Chapter 12

The semiconductor CaSe has a band gap of 1.74 eV. What wavelength of light would be emitted from an LED made from CdSe? What region of the electromagnetic spectrum is this?

The first LEDs were made from GaAs, which has a band gap of 1.43 eV. What wavelength of light would be emitted from an LED made from GaAs? What region of the electromagnetic spectrum does this light correspond to: ultraviolet, visible, or infrared?

GaAs and GaP make solid solutions that have the same crystal structure as the parent materials, with As and Prandomly distributed throughout the crystal. GaP As \(_{1-x}\) exists for any value of \(x .\) If we assume that the band gap varies linearly with composition between \(x=0\) and \(x=1,\) estimate the band gap for GaP \(_{0.5} \mathrm{As}_{0.5}\) . (GaAs and GaP band gaps are 1.43 \(\mathrm{eV}\) and 2.26 \(\mathrm{eV}\) , respectively.) What wavelength of light does this correspond to?

Red light-emitting diodes are made from GaAs and GaP solid solutions, GaP \(_{x} A s_{1-x}(\) see Exercise 12.79\() .\) The original red LEDs emitted light with a wavelength of 660 nm. If we assume that the band gap varies linearly with composition between \(x=0\) and \(x=1,\) estimate the composition (the value of \(x\) ) that is used in these LEDs.

(a) What is a monomer? (b) Which of these molecules can be used as a monomer: ethanol, ethene (also called ethylene), methane?

The molecular formula of \(n\) -decane \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{8} \mathrm{CH}_{3} . \mathrm{De}-\) cane is not considered a polymer, whereas polyethylene is. What is the distinction?

State whether each of these numbers is a reasonable value for a polymer's molecular weight: 100 amu, \(10,000\) amu, \(100,000\) amu, \(1,000,000\) amu?

Indicate whether the following statement is true or false: For an addition polymerization, there are no by-products of the reaction (assuming 100\(\%\) yield).

An ester is a compound formed by a condensation reaction between a carboxylic acid and an alcohol that eliminates a water molecule. Read the discussion of esters in Section 24.4 and then give. an example of a reaction forming an ester. How might this kind of reaction be extended to form a polymer (a polyester)?

Write a balanced chemical equation for the formation of polymer via a condensation reaction from the monomers succinic acid (HOOCCH \(_{2} \mathrm{CH}_{2} \mathrm{COOH}\) ) and ethylenediamine \(\left(\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)\)

An addition polymerization forms the polymer originally used as Saran" wrap. It has the following structure \(+\mathrm{CCl}_{2}-\mathrm{CH}_{2} \mathrm{J}_{n} .\) Draw the structure of the monomer.

Write the chemical equation that represents the formation of $$ \begin{array}{l}{\text { (a) polychloroprene from chloroprene (polychloroprene is }} \\ {\text { used in highway-pavement seals, expansion joints, con- }} \\\ {\text { veyor belts, and wire and cable jackets) }}\end{array} $$ $$ \begin{array}{c}{\mathrm{CH}_{2}=\mathrm{CH}-\underset{\mathrm{C}}{\mathrm{C}=\mathrm{CH}_{2}}} \\\ {\text { Chloroprene }}\end{array} $$ $$ \begin{array}{l}{\text { (b) polyacrylonitrile from acrylonitrile (polyacrylonitrile }} \\ {\text { is used in home furnishings, craft yarns, clothing, and }} \\ {\text { many other items). }}\end{array} $$ $$ \begin{array}{c}{\mathrm{CH}_{2}=\mathrm{CH}} \\ {\mathrm{I}} \\ {\text { Acrylonitrile }}\end{array} $$

(a) What molecular features make a polymer flexible? (b) If you cross-link a polymer, is it more flexible or less flexible than it was before?

What molecular structural features cause high-density polyethylene to be denser than low-density polyethylene?

If you want to make a polymer for plastic wrap, should you strive to make a polymer that has a high or low degree of crystallinity?

Indicate whether each statement is true or false: $$ \begin{array}{l}{\text { (a) Elastomers are rubbery solids. }} \\ {\text { (b) Thermosets cannot be reshaped. }} \\ {\text { (c) Thermoplastic polymers can be recycled. }}\end{array} $$

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? (b) Would appropriately sized Cds quantum dots be able to emit blue light? (c) What about red light?

Indicate whether each statement is true or false: $$ \begin{array}{l}{\text { (a) The band gap of a semiconductor decreases as the parti- }} \\ {\text { cle size decreases in the } 1-10 \text { -nm range. }} \\\ {\text { (b) The light that is emitted from a semiconductor, upon }} \\\ {\text { external stimulation, becomes longer in wavelength as }} \\ {\text { the particle size of the semiconductor decreases. }}\end{array} $$

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.

An ideal quantum dot for use in TVs does not contain any cadmium due to concerns about disposal. One potential material for this purpose is InP, which adopts the zinc blende \((\mathrm{ZnS})\) structure (face-centered cubic). The unit cell edge length is 5.869 \&. (a) If the quantum dot is shaped like a cube, how many of each type of atom are there in a cubic crystal with an edge length of 3.00 \(\mathrm{nm} ? 5.00 \mathrm{nm}\) ? (b) If one of the nanoparticles in part (a) emits blue light and the other emits orange light, which color is emitted by the crystal with the 3.00 -nm edge length? With the 5.00 -nm edge length?

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 \(s p^{2}\) hybridized in graphene but \(s p^{3}\) hybridized in graphite.

What evidence supports the notion that buckyballs are actual molecules and not extended materials? $$ \begin{array}{l}{\text { (a) Buckyballs are made of carbon. }} \\ {\text { (b) Buckyballs have a well-defined atomic structure and }} \\ {\text { molecular weight. }} \\ {\text { (c) Buckyballs have a well-defined melting point. }} \\ {\text { (a) Buckyballs are semiconductors. }} \\ {\text { (e) More than one of the previous choices. }}\end{array} $$

Selected chlorides have the following melting points: NaCl \(\left(801^{\circ} \mathrm{C}\right), \mathrm{MgCl}_{2}\left(714^{\circ} \mathrm{C}\right), \mathrm{PCl}_{3}\left(-94^{\circ} \mathrm{C}\right), \mathrm{SCl}_{2}\left(-121^{\circ} \mathrm{C}\right)\) $$ \begin{array}{l}{\text { (a) For each compound, indicate what type its solid }} \\ {\text { form is (molecular, metallic, ionic, or covalent-network). }} \\\ {\text { (b) Predict which of the following compounds has a }} \\ {\text { higher melting point: } \mathrm{CaCl}_{2} \text { or } \mathrm{SiCl}_{4} \text { . }}\end{array} $$

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 \(90^{\circ} .\) What kind of primitive lattice have you made?

Pure iron crystallizes in a body-centered cubic structure, but small amounts of impurities can stabilize a face-centered 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.

Cinnabar (HgS) was utilized as a pigment known as ver-million. 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?

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 \(1 \times 10^{-19} \mathrm{J}\) . 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. (a) How many copper atoms are in a piece of copper metal in the shape of a cube with edge length 0.5 \(\mathrm{mm} ?\) The density of copper is 8.96 \(\mathrm{g} / \mathrm{cm}^{3} .\) (b) Determine the average spacing in J between energy levels in the copper metal in part (a).(c) Is this spacing larger, substantially smaller, or about the same as the 1 \(\times 10^{-18}\) J separation between energy levels in a hydrogen atom?

Unlike metals, semiconductors increase their conductivity as you heat them (up to a point). Suggest an explanation.

Sodium oxide \(\left(\mathrm{Na}_{2} \mathrm{O}\right)\) adopts a cubic structure with Na atoms represented by green spheres and O atoms by red spheres. $$ \begin{array}{l}{\text { (a) How many atoms of each type are there in the unit cell? }} \\ {\text { (b) Determine the coordination number and describe the }} \\ {\text { shape of the coordination environment for the sodium }} \\\ {\text { ion. }} \\ {\text { (c) The unit cell edge length is } 5.550 \text { A. Determine the den- }} \\ {\text { sity of } \mathrm{Na}_{2} \text { O. }}\end{array} $$

Teflon is a polymer formed by the polymerization of \(\mathrm{F}_{2} \mathrm{C}=\mathrm{CF}_{2}\) . (a) Draw the structure of a section of this polymer. (b) What type of polymerization reaction is required to form Teflon?

Explain why X rays can be used to measure atomic distances in crystals but visible light cannot be used for this purpose.

In their study of X-ray diffraction, William and Lawrence Bragg determined that the relationship among the wavelength of the radiation \((\lambda),\) the angle at which the raveation is diffracted \((\theta),\) and the distance between planes of atoms in the crystal that cause the diffraction \((d)\) is given by \(n \lambda=2 d \sin \theta . X\) rays from a copper \(X\) -ray tube that have a wavelength of 1.54\(\hat{\mathrm{A}}\) 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).

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?

(a) What are the \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles in diamond? (b) What are they in graphite (in one sheet)? (c) What atomic orbitals are involved in the stacking of graphite sheets with each other?

One method to synthesize ionic solids is by the heating of two reactants at high temperatures. Consider the reaction of FeO with \(\mathrm{TiO}_{2}\) to form FeTiO \(_{3} .\) Determine the amount of each of the two reactants to prepare 2.500 \(\mathrm{g}\) FeTiO \(_{3},\) assuming the reaction goes to completion. (a) Write a balanced chemical reaction. (b) Calculate the formula weight of FeTiO_{3} . (c) Determine the moles of FeTiO_{3} . (d) Determine moles and mass (g) of FeO required. (e) Determine moles and mass (g) of TiO_ \(_{2}\) required.