usual volume units for density.)
Then, the density of
Check Your Learning
Silver crystallizes in an FCC structure. The edge length of its unit cell is 409 pm. (a) What is the atomic radius of Ag in this structure?
(b) Calculate the density of Ag.
Answer:
(a) 144 pm; (b) 10.5 g/cm3
In general, a unit cell is defined by the lengths of three axes (a, b, and c) and the angles (α, β, and γ) between them, as illustrated in Figure 10.55. The axes are defined as being the lengths between points in the space lattice. Consequently, unit cell axes join points with identical environments.
Figure 10.55 A unit cell is defined by the lengths of its three axes (a, b, and c) and the angles (α, β, and γ) between the axes.
There are seven different lattice systems, some of which have more than one type of lattice, for a total of fourteen different unit cells, which have the shapes shown in Figure 10.56.
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