Chapter 12

If you want to dope GaAs to make a p-type semiconductor with an element to replace As, which element(s) would you pick?

The semiconductor gallium nitride (GaN) has a band gap of \(3.4 \mathrm{eV}\). What wavelength of light would be emitted from an LED made from GaN? What region of the electromagnetic spectrum is this?

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?

Orange light-emitting diodes are made from GaAs and GaP solid solutions, \(\mathrm{GaP}_{x} \mathrm{As}_{1-x}\) (see Exercise 12.79). The original orange LEDs emitted light with a wavelength of \(590 \mathrm{nm}\). 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: ethanol, 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: \(100 \mathrm{u}, 10,000 \mathrm{u},\) \(100,000 \mathrm{u}, 1,000,000 \mathrm{u} ?\)

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 a polymer via a condensation reaction from the monomers 1,4-phenylenediamine \(\left(\mathrm{H}_{2} \mathrm{NC}_{6} \mathrm{H}_{4} \mathrm{NH}_{2}\right)\) and terephthalic acid \(\left(\mathrm{HOOCC}_{6} \mathrm{H}_{4} \mathrm{COOH}\right)\)

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

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).

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 R3), draw the peptide that results from their condensation reactions. (c) The order in which the 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 \({ }^{\prime \prime} \mathrm{N}\) 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 "N terminus" and "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?

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.

GaP has a band gap of \(2.26 \mathrm{eV}\). If GaP is illuminated with ultraviolet light, it emits light equal to the band gap energy. (a) What color is the emitted light? (b) Would appropriately sized GaP 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 \(1-10-\mathrm{nm}\) 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.

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 408 pm (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}$.

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 (ZnS) structure (face-centered cubic). The unit cell edge length is \(586.9 \mathrm{pm} .(\mathbf{a})\) 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 \(3.00 \mathrm{nm} ? 5.00 \mathrm{nm} ?(\mathbf{b})\) 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 \(3.00-\mathrm{nm}\) edge length? With the \(5.00-\mathrm{nm}\) 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. \((\mathbf{e})\) 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.

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

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?

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 (a) NaF, (b) Ag, (c) Fe, (d) \(\mathrm{CsCl}\) structure types possess: (e) \(\mathrm{ScF}_{3} ?\)

Greenockite (CdS) was utilized as a pigment known as vermillion. It has a band gap of \(2.6 \mathrm{eV}\) near room temperature for the bulk solid. What wavelength of light (in \(\mathrm{nm}\) ) 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 \(\mathrm{Na}\) atoms represented by green spheres and \(\mathrm{O}\) atoms by red spheres. (a) How many atoms of each type are there in the unit cell? (b) Determine the coordination number and describe the shape of the coordination environment for the sodium ion. (c) The unit cell edge length is \(555 \mathrm{pm}\). Determine the density of \(\mathrm{Na}_{2} \mathrm{O}\)

Teflon is a polymer formed by the polymerization of \(\mathrm{F}_{2} \mathrm{C}=\mathrm{CF}_{2} .(\mathbf{a})\) 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 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 \(154 \mathrm{pm}\) 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?

The karat scale used to describe gold alloys is based on mass percentages. (a) If an alloy is formed that is \(75 \mathrm{~mol} \%\) silver and \(25 \mathrm{~mol} \%\) gold, what is the karat number of the alloy? Use Figure 12.18 to estimate the color of this alloy. (b) If an alloy is formed that is 75 mol\% copper and 25 mol\% gold, what is the karat number of the alloy? What is the color of this alloy?

(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 \(543 \mathrm{pm}\) 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?

One method to synthesize ionic solids is by the heating of two reactants at high temperatures. Consider the reaction of \(\mathrm{MgO}\) with \(\mathrm{TiO}_{2}\) to form \(\mathrm{MgTiO}_{3}\). Determine the amount of each of the two reactants to prepare \(3.250 \mathrm{~g} \mathrm{MgTiO}_{3}\), assuming the reaction goes to completion. (a) Write a balanced chemical reaction. (b) Calculate the formula weight of \(\mathrm{MgTiO}_{3}\). (c) Determine the moles of \(\mathrm{MgTiO}_{3}\). (d) Determine moles and mass (g) of MgO required. (e) Determine moles and mass (g) of \(\mathrm{TiO}_{2}\) required.

Look up the diameter of a silicon atom, in pm. The latest semiconductor chips have fabricated lines as small as \(14 \mathrm{nm}\). How many silicon atoms does this correspond to?