13. Liquids, Solids & Intermolecular Forces

Two solids are shown below. One is a semiconductor and one is an insulator. Which one is which? Explain your reasoning.

Diffraction of X rays with l = 131.5 pm occurred at an angle of 25.5 degrees by a crystal of aluminum. Assuming first-order diffraction, what is the interplanar spacing in aluminum? (LO 12.2) (a) 76.4 pm (b) 183.1 pm (c) 305.5 pm (d) 152.7 pm

For each of the two-dimensional structures shown here (a) draw the unit cell (i)

(ii)

Which arrangement of cations (yellow) and anions (blue) in a lattice is the more stable? Explain your reasoning. (a)

(b)

Which of these molecular fragments would you expect to be more likely to give rise to electrical conductivity? Explain your reasoning. (a)

(b)

The following diagrams represent the electron population of molecular orbitals for different substances. What diagram corresponds to magnesium oxide, germanium, and tin? (LO 12.8)

(a) Diagram 1 = tin, diagram 2 = magnesium oxide, diagram 3 = germanium (b) Diagram 1 = germanium, diagram 2 = magnesium oxide, diagram 3 = tin (c) Diagram 1 = germanium, diagram 2 = tin, diagram 3 = magnesium oxide (d) Diagram 1 = magnesium oxide, diagram 2 = tin, diagram 3 = germanium

The electronic structure of a doped semiconductor is shown here. (c) Which region of the diagram represents the band gap?

The molecular orbital diagram of a doped semiconductor is shown below. If the semiconductor is silicon, does the diagram represent n-type or p-type doping and which of the following elements could be dopant? (LO 12.9)

(a) n-type, As (b) n-type, Ga (c) p-type, As (d) p-type, Ga

Shown here are cartoons of two different polymers. Which one would have the higher melting point?

The accompanying image shows photoluminescence from four different samples of CdTe nanocrystals, each embedded in a polymer matrix. The photoluminescence occurs because the samples are being irradiated by a UV light source. The nanocrystals in each vial have different average sizes. The sizes are 4.0, 3.5, 3.2, and 2.8 nm. (a) Which vial contains the 4.0-nm nanocrystals?

If the band-gap energy of a gallium phosphide (GaP) semiconductor is 222 kJ/mol, calculate the wavelength of light emitted in a GaP light-emitting diode (LED). (LO 12.11) (a) 186 nm (b) 245 nm (c) 539 nm (d) 854 nm

A superconductor is a material that loses all electrical resistance below a characteristic temperature called the superconducting transition temperature. Which graph represents the behavior of a superconductor? (LO 12.13) (a)

(b)

(c)

(d)

(b) Now draw a picture that represents an amorphous solid at the atomic level.

(a) Draw a picture that represents a crystalline solid at the atomic level.

Two patterns of packing for two different circles of the same size are shown here. For each structure (b) determine the angle between the lattice vectors, g, and determine whether the lattice vectors are of the same length or of different lengths; (i)

(ii)

The following diagrams show the electron populations of the bands of MO energy levels for four different materials:

. (c) Tell whether the conductivity of each material increases or decreases when the temperature increases.

The following diagrams show the electron populations of the bands of MO energy levels for four different materials: (a) Classify each material as an insulator, a semiconductor, or a conducting metal.

Two patterns of packing two different circles of the same size are shown here. For each structure (c) determine the type of two-dimensional lattice (from Figure 12.4). (i)

(ii)

The following diagram represents the electron population of the bands of MO energy levels for elemental silicon:

(a) Identify the valence band, conduction band, and band gap.

Diagrams (1) and (2) are energy-level diagrams for two different LEDs. One LED emits red light, and the other emits blue light. Which one emits red, and which blue? Explain. (1)

(2)

List the four main classes of crystalline solids, and give a specific example of each.

An X-ray beam with l = 154 pm incident on the surface of a crystal produced a maximum reflection at an angle of u = 28.3°. Assuming n = 1, calculate the separation between layers of atoms in the crystal.

An increase in temperature causes most metals to undergo thermal expansion, which means the volume of the metal increases upon heating. How does thermal expansion affect the unit cell length? What is the effect of an increase in temperature on the density of a metal?

Which solid would you expect to have little or no band gap? a. Zn(s) b. Si(s) c. As(s)

Which solid would you expect to have the largest band gap? a. As(s) b. Sb(s) c. Bi(s)

How many molecular orbitals are present in the conduction band of a lithium crystal with a mass of 11.2 g?

A substance has a band gap of 6.9 eV at 273 K. Is this substance best classified as an insulator, a semiconductor, or a metal?

Indicate if each solid forms an n-type or a p-type semiconductor. b. germanium doped with antimony

Does a photon of red light with a frequency of 4.29 * 1014 Hz have sufficient energy to promote an electron from the valence band to the conduction band in a sample of silicon (the band gap in silicon is 1.11 eV)?

For each of the following pairs of semiconductors, which one will have the larger band gap: (a) CdS or CdTe?

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

Cadmium telluride is an important material for solar cells. (d) With respect to silicon, does CdTe absorb a larger or smaller portion of the solar spectrum?

Cadmium telluride is an important material for solar cells. (b) What wavelength of light would a photon of this energy correspond to?

Tell what is meant by each of the following terms. (c) Band gap

Draw the bands of MO energy levels and the electron population for: (a) A semiconductor (b) An electrical insulator Explain why a semiconductor has the higher electrical conductivity.

Classify the following semiconductors as n-type or p-type. (a) Si doped with In (b) Ge doped with Sb (c) Gray Sn doped with As

X-ray diffractometers often use metals that have had their core electrons excited as a source of X-rays. Consider the 2p ¡ 1s transition for copper, which is called the Ka transition. Calculate the wavelength of X-rays (in Å) given off by the Ka transition if the energy given off by a mole of copper atoms is 7.77 * 105 kJ.(1Å = 10-10 m)

Arrange the following materials in order of increasing electrical conductivity. (a) Cu (b) Al2O3 (c) Fe (d) Pure Ge (e) Ge doped with In

What are the main differences between an LED and a photovoltaic cell?

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. (c) What about red light?

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. (b) Would appropriately sized CdS quantum dots be able to emit blue light?

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?

Considering only electronegativity, rank the LED semiconductors made of solid solutions in order of increasing bandgap energy. Al0.40Ga0.60As, Al0.25Ga0.75As, Al0.05Ga0.95As

Gallium arsenide, a material used to manufacture laser printers and compact disc players, has a band gap of 130 kJ/mol. Is GaAs a metallic conductor, a semiconductor, or an electrical insulator? With what group 4A element is GaAs isoelectronic? (Isoelectronic substances have the same number of electrons.)

We will see in Chapter 12 that semiconductors are materials that conduct electricity better than nonmetals but not as well as metals. The only two elements in the periodic table that are technologically useful semiconductors are silicon and germanium. Integrated circuits in computer chips today are based on silicon. Compound semiconductors are also used in the electronics industry. Examples are gallium arsenide, GaAs; gallium phosphide, GaP; cadmium sulfide, CdS; and cadmium selenide, CdSe. (b) Workers in the semiconductor industry refer to 'II–VI' and 'III–V' materials, using Roman numerals. Can you identify which compound semiconductors are II–VI and which are III–V?

We will see in Chapter 12 that semiconductors are materials that conduct electricity better than nonmetals but not as well as metals. The only two elements in the periodic table that are technologically useful semiconductors are silicon and germanium. Integrated circuits in computer chips today are based on silicon. Compound semiconductors are also used in the electronics industry. Examples are gallium arsenide, GaAs; gallium phosphide, GaP; cadmium sulfide, CdS; and cadmium selenide, CdSe. (a) What is the relationship between the compound semiconductors' compositions and the positions of their elements on the periodic table relative to Si and Ge?

Looking at Figure 12.27 identify the coordination numbers of the Cu, Y, and Ba atoms.

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 * 10–19 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. (b) Determine the average spacing in J between energy levels in the copper metal in part (a).

In their study of X-ray diffraction, William and Lawrence Bragg determined that the relationship among the wavelength of the radiation 1l2, the angle at which the radiation is diffracted 1u2, and the distance between planes of atoms in the crystal that cause the diffraction (d) is given by nl = 2d sin u. X rays from a copper X-ray tube that have a wavelength of 1.54 Å 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).

Germanium has the same structure as silicon, but the unit cell size is different because Ge and Si atoms are not the same size. If you were to repeat the experiment described in the previous problem but replace the Si crystal with a Ge crystal, would you expect the X rays to be diffracted at a larger or smaller angle u?

Europium(II) oxide is a semiconductor with a band gap of 108 kJ/mol. Below 69 K, it is also ferromagnetic, meaning all the unpaired electrons on europium are aligned in the same direction. How many f electrons are present on each europium ion in EuO? (In lanthanide ions the 4f orbitals are lower in energy than the 6s orbitals.)

The mineral wustite is a nonstoichiometric iron oxide with the empirical formula FexO, where x is a number slightly less than 1. Wustite can be regarded as an FeO in which some of the Fe sites are vacant. It has a density of 5.75 g>cm3, a cubic unit cell with an edge length of 431 pm, and a facecentered cubic arrangement of oxygen atoms. (d) Using X rays with a wavelength of 70.93 pm, at what angle would third-order diffraction be observed from the planes of atoms that coincide with the faces of the unit cells? Third-order diffraction means that the value of n in the Bragg equation is equal to 3.

Which of these molecular fragments would you expect to be more likely to give rise to electrical conductivity?