Back
Problem 110e
What type of lattice—primitive cubic, body-centered cubic, or face-centered cubic—does each of the following structure types possess: (e) ZnS?
- Cinnabar (HgS) was utilized as a pigment known as vermillion. It has a band gap of 2.20 eV near room temperature for the bulk solid. What wavelength of light (in nm) would a photon of this energy correspond to?
Problem 111
- The electrical conductivity of aluminum is approximately 109 times greater than that of its neighbor in the periodic table, silicon. Aluminum has a face-centered cubic structure, and silicon has the diamond structure. A classmate of yours tells you that density is the reason aluminum is a metal but silicon is not; therefore, if you were to put silicon under high pressure, it too would act like a metal. Discuss this idea with your classmates, looking up data about Al and Si as needed.
Problem 112
Problem 113b
Silicon carbide, SiC, has the three-dimensional structure shown in the figure.
(b) Would you expect the bonding in SiC to be predominantly ionic, metallic, or covalent?
- (a) How many copper atoms are in a piece of copper metal in the shape of a cube with an edge length of 0.5 mm? The density of copper is 8.96 g/cm³. (c) Is this spacing larger, substantially smaller, or about the same as the 1 * 10⁻¹⁸ J separation between energy levels in a hydrogen atom?
Problem 114
Problem 114b
Energy bands are considered continuous due to the large number of closely spaced energy levels. The range of energy levels in a crystal of copper is approximately 1 × 10–19 J. Assuming equal spacing between levels, the spacing between energy levels may be approximated by dividing the range of energies by the number of atoms in the crystal. (b) Determine the average spacing in J between energy levels in the copper metal in part (a).
- Unlike metals, semiconductors increase their conductivity as you heat them (up to a point). Suggest an explanation.
Problem 115
Problem 116c
Sodium oxide (Na2O) adopts a cubic structure with Na atoms represented by green spheres and O atoms by red spheres.
(c) The unit cell edge length is 5.550 Å. Determine the density of Na2O.
- Teflon is a polymer formed by the polymerization of F2C=CF2. (a) Draw the structure of a section of this polymer. (b) What type of polymerization reaction is required to form Teflon?
Problem 117
- Hydrogen bonding between polyamide chains plays an important role in determining the properties of a nylon such as nylon 6,6 (Table 12.6). Draw the structural formulas for two adjacent chains of nylon 6,6 and show where hydrogen-bonding interactions could occur between them.
Problem 118
- Explain why X-rays can be used to measure atomic distances in crystals but visible light cannot be used for this purpose.
Problem 119
Problem 120
In their study of X-ray diffraction, William and Lawrence Bragg determined that the relationship among the wavelength of the radiation 1l2, the angle at which the radiation is diffracted 1u2, and the distance between planes of atoms in the crystal that cause the diffraction (d) is given by nl = 2d sin u. X rays from a copper X-ray tube that have a wavelength of 1.54 Å are diffracted at an angle of 14.22 degrees by crystalline silicon. Using the Bragg equation, calculate the distance between the planes of atoms responsible for diffraction in this crystal, assuming n = 1 (first-order diffraction).
Problem 121
Germanium has the same structure as silicon, but the unit cell size is different because Ge and Si atoms are not the same size. If you were to repeat the experiment described in the previous problem but replace the Si crystal with a Ge crystal, would you expect the X rays to be diffracted at a larger or smaller angle u?
- X-ray diffraction studies of buckminsterfullerene show that it has a face-centered cubic lattice of C60 molecules. The length of an edge of the unit cell is 14.2 Å. Calculate the density of buckminsterfullerene.
Problem 122
Problem 122a
(a) The density of diamond is 3.5 g/cm3, and that of graphite is 2.3 g/cm3. Based on the structure of buckminsterfullerene, what would you expect its density to be relative to these other forms of carbon?
Problem 122b
(b) X-ray diffraction studies of buckminsterfullerene show that it has a face-centered cubic lattice of C60 molecules. The length of an edge of the unit cell is 14.2 Å. Calculate the density of buckminsterfullerene.
- When you shine light of band gap energy or higher on a semiconductor and promote electrons from the valence band to the conduction band, do you expect the conductivity of the semiconductor to (a) remain unchanged, (b) increase, or (c) decrease?
Problem 123
Problem 124a
The karat scale used to describe gold alloys is based on mass percentages. (a) If an alloy is formed that is 50 mol% silver and 50 mol% gold, what is the karat number of the alloy? Use Figure 12.18 to estimate the color of this alloy.
Problem 124b
The karat scale used to describe gold alloys is based on mass percentages. (b) If an alloy is formed that is 50 mol% copper and 50 mol% gold, what is the karat number of the alloy? What is the color of this alloy?
- Spinel is a mineral that contains 37.9% Al, 17.1% Mg, and 45.0% O, by mass, and has a density of 3.57 g/cm³. The unit cell is cubic with an edge length of 8.09 Å. How many atoms of each type are in the unit cell?
Problem 125
Problem 126a
(a) What are the C—C—C bond angles in diamond?
Problem 126b
(b) What are they in graphite (in one sheet)?
Problem 126c
(c) What atomic orbitals are involved in the stacking of graphite sheets with each other?
Problem 127
Employing the bond enthalpy values listed in Table 8.4, estimate the molar enthalpy change occurring upon (a) polymerization of ethylene. (b) formation of nylon 6,6. (c) formation of polyethylene terephthalate (PET).
Problem 128a
Although polyethylene can twist and turn in random ways, the most stable form is a linear one with the carbon backbone oriented as shown in the following figure:
The solid wedges in the figure indicate bonds from carbon that come out of the plane of the page; the dashed wedges indicate bonds that lie behind the plane of the page. (a) What is the hybridization of orbitals at each carbon atom? What angles do you expect between the bonds?
Problem 129a
(a) In polyvinyl chloride shown in Table 12.6, which bonds have the lowest average bond enthalpy?
Problem 129b
(b) When subjected to high pressure and heated, polyvinyl chloride converts to diamond. During this transformation which bonds are most likely to break first?
Problem 129c
(c) Employing the values of average bond enthalpy in Table 8.3, estimate the overall enthalpy change for converting PVC to diamond.
Problem 130a
Silicon has the diamond structure with a unit cell edge length of 5.43 Å and eight atoms per unit cell. (a) How many silicon atoms are there in 1 cm3 of material?
Problem 130b
Silicon has the diamond structure with a unit cell edge length of 5.43 Å and eight atoms per unit cell. (b) Suppose you dope that 1 cm3 sample of silicon with 1 ppm of phosphorus that will increase the conductivity by a factor of a million. How many milligrams of phosphorus are required?