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Problem 96a
CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy. (a) What color is the emitted light?
Problem 96b
CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy. (b) Would appropriately sized CdS quantum dots be able to emit blue light?
Problem 96c
CdS has a band gap of 2.4 eV. If large crystals of CdS are illuminated with ultraviolet light, they emit light equal to the band gap energy. (c) What about red light?
- Indicate whether each statement is true or false: (a) The band gap of a semiconductor decreases as the particle size decreases in the 1–10-nm range. (b) The light that is emitted from a semiconductor, upon external stimulation, becomes longer in wavelength as the particle size of the semiconductor decreases.
Problem 97
- Indicate whether this statement is true or false: If you want a semiconductor that emits blue light, you could either use a material that has a band gap corresponding to the energy of a blue photon or you could use a material that has a smaller band gap but make an appropriately sized nanoparticle of the same material.
Problem 98
Problem 101
Which statement correctly describes a difference between graphene and graphite? (a) Graphene is a molecule but graphite is not. (b) Graphene is a single sheet of carbon atoms and graphite contains many, and larger, sheets of carbon atoms. (c) Graphene is an insulator but graphite is a metal. (d) Graphite is pure carbon but graphene is not. (e) The carbons are sp2 hybridized in graphene but sp3 hybridized in graphite.
- What evidence supports the notion that buckyballs are actual molecules and not extended materials? (a) Buckyballs are made of carbon. (b) Buckyballs have a well-defined atomic structure and molecular weight. (c) Buckyballs have a well-defined melting point. (d) Buckyballs are semiconductors. (e) More than one of the previous choices.
Problem 102
- Selected chlorides have the following melting points: NaCl (801 °C), MgCl2 (714 °C), PCl3 (-94 °C), SCl2 (-121 °C). (b) Predict which of the following compounds has a higher melting point: CaCl2 or SiCl4.
Problem 103
Problem 105
Imagine the primitive cubic lattice. Now imagine pushing on top of it, straight down. Next, stretch another face by pulling it to the right. All angles remain 90°. What kind of primitive lattice have you made?
Problem 106
Pure iron crystallizes in a body-centered cubic structure, shown in the figure. but small amounts of impurities can stabilize a facecentered cubic structure. Which form of iron has a higher density?
- Introduction of carbon into a metallic lattice generally results in a harder, less ductile substance with lower electrical and thermal conductivities. Explain why this might be so.
Problem 107
- For each of the intermetallic compounds shown in Figure 12.17 determine the number of each type of atom in the unit cell. Do your answers correspond to the ratios expected from the empirical formulas: Ni3Al?
Problem 109
- 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
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?
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?
