Chapter 12

The first LEDs were made from GaAs, which has a band gap of \(1.43 \mathrm{eV}\). 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 \(\mathrm{As}\) and \(\mathrm{P}\) randomly distributed throughout the crystal. \(\mathrm{GaP}_{x} \mathrm{~A} s_{1-x}\) 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 \(\mathrm{GaP}_{0.5} \mathrm{As}_{05}\). (See the previous two exercises for GaAs and GaP band gaps.) What wavelength of light does this correspond to?

Red light-emitting diodes are made from GaAs and GaP solid solutions, \(\mathrm{GaP}_{x} \mathrm{As}_{1-x}\) (see Exercise 12.75). 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.

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

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?

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

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

Proteins are naturally occurring polymers formed by condensation reactions of amino acids, which have the general structure In this structure, \(-\mathrm{R}\) represents \(-\mathrm{H},-\mathrm{CH}_{3}\), or another group of atoms; there are 20 different natural amino acids, and each has one of 20 different \(R\) groups. (a) Draw the general structure of a protein formed by condensation polymerization of the generic amino acid shown here. (b) When only a few amino acids react to make a chain, the product is called a "peptide" rather than a protein; only when there are 50 amino acids or more in the chain would the molecule be called a protein. For three amino acids (distinguished by having three different \(R\) groups, R1, R2, and \(R 3\) ), draw the peptide that results from their condensation reactions. (c) The order in which the \(\mathrm{R}\) groups exist in a peptide or protein has a huge influence on its biological activity. To distinguish different peptides and proteins, chemists call the first amino acid the one at the " \(\mathrm{N}\) terminus" and the last one the one at the "C terminus." From your drawing in part (b) you should be able to figure out what " \(\mathrm{N}\) terminus" and " \(\mathrm{C}\) terminus" mean. How many different peptides can be made from your three different amino acids?

(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? \(12.90\) Indicate whether each statement is true or false: (a) Elastomers are rubbery solids. (b) Thermosets cannot be reshaped. (c) Thermoplastic polymers can be recycled.

Indicate whether each statement is true or false: (a) Elastomers are rubbery solids. (b) Thermosets cannot be reshaped. (c) Thermoplastic polymers can be recycled.

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

\mathrm{CdS}\( has a band gap of \)2.4 \mathrm{eV}\(. If large crystals of \)\mathrm{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: (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.

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.

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, adopts the zinc blende structure 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 \(5.00 \mathrm{~nm}\) ?

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? (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.

A face-centered tetragonal lattice is not one of the 14 threedimensional lattices. Show that a face-centered tetragonal unit cell can be redefined as a body-centered tetragonal lattice with a smaller unit cell.

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.

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

Tin exists in two allotropic forms: Gray tin has the 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. (a) Which one is which? (b) Which form would you expect to have the longer \(\mathrm{Sn}-\mathrm{Sn}\) bond distance?

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

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 \(\mathrm{X}\) 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 \(n \lambda=2 d \sin \theta\). \(\mathrm{X}\) rays from a copper \(\mathrm{X}\)-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).

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?

Spinel is a mineral that contains \(37.9 \% \mathrm{Al}, 17.1 \% \mathrm{Mg}\), 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 (in one sheet)? (c) What atomic orbitals are involved in the stacking of graphite sheets with each other?

Silicon has the diamond structure with a unit cell edge length of \(5.43 \AA\) and eight atoms per unit cell. (a) How many silicon atoms are there in \(1 \mathrm{~cm}^{3}\) of material? (b) Suppose you dope that \(1 \mathrm{~cm}^{3}\) 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?

\(\mathrm{KCl}\) has the same structure as \(\mathrm{NaCl}\). The length of the unit cell is \(6.28 \AA \AA\). The density of \(\mathrm{KCl}\) is \(1.984 \mathrm{~g} / \mathrm{cm}^{3}\), and its formula mass is \(74.55\) amu. Using this information, calculate Avogadro's number.

Look up the diameter of a silicon atom, in \(\hat{A}\). The latest semiconductor chips have fabricated lines as small as \(22 \mathrm{~nm}\). How many silicon atoms does this correspond to?