Chapter 12

GaAs and GaP \(\left(E_{\mathrm{g}}=2.26 \mathrm{eV}\right)\) make solid solutions that have the same crystal structure as the parent materials, with As and Prandomly distributed throughout the crystal. \(\mathrm{GaP}_{x}\) 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 \(\mathrm{GaP}_{0.5} \mathrm{As}_{0.5} .\) What wavelength of light does this correspond to?

Red light-emitting diodes are made from GaAs and GaP solid solutions, \(\mathrm{GaP}_{x}\) As \(_{1-x}\) (see Exercise 12.73 ). The original red LEDs emitted light with a wavelength of \(660 \mathrm{nm}\). 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.

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

An ester is a compound formed by a condensation reaction between a carboxylic acid and an alcohol. 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 chemical equation for formation of a polymer via a condensation reaction from the monomers succinic acid \(\quad\left(\mathrm{HOOCCH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\right) \quad\) and \(\quad\) ethylenediamine \(\left(\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\right)\)

Write the chemical equation that represents the formation of (a) polychloroprene from chloroprene (polychloroprene is used in highway-pavement seals, expansion joints, conveyor belts, and wire and cable jackets); (b) polyacrylonitrile from acrylonitrile (polyacrylonitrile is used in home furnishings, craft yarns, clothing, and many other items).

What molecular features make a polymer flexible? Explain how cross-linking affects the chemical and physical properties of the polymer.

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

Are high molecular weights and a high degree of crystallinity always desirable properties of a polymer? Explain.

Briefly describe each of the following: (a) elastomer, (b) thermoplastic, (c) thermosetting plastic.

Explain why "bands" may not be the most accurate description of bonding in a solid when the solid has nanoscale dimensions.

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?

True or false: (a) The band gap of a semiconductor decreases as the particle size decreases in the \(1-10-\mathrm{nm}\) 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.

Gold adopts a face-centered cubic structure with a unit cell edge of \(4.08 \AA\) (Figure 12.11 ). How many gold atoms are there in a sphere that is \(20 \mathrm{nm}\) in diameter? Recall that the volume of a sphere is \(\frac{4}{3} \pi r^{3}\).

Cadmium telluride, CdTe, takes the zinc blende structure (Figure 12.26 ) with a unit cell edge length of \(6.49 \AA\). There are four cadmium atoms and four tellurium atoms per unit cell. How many of each type of atom are there in a cubic crystal with an edge length of \(5.00 \mathrm{nm} ?\)

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.

What type of lattice-primitive cubic, body-centered cubic, or face-centered cubic-does each of the following structure types possess: (a) \(\mathrm{CsCl},(\mathbf{b}) \mathrm{Au},\) (c) \(\mathrm{NaCl}\) (d) Po, (e) \(\mathrm{ZnS?}\) ?

Tin exists in two allotropic forms: Gray tin has a diamond structure, and white tin has a close-packed structure. One of these allotropic forms is a semiconductor with a small band gap while the other is a metal. Which one is which? Which form would you expect to have the longer \(\mathrm{Sn}-\mathrm{Sn}\) bond distance?

The electrical conductivity of titanium is approximately 2500 times greater than that of silicon. Titanium has a hexagonal close-packed structure, and silicon has the diamond structure. Explain how the structures relate to the relative electrical conductivities of the elements.

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

Hydrogen bonding between polyamide chains plays an important role in determining the properties of a nylon such as nylon 6,6 (Table 12.5 ). Draw the structural formulas for two adjacent chains of nylon 6,6 and show where hydrogenbonding interactions could occur between them.

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 radiation 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 \(1.54 \AA\) 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).

The valence band of a semiconductor is made up of bonding molecular orbitals and the conduction band of antibonding molecular orbitals. (a) Given this fact would you expect n-type doping to strengthen or weaken the bonds in a semiconductor? (b) Would you expect p-type doping to strengthen or weaken the bonds in a semiconductor?

Spinel is a mineral that contains \(37.9 \%\) Al, \(17.1 \% \mathrm{Mg}\), and \(45.0 \% \mathrm{O},\) by mass, and has a density of \(3.57 \mathrm{~g} / \mathrm{cm}^{3} .\) The unit cell is cubic with an edge length of \(8.09 \AA\). How many atoms of each type are in the unit cell?

(a) What are the \(\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles in diamond? (b) What are they in graphite?