5. The structure shows anions (dark circles) in a simple cubic array with cations (white circles) in alternating body centers. One unit cell is shown. Complete the following table for one unit cell to determine the ratio of cations to anions. f is the fraction each atom in in the indicated position contributes to the cell. Cation alculate the LI-Br distance in the crystal structure in pm. Anion Corners # # Faces # Edges f # Body f TOTAL ION PER CELL

What is the relationship between the structures of buckminsterfullerene and carbon nanotubes?

8.76 Using circles, draw regular two-dimensional arrangements that demonstrate low packing efficiency and high packing efficieny.

Outline a two-dimensional unit cell for the pattern shown here. If the black squares are labeled A and the white squares are B, what is the simplest formula for a compound based on this pattern?

Explain in words how Avogadros number could be obtained from the unit-cell edge length of a cubic crystal. What other data are required?

CaTiO3, a perovskite, has the structure below. (a) If the density of the solid is 4.10 g/cm3, what is the length of a side of the unit cell? (b) Calculate the radius of the Ti4+ ion in the center of the unit cell. How well does your calculation agree with a literature value of 75 pm? Unit cell of the perovskite CaTiO3 A sample of perovskite, iO3 FIGURE 7.11 Relative sizes of some common ions. Rodii are given in picometers (1 pm 1 1012 m). (Data taken from J. Emsley, The Elements, Clarendon Press, Oxford, 1998, 3rd edition.)

At 25 C, how high will water rise in a glass capillary tube with an inner diameter of 0.63 mm? Refer to Example 10.4 for the required information.

A metal burns in air at 600c under high pressure to form an oxide with formula MO2. This compound is 23.72% oxygen by mass. The distance between the centers of touching atoms in a cubic closest packed crystal of this metal is 269.0 pm. What is this metal? What is its density?

• describe the arrangement of atoms in the common cubic crystal lattices and calculate the packing efficiency for a lattice.

8.97 The doping of semiconductors can be done with enough precision to tune the size of the band gap in the material. Generally, in order to have a larger band gap, the dopant should be smaller than the main material. If you are a materials engineer and need a semiconductor that has lower conductivity thin pure silicon, what clement or elements could you use as your dopant? (You do not want either an n- or a p- type material) Explain your reasoning.