13. Liquids, Solids & Intermolecular Forces

Crystalline Solids

Gen Chem II - Lec 6 - Crystal Lattices of Solid Structures

Doing Solids: Crash Course Chemistry #33

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) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/08409e57d3ae49cf-1671477306921.jpg" alt="" />
(2) <img src="" alt="" />

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) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/347a2d9b7a887292-1665593658692.jpg" alt="" />
(ii) <img src="" alt="" />

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

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

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?

Crystalline Solids Concept 2

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

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?

For each of the two-dimensional structures shown here
(a) draw the unit cell
(i) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/7ad0d0bcd1b08400-1665591562984.jpg" alt="" />
(ii) <img src="" alt="" />

Crystal lattice and unit cell

Shown here are cartoons of two different polymers. Which one would have the higher melting point?
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/037a37612b8123b3-1665754826068.jpg" alt="" />

Crystalline Solids Example 1

An LED produces light only when the n- and p-type 
semiconductors are connected to the proper terminals of a 
battery. Explain why no light is produced if you reverse the 
battery connections.

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)
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/5ab2b16b4306c2a3-1671223063443.jpg" alt="" />
(a) n-type, As (b) n-type, Ga 
(c) p-type, As (d) p-type, Ga

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).

Which of these molecular fragments would you expect to
be more likely to give rise to electrical conductivity? Explain
your reasoning.
(a) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/3e0dd288a8a3859c-1665592576362.jpg" alt="" /> 
(b) <img src="" alt="" />

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) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/9af34adf73fb61db-1665592950759.jpg" alt="" />
(ii) <img src="" alt="" />

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)?

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?

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

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.)

AMORPHOUS AND CRYSTALLINE SOLIDS

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).

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?

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?

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

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) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/02ef7624266596ed-1671227226561.jpg" alt="" />
(b) <img src="" alt="" />
(c) <img src="" alt="" />
(d) <img src="" alt="" />

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?

The electronic structure of a doped semiconductor is
shown here. (c) Which region of the diagram represents the band gap?
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/70ce82c685410f4e-1665679011594.jpg" alt="" />

Looking at Figure 12.27 identify the coordination numbers 
of the Cu, Y, and Ba atoms.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/b7b3173c78c02039-1671551646708.jpg" alt="" />

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?

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?

Which arrangement of cations (yellow) and anions (blue)
in a lattice is the more stable? Explain your reasoning.
(a) <img src="https://lightcat-files.s3.amazonaws.com/problem_images/eaf4c31a46a542db-1665591816574.jpg" alt="" />
(b) <img src="" alt="" />

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

The Structure of Crystalline Solids

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

Crystalline Solids Concept 1

Two solids are shown below. One is a semiconductor and
one is an insulator. Which one is which? Explain your reasoning.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/961853e5b02def52-1668537110180.jpg" alt="" />

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

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.

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

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 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.

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

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

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?

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.

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)

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

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?

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

The following diagrams show the electron populations of 
the bands of MO energy levels for four different materials: 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/c0090e2633ffe716-1671472541540.jpg" alt="" />. 
(c) Tell whether the conductivity of each material increases 
or decreases when the temperature increases.

The following diagram represents the electron population of
the bands of MO energy levels for elemental silicon:
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/2af496ef6586d12b-1671474091364.jpg" alt="" />
(a) Identify the valence band, conduction band, and 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.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/829b70d967efe061-1671545672368.jpg" alt="" />

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

As complexity increases, coordination number and packing efficiency increase as well.

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)
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/015c2fa4836811c2-1671219455458.jpg" alt="" />
(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

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?

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

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1. Intro to General Chemistry

2. Atoms & Elements

3. Chemical Reactions

4. BONUS: Lab Techniques and Procedures

5. BONUS: Mathematical Operations and Functions

6. Chemical Quantities & Aqueous Reactions

7. Gases

8. Thermochemistry

9. Quantum Mechanics

10. Periodic Properties of the Elements

11. Bonding & Molecular Structure

12. Molecular Shapes & Valence Bond Theory

14. Solutions

15. Chemical Kinetics

16. Chemical Equilibrium

17. Acid and Base Equilibrium

18. Aqueous Equilibrium

19. Chemical Thermodynamics

20. Electrochemistry

21. Nuclear Chemistry

22. Organic Chemistry

23. Chemistry of the Nonmetals

24. Transition Metals and Coordination Compounds

[BOOK CHEM] Clutch Version

Body Centered Cubic Unit Cell

Body Centered Cubic Unit Cell contains 2 atoms total.

Phase Diagrams

Phase&nbsp;Diagrams show&nbsp;what&nbsp;effect&nbsp;temperature and pressure have&nbsp;on a pure substance in a closed system without any air.

Intermolecular Forces and Physical Properties

Intermolecular forces influence physical properties. &nbsp;We will look at direct and indirect relationships.

Face Centered Cubic Unit Cell

Face Centered Cubic Unit Cell contains 4 atoms in total.

Heating and Cooling Curves

Heating and Cooling Curves represent amount of heat (q) absorbed or released by a substance during phase changes.

Clausius-Clapeyron Equation

The Clausius-Clapeyron Equation establishes a quantitative relationship between vapor pressure and temperature.&nbsp;

Molecular Polarity

Polarity of chemical bonds happen in molecules when there is an unequal sharing of electrons.&nbsp;

Intermolecular Forces

Intramolecular Forces are the bonding forces within a molecule. Intermolecular Forces are the attractive forces between 2 molecules.

Simple Cubic Unit Cell

Simple Cubic Unit Cell is the least complex&nbsp;cubic unit cell and contains only 1 atom.

Atomic, Ionic, and Molecular Solids

<div dir="auto"><div contenteditable="true"dir="auto"spellcheck="true">Crystalline solids represent structures with well-organized patterns and shapes. Amorphous solids represent structures that lack an organized pattern or shape.&nbsp;</div></div>

Crystalline Solids are composed of unit cells, crystal lattice and lattice point.