Chapter 6

The gold color of a certain brass is due to the absorption of light in the violet region of the spectrum, at wavelengths of \(445 \mathrm{~nm}\). To what energy separation (in joules) does that wavelength correspond?

The pink color of a certain bronze is due to the absorption of light in the blue-violet region of the spectrum, at wavelengths of \(465 \mathrm{~nm}\). To what energy separation (in joules) does that wavelength correspond?

What metal is generally added to steel to make it corrosion resistant?

How do alloys differ from the pure metals from which they are made?

What is the difference between homogeneous and heterogeneous alloys?

When iron surfaces are exposed to ammonia at high temperatures, "nitriding"-the incorporation of nitrogen into the iron lattice-occurs. The atomic radius of iron is \(124 \mathrm{pm}\). (a) Is the alloy interstitial or substitutional? Justify your answer. (b) How do you expect nitriding to change the properties of iron?

Silicon can be doped with small amounts of phosphorus to create a semiconductor used in transistors. (a) Is the alloy interstitial or substitutional? Justify your answer. (b) How do you expect the properties of the doped material to differ from those of pure silicon?

Calculate the relative number of atoms of each element contained in each of the following alloys: (a) coinage cupronickel, which is \(25 \%\) Ni by mass in copper; (b) a type of pewter that is about \(7 \%\) antimony and \(3 \%\) copper by mass in tin.

Compare the hybridization and structure of carbon in diamond and graphite. How do these features explain the physical properties of the two allotropes?

Iron pyrite \(\left(\mathrm{FeS}_{2}\right)\) is known as Fool's Gold because of its resemblance to gold metal. However, it can easily be distinguished from gold by the difference in their densities. The density of gold is \(19.28 \mathrm{~g}^{\mathrm{cm}} \mathrm{cm}^{3}\) and that of Fool's Gold is \(5.01 \mathrm{~g}^{\prime} \mathrm{cm}^{3}\). What volume of Fool's Gold would have the same mass as a \(4.0 \mathrm{~cm}^{3}\) piece of gold?

Mica with a density of \(1.5 \mathrm{~g}^{+} \mathrm{cm}^{3}\) can be expanded into vermiculite, which is used as a low-density soil amendment. The vermiculite used in soils has an average density of \(0.10 \mathrm{~g}^{\circ} \mathrm{cm}^{3}\). Estimate the volume of the vermiculite obtained by expanding \(12.0 \mathrm{~cm}^{3}\) of mica.

Write a Lewis structure for the orthosilicate anion, \(\mathrm{SiO}_{4}{\underline{\phantom{xx}}}^{4-}\), and deduce the formal charges and oxidation numbers of the atoms. Use the VSEPR model to predict the shape of the ion.

Use the VSEPR model to estimate the \(\mathrm{Si}-\mathrm{O}-\mathrm{Si}\) bond angle in silica.

Describe the structures of a silicate in which the silicate tetrahedra share (a) one \(\mathrm{O}\) atom; (b) two \(\mathrm{O}\) atoms.

What is the empirical formula of a potassium silicate in which the silicate tetrahedra share (a) two \(\mathrm{O}\) atoms and form a chain or (b) three \(\mathrm{O}\) atoms and form a sheet? In each case, there are single negative charges on the unshared \(\mathrm{O}\) atoms.

What is the oxidation number of (a) phosphorus in \(\mathrm{Li}_{7} \mathrm{P}_{3} \mathrm{~S}_{11}\), which forms in some ceramic electrolytes; (b) titanium in \(\mathrm{BaTiO}_{3}\) ?

Assuming that the oxidation number of aluminum is \(+3\) in both compounds, what is the oxidation number of silicon in (a) clay, \(\mathrm{Al}_{2} \mathrm{Si}_{2} \mathrm{O}_{5}(\mathrm{OH})_{4}\); (b) mica, \(\mathrm{KMg}_{3}\left(\mathrm{Si}_{3} \mathrm{AlO}_{10}\right)(\mathrm{OH})_{2}\) ?

How does the change in conductivity of a semiconductor differ from that of a metal as temperature is increased?

Normally, in conducting materials, we think of current as being carried by electrons as they move through a solid. In semiconductors, it is also common to talk about the current being carried by the "holes" in the valence band. (a) Explain how holes move through a solid material. (b) If, in a p-type semiconductor device, electric current is moving from left to right, in which direction will the holes be moving?

What is the resistance of an aluminum wire of length \(2.0 \mathrm{~m}\), cross- sectional area \(0.12 \mathrm{~mm}^{2}\) ? The conductivity of aluminum at room temperature is \(60.7 \mathrm{MS}^{-\mathrm{m}^{-1}}\).

Estimate the value of \(n\) for the uppermost filled level in a one-dimensional line of silver atoms of length \(1.0 \mathrm{~mm}\). Hint: Take the radius of an Ag atom as \(144 \mathrm{pm}\).

Distinguish between fluorescence and phosphorescence.

Describe how triboluminescence and fluorescence are produced.

What is the main advantage of using a fluorescent dye to trace the function of biomolecules in a living cell?

In fluorescence, how does the energy of the emitted radiation compare with the energy of the exciting radiation?

Describe the differences between diamagnetism, paramagnetism, ferromagnetism, and antiferromagnetism.

Distinguish between the "top down" and "bottom up" approaches to manufacturing nanomaterials.

An electron trapped within a nanoparticle can be approximated as a particle of mass \(m_{e}\) confined to a cubic box of side \(L\). The energy levels of the electron are $$ E=\frac{h^{2}}{8 m_{e} L^{2}}\left(n_{x}^{2}+n_{y}^{2}+n_{z}^{2}\right) $$ (a) Write expressions for the energies of the three lowest levels. Which of these levels are degenerate? For those levels that are degenerate, give the quantum numbers corresponding to each degenerate level.

Solid silicon carbide reacts with molten sodium hydroxide and oxygen gas at high temperatures to form solid \(\mathrm{Na}_{2} \mathrm{SiO}_{3}\), gaseous water, and carbon dioxide. Write a balanced equation for the reaction.

Aluminum carbide is considered a covalent carbide. However, it reacts with water as ionic carbides do, to produce solid aluminum hydroxide and methane gas, \(\mathrm{CH}_{4}\). Write a balanced equation for the reaction.

Zinc oxide is a semiconductor. Its conductivity increases when it is heated in a vacuum but decreases when it is heated in oxygen. Account for these observations.

Light-emitting diodes (LEDs) contain \(\mathrm{P}-\mathrm{n}\) junctions. The circuit in an LED is arranged so that electrons from the power source flow into the conduction band of the n-type side. As electrons continue to flow, they are pushed to the conduction band of the p-type side, which can hold more electrons. These electrons enter the conduction band of the p-type side, because they already occupy the higher-energy band in the n-type side. However, once the electrons are in the higher-energy band of the p-type side, they fall into the lower-energy band unless it is full. As these electrons make transitions to the lower-energy band, energy is released in the form of light. (a) Explain, in terms of the movement of electrons, why an LED cannot be made from the junction of pure silicon and silicon doped with phosphorus. (b) If the direction of the circuit in the LED is reversed, so that the electrons flow from the power source into the \(\mathrm{p}\)-type side of the \(\mathrm{p}-\mathrm{n}\) junction directly, where would the electrons go once they enter the \(\mathrm{p}-\mathrm{n}\) junction? (That is, indicate which bands would receive the electrons and whether the electrons would then migrate to other bands.) (c) Would you expect the LED to emit light when it is placed in the reverse circuit described in part (b)? Explain your answer.