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Chapter 43
Molecules and Solids
Molecules
Molecules are aggregates of atoms.
The arrangement of the atoms affects the properties of the material.
In the 1800s gas was well understood.
 Gas is the most random atomic arrangement.
Solids may be crystalline or amorphous.
 In crystalline solids, the atoms form a regular array.
 In an amorphous solid, the atoms do not form a regular array.
Understanding about liquids has also advanced in the 20th century.
Introduction
Molecular Bonds – Introduction
The bonding mechanisms in a molecule are fundamentally due to electric forces.
The forces are related to a potential energy function.
A stable molecule would be expected at a configuration for which the potential
energy function for the molecule has its minimum value.
Section 43.1
Features of Molecular Bonds
The force between atoms is repulsive at very small separation distances.
 This repulsion is partially electrostatic and partially due to the exclusion
principle.
 Due to the exclusion principle, some electrons in overlapping shells are
forced into higher energy states.
 The energy of the system increases as if a repulsive force existed between
the atoms.
The force between the atoms is attractive at larger distances.
Section 43.1
Potential Energy Function
The potential energy for a system of two atoms can be expressed in the form
U (r )  
A B
 m
n
r
r
 r is the internuclear separation distance.
 m and n are small integers.
 A is associated with the attractive force.
 B is associated with the repulsive force.
Section 43.1
Potential Energy Function, Graph
At large separations, the slope of the
curve is positive.
 Corresponds to a net attractive
force
At the equilibrium separation distance,
the attractive and repulsive forces just
balance.
 At this point the potential energy is
a minimum.
 The slope is zero.
Section 43.1
Molecular Bonds – Types
Simplified models of molecular bonding include:
 Ionic
 Covalent
 van der Waals
 Hydrogen
Section 43.1
Ionic Bonding
Ionic bonding occurs when two atoms combine in such a way that one or more
outer electrons are transferred from one atom to the other.
Ionic bonds are fundamentally caused by the Coulomb attraction between
oppositely charged ions.
When an electron makes a transition from the E = 0 to a negative energy state,
energy is released.
 The amount of this energy is called the electron affinity of the atom.
The dissociation energy is the amount of energy needed to break the molecular
bonds and produce neutral atoms.
Section 43.1
Ionic Bonding, NaCl Example
The graph shows the total energy of the molecule vs the internuclear distance.
The minimum energy is at the equilibrium separation distance.
Section 43.1
Ionic Bonding,final
The energy of the molecule is lower than the energy of the system of two neutral
atoms.
It is said that it is energetically favorable for the molecule to form.
 The system of two atoms can reduce its energy by transferring energy out of
the system and forming a molecule.
Section 43.1
Covalent Bonding
A covalent bond between two atoms is one in which electrons supplied by either
one or both atoms are shared by the two atoms.
Covalent bonds can be described in terms of atomic wave functions.
The example will be two hydrogen atoms forming H2.
Section 43.1
Wave Function – Two Atoms Far Apart
Each atom has a wave function.
ψ1s (r ) 
1
πao3
e  r ao
There is little overlap between the wave
functions of the two atoms when they
are far away from each other.
Section 43.1
Wave Function – Molecule
The two atoms are brought close
together.
The wave functions overlap and form
the compound wave shown.
The probability amplitude is larger
between the atoms than on either side.
Section 43.1
Covalent Bonding, Final
The probability is higher that the electrons associated with the atoms will be
located between them.
This can be modeled as if there were a fixed negative charge between the atoms,
exerting attractive Coulomb forces on both nuclei.
The result is an overall attractive force between the atoms, resulting in the
covalent bond.
Section 43.1
Van der Waals Bonding
Two neutral molecules are attracted to each other by weak electrostatic forces
called van der Waals forces.
 Atoms that do not form ionic or covalent bonds are often attracted to each
other by van der Waals forces.
The van der Waals force is due to the fact that the molecule has a charge
distribution with positive and negative centers at different positions in the
molecule.
As a result of this charge distribution, the molecule may act as an electric dipole.
Because of the dipole electric fields, two molecules can interact such that there is
an attractive force between them.
 Remember, this occurs even though the molecules are electrically neutral.
Section 43.1
Types of Van der Waals Forces
Dipole-dipole force
 An interaction between two molecules each having a permanent electric
dipole moment.
Dipole-induced dipole force
 A polar molecule having a permanent dipole moment induces a dipole
moment in a nonpolar molecule.
Dispersion force
 An attractive force occurs between two nonpolar molecules.
 The interaction results from the fact that, although the average dipole
moment of a nonpolar molecule is zero, the average of the square of the
dipole moment is nonzero because of charge fluctuations.
 The two nonpolar molecules tend to have dipole moments that are correlated
in time so as to produce van der Waals forces.
Section 43.1
Hydrogen Bonding
In addition to covalent bonds, a hydrogen atom in a molecule can also form a
hydrogen bond.
Using water (H2O) as an example
 There are two covalent bonds in the molecule.
 The electrons from the hydrogen atoms are more likely to be found near the
oxygen atom than the hydrogen atoms.
This leaves essentially bare protons at the positions of the hydrogen atoms.
The negative end of another molecule can come very close to the proton.
This bond is strong enough to form a solid crystalline structure.
Section 43.1
Hydrogen Bonding, cont.
The hydrogen bond is relatively weak
compared with other electrical bonds.
Hydrogen bonding is a critical
mechanism for the linking of biological
molecules and polymers.
DNA is an example.
Section 43.1
Energy States of Molecules
The energy of a molecule (assume one in a gaseous phase) can be divided into
four categories.
 Electronic energy
 Due to the interactions between the molecule’s electrons and nuclei
 Translational energy
 Due to the motion of the molecule’s center of mass through space
 Rotational energy
 Due to the rotation of the molecule about its center of mass.
 Vibrational energy
 Due to the vibration of the molecule’s constituent atoms
The total energy of the molecule is the sum of the energies in these categories:
 E = Eel + Etrans + Erot + Evib
Section 43.2
Spectra of Molecules
The translational energy is unrelated to internal structure and therefore
unimportant to the interpretation of the molecule’s spectrum.
By analyzing its rotational and vibrational energy states, significant information
about molecular spectra can be found.
Section 43.2
Rotational Motion of Molecules
A diatomic model will be used, but the
same ideas can be extended to
polyatomic molecules.
A diatomic molecule aligned along a y
axis has only two rotational degrees of
freedom.
 Corresponding to rotations about
the x and z axes
Section 43.2
Rotational Motion of Molecules, Energy
The rotational energy is given by
Erot 
1
I ω2
2
I is the moment of inertia of the molecule.
 mm 
I   1 2  r 2  μr 2
 m1  m2 
 µ is called the reduced mass of the molecule.
Section 43.2
Rotational Motion of Molecules, Angular Momentum
Classically, the value of the molecule’s angular momentum can have any value
L = Iω
Quantum mechanics restricts the values of the angular momentum to
L  J  J  1
J  0, 1, 2,
 J is an integer called the rotational quantum number.
Section 43.2
Rotational Kinetic Energy of Molecules, Allowed Levels
The allowed values are
Erot  EJ 
2
2I
J  J  1
J  0 , 1, 2,
The rotational kinetic energy is quantized and depends on its moment of inertia.
As J increases, the states become farther apart.
Section 43.2
Allowed Levels, cont.
For most molecules, transitions result in
radiation that is in the microwave
region.
Allowed transitions are given by the
condition
2
E photon  Erot 
h2

J
2
4π I
I
J
J  1, 2, 3 ,
 J is the number of the higher state.
Section 43.2
Vibrational Motion of Molecules
A molecule can be considered to be a
flexible structure where the atoms are
bonded by “effective springs”.
Therefore, the molecule can be
modeled as a simple harmonic
oscillator.
 As long as the atoms in the
molecules are not too far from their
equilibrium positions .
Section 43.2
Vibrational Motion of Molecules, Potential Energy
A plot of the potential energy function.
ro is the equilibrium atomic separation.
For separations close to ro, the shape
closely resembles a parabola.
Section 43.2
Vibrational Energy
Classical mechanics describes the frequency of vibration of a simple harmonic
oscillator.
Quantum mechanics predicts that a molecule will vibrate in quantized states.
The vibrational and quantized vibrational energy can be altered if the molecule
acquires energy of the proper value to cause a transition between quantized
states.
The allowed vibrational energies are
1

Evib   v   h ƒ
2

v  0 , 1, 2,
 v is an integer called the vibrational quantum number.
When v = 0, the molecule’s ground state energy is ½hƒ.
 The accompanying vibration is always present, even if the molecule is not
excited.
Section 43.2
Vibrational Energy, Final
The allowed vibrational energies can be
expressed as
1 h

Evib   v  
2  2π

v  0 , 1, 2,
k
μ
Selection rule for allowed transitions is
Δv = ±1.
The energy of an absorbed photon is
Ephoton = ΔEvib = hƒ.
Section 43.2
Molecular Spectra
In general, a molecule vibrates and rotates simultaneously.
To a first approximation, these motions are independent of each other.
The total energy is the sum of the energies for these two motions:
2
1

E   v   hƒ 
J  J  1
2
2
I


Section 43.2
Molecular Energy-Level Diagram
For each allowed state of v, there is a
complete set of levels corresponding to
the allowed values of J.
The energy separation between
successive rotational levels is much
smaller than between successive
vibrational levels.
Most molecules at ordinary
temperatures vibrate at v = 0 level.
Section 43.2
Molecular Absorption Spectrum
The spectrum consists of two groups of lines.
 One group to the right of center satisfying the selection rules ΔJ = +1 and Δv
= +1.
 The other group to the left of center satisfying the selection rules ΔJ = -1 and
Δv = +1.
Adjacent lines are separated by h/2πI.
Section 43.2
Absorption Spectrum of HCl
It fits the predicted pattern very well.
A peculiarity shows, each line is split into a doublet.
 Two chlorine isotopes were present in the same sample.
 Because of their different masses, different I’s are present in the sample.
Section 43.2
Intensity of Spectral Lines
The intensity is determined by the product of two functions of J.
 The first function is the number of available states for a given value of J.
 There are 2J + 1 states available.
 The second function is the Boltzmann factor.

n  noe

J (J 1)/(2 I kBT )
2
Taking into account both factors by multiplying them,
I   2J  1 e

2
J (J 1)/(2 I kBT )
 The 2J + 1 term increases with J.
 The exponential term decreases.
This is in good agreement with the observed envelope of the spectral lines.
Section 43.2
Bonding in Solids
Bonds in solids can be of the following types:
 Ionic
 Covalent
 Metallic
Section 43.3
Ionic Bonds in Solids
The dominant interaction between ions is through the Coulomb force.
Many crystals are formed by ionic bonding.
Multiple interactions occur among nearest-neighbor atoms.
The net effect of all the interactions is a negative electric potential energy.
e2
Uattractive  αke
r
 α is a dimensionless number known as the Madelung constant.
 The value of α depends only on the particular crystalline structure of the
solid.
Ionic Bonds, NaCl Example
The crystalline structure is shown (a).
Each positive sodium ion is surrounded by six negative chlorine ions (b).
Each chlorine ion is surrounded by six sodium ions ©.
α = 1.747 6 for the NaCl structure.
Section 43.3
Total Energy in a Crystalline Solid
As the constituent ions of a crystal are brought close together, a repulsive force
exists.
The potential energy term B/rm accounts for this repulsive force.
 This repulsive force is a result of electrostatic forces and the exclusion
principle.
Section 43.3
Total Energy in a Crystalline Solid, cont.
The total potential energy of the crystal
is
Utotal
e2 B
 αke
 m
r
r
The minimum value of Utotal occurs at r
= ro.
This minimum value, Uo, is called the
ionic cohesive energy of the solid.
 It represents the energy needed to
separate the solid into a collection
of isolated positive and negative
ions.
Section 43.3
Properties of Ionic Crystals
They form relatively stable, hard crystals.
They are poor electrical conductors.
 They contain no free electrons.
 Each electron is bound tightly to one of the ions.
They have high melting points.
They are transparent to visible radiation, but absorb strongly in the infrared
region.
 The shells formed by the electrons are so tightly bound that visible light does
not possess sufficient energy to promote electrons to the next allowed shell.
 Infrared is absorbed strongly because the vibrations of the ions have natural
resonant frequencies in the low-energy infrared region.
Section 43.3
Properties of Solids with Covalent Bonds
Properties include:
 Usually very hard
 Due to the large atomic cohesive energies
 High bond energies
 High melting points
 Good electrical conductors
Section 43.3
Cohesive Energies for Some Covalent Solids
Section 43.3
Covalent Bond Example – Diamond
Each carbon atom in a diamond crystal is covalently bonded to four other carbon
atoms.
This forms a tetrahedral structure.
Section 43.3
Another Carbon Example – Buckyballs
Carbon can form many different
structures.
The large hollow structure is called
buckminsterfullerene.
 Also known as a “buckyball”
Section 43.3
Metallic Solids
Metallic bonds are generally weaker than ionic or covalent bonds.
The outer electrons in the atoms of a metal are relatively free to move through
the material.
The number of such mobile electrons in a metal is large.
Section 43.3
Metallic Solids, cont.
The metallic structure can be viewed as
a “sea” or “gas” of nearly free electrons
surrounding a lattice of positive ions.
The bonding mechanism is the
attractive force between the entire
collection of positive ions and the
electron gas.
Section 43.3
Properties of Metallic Solids
Light interacts strongly with the free electrons in metals.
 Visible light is absorbed and re-emitted quite close to the surface.
 This accounts for the shiny nature of metal surfaces.
High electrical conductivity
The metallic bond is nondirectional.
 This allows many different types of metal atoms to be dissolved in a host
metal in varying amounts.
 The resulting solid solutions, or alloys, may be designed to have particular
properties.
Metals tend to bend when stressed.
 Due to the bonding being between all of the electrons and all of the positive
ions.
Section 43.3
Free-Electron Theory of Metals
The quantum-based free-electron theory of electrical conduction in metals takes
into account the wave nature of the electrons.
The model is that the outer-shell electrons are free to move through the metal,
but are trapped within a three-dimensional box formed by the metal surfaces.
Each electron can be represented as a particle in a box.
Section 43.4
Fermi-Dirac Distribution Function
Applying statistical physics to a collection of particles can relate microscopic
properties to macroscopic properties.
For electrons, quantum statistics requires that each state of the system can be
occupied by only two electrons.
The probability that a particular state having energy E is occupied by one of the
electrons in a solid is given by
ƒ(E ) 
1
e(E EF )
kBT
1
ƒ(E) is called the Fermi-Dirac distribution function.
EF is called the Fermi energy.
Section 43.4
Fermi-Dirac Distribution Function at T = 0
At T = 0, all states having energies less than the Fermi energy are occupied.
All states having energies greater than the Fermi energy are vacant.
Section 43.4
Fermi-Dirac Distribution Function at T > 0
As T increases, the distribution rounds
off slightly.
Because of thermal excitation,
 States near and below EF lose
population
 States near and above EF gain
population
The Fermi energy also depends on
temperature, but the dependence is
weak in metals.
Section 43.4
Electrons as a Particle in a Three-Dimensional Box
The energy levels for the electrons are very close together.
The density-of-states function gives the number of allowed states per unit
volume that have energies between E and E + dE:
8 2πme3 2 1 2
g (E )dE 
E dE
h3
Section 43.4
Fermi Energy at T = 0 K
The Fermi energy at T = 0 K is
h2  3ne 
EF (0) 


2me  8π 
2 3
The Fermi energies for metals are in the range of a few eV.
The average energy of a free electron in a metal at 0 K is Eavg = (3/5) EF.
Section 43.4
Fermi Energies for Some Metals
Section 43.4
Metals – Summary
A metal can be considered to be a system comprising of a very large number of
energy levels available to the free electrons.
These electrons fill the levels in accordance with the Pauli exclusion principle.
 Beginning with E = 0 and ending at EF
 At T = 0, all levels below the Fermi energy are filled and all levels above the
Fermi energy are empty.
 At 300 K, a small fraction of the free electrons are excited above the Fermi
energy.
Section 43.4
Wave Functions of Solids
To make the model of a metal more complete, the contributions of the parent
atoms that form the crystal must be incorporated.
Two wave functions are valid for an atom with atomic number Z and a single s
electron outside a closed shell:
ψs (r )   A ƒ(r )e  Zr
nao
ψs (r )   A ƒ(r )e  Zr
nao
 A is a normalization constant.
 ƒ(r) is a function of r that varies with the value of n.
 Choosing either value of these wave functions leads to the same value of
|Ψ|², so both choices are equivalent.
 A difference arises when two atoms are combined.
Section 43.5
Combined Wave Functions
The wave functions can combine in the
various ways shown.
 Ψs+ (r) + Ψs+ (r) is equivalent to
Ψs- (r)+ Ψs- (r)
These two possible combinations of
wave functions represent two possible
states of the two-atom system.
Section 43.5
Splitting of Energy Levels
The states are split into two energy
levels due to the two ways of combining
the wave functions.
The energy difference is relatively
small, so the two states are close
together on an energy scale.
For large values of r, the electron
clouds do not overlap and there is no
splitting of the energy level.
Section 43.5
Splitting of Energy Levels, cont.
As the number of atoms increases, the
number of combinations in which the
wave functions combine increases.
Each combination corresponds to a
different energy level.
Section 43.5
Splitting of Energy Levels, final
When this splitting is extended to the
large number of atoms present in a
solid, there is a large number of levels
of varying energy.
These levels are so closely spaced they
can be thought of as a band of energy
levels.
Section 43.5
Energy Bands in a Crystal
In general, a crystalline solid will have a
large number of allowed energy bands.
The white areas represent energy gaps,
corresponding to forbidden energies.
Some bands exhibit an overlap.
Blue represents filled bands and gold
represents empty bands in this example
of sodium.
Band theory allows us to build simple
models to understand the behavior of
conductors, insulators, and
semiconductors.
Section 43.5
Electrical Conduction – Classes of Materials
Good electrical conductors contain a high density of free charge carriers.
The density of free charge carriers in an insulator is nearly zero.
Semiconductors are materials with a charge density between those of insulators
and conductors.
These classes can be discussed in terms of a model based on energy bands.
Section 43.6
Metals
To be a good conductor, the charge carriers in a material must be free to move in
response to an electric field.
 We will consider electrons as the charge carriers.
The motion of electrons in response to an electric field represents an increase in
the energy of the system.
When an electric field is applied to a conductor, the electrons move up to an
available higher energy state.
Section 43.6
Metals – Energy Bands
At T = 0, the Fermi energy lies in the
middle of the band.
 All levels below EF are filled and
those above are empty.
If a potential difference is applied to the
metal, electrons having energies near
EF require only a small amount of
additional energy from the applied field
to reach nearby empty states above the
Fermi energy.
Section 43.6
Metals As Good Conductors
The electrons in a metal experiencing only a weak applied electric field are free
to move because there are many empty levels available close to the occupied
energy level.
This shows that metals are excellent electrical conductors.
Section 43.6
Insulators
There are no available states that lie close in energy into which electrons can
move upward in response to an electric field.
Although an insulator has many vacant states in the conduction band, these
states are separated from the filled band by a large energy gap.
Only a few electrons can occupy the higher states, so the overall electrical
conductivity is very small.
Section 43.6
Insulator – Energy Bands
The valence band is filled and the
conduction band is empty at T = 0.
The Fermi energy lies somewhere in
the energy gap.
At room temperature, very few
electrons would be thermally excited
into the conduction band.
Section 43.6
Semiconductors
The band structure of a semiconductor
is like that of an insulator with a smaller
energy gap.
Typical energy gap values are shown in
the table.
Section 43.6
Semiconductors – Energy Bands
Appreciable numbers of electrons are
thermally excited into the conduction
band.
A small applied potential difference can
easily raise the energy of the electrons
into the conduction band.
Section 43.6
Semiconductors – Movement of Charges
Charge carriers in a semiconductor can be positive, negative, or both.
When an electron moves into the conduction band, it leaves behind a vacant site,
called a hole.
Section 43.6
Semiconductors – Movement of Charges, cont.
The holes act as charge carriers.
 Electrons can transfer into a hole, leaving another hole at its original site.
The net effect can be viewed as the holes migrating through the material in the
direction opposite the direction of the electrons.
 The hole behaves as if it were a particle with charge +e.
Section 43.6
Intrinsic Semiconductors
A pure semiconductor material containing only one element is called an intrinsic
semiconductor.
It will have equal numbers of conduction electrons and holes.
 Such combinations of charges are called electron-hole pairs.
Section 43.6
Doped Semiconductors
Impurities can be added to a semiconductor.
This process is called doping.
Doping
 Modifies the band structure of the semiconductor
 Modifies its resistivity
 Can be used to control the conductivity of the semiconductor
Section 43.6
n-Type Semiconductors
An impurity can add an electron to the
structure.
This impurity would be referred to as a
donor atom.
Semiconductors doped with donor
atoms are called n-type
semiconductors.
Section 43.6
n-Type Semiconductors, Energy Levels
The energy level of the extra electron is
just below the conduction band.
The electron of the donor atom can
move into the conduction band as a
result of a small amount of energy.
Section 43.6
p-Type Semiconductors
An impurity can add a hole to the
structure.
 This is an electron deficiency .
This impurity would be referred to as a
acceptor atom.
Semiconductors doped with acceptor
atoms are called p-type
semiconductors.
Section 43.6
p-Type Semiconductors, Energy Levels
The energy level of the hole is just
above the valence band.
An electron from the valence band can
fill the hole with an addition of a small
amount of energy.
A hole is left behind in the valance
band.
This hole can carry current in the
presence of an electric field.
Section 43.6
Extrinsic Semiconductors
When conduction in a semiconductor is the result of acceptor or donor
impurities, the material is called an extrinsic semiconductor.
Doping densities range from 1013 to 1019 cm-3 .
The typical electron density in a typical semiconductor is about 1021 cm-3 .
Section 43.6
Semiconductor Devices
Many electronic devices are based on semiconductors.
These devices include:
 Junction diode
 Light-emitting and light-absorbing diodes
 Transistor
 Integrated Circuit
Section 43.7
The Junction Diode
A p-type semiconductor is joined to an n-type.
This forms a p-n junction.
A junction diode is a device based on a single p-n junction.
The role of the diode is to pass current in one direction, but not the other.
Section 43.7
The Junction Diode, 2
The junction has three distinct regions:
 a p region
 an n region
 a depletion region
The depletion region is caused by the
diffusion of electrons to fill holes.
 This can be modeled as if the
holes being filled were diffusing to
the n region.
Section 43.7
The Junction Diode, 3
Because the two sides of the depletion region each carry a net charge, an
internal electric field exists in the depletion region.
This internal field creates an internal potential difference that prevents further
diffusion and ensures zero current in the junction when no potential difference is
applied.
Section 43.7
Junction Diode, Biasing
A diode is forward biased when the p side is connected to the positive terminal of
a battery.
 This decreases the internal potential difference which results in a current that
increases exponentially.
A diode is reverse biased when the n side is connected to the positive terminal of
a battery.
 This increases the internal potential difference and results in a very small
current that quickly reaches a saturation value.
The current-voltage relationship for an ideal diode is
I  Io  eeV kBT  1
Section 43.7
Junction Diode: Biasing and I-V Characteristics
Section 43.7
Light-Emitting and Light-Absorbing Diodes
Light emission and absorption in semiconductors is similar to that in gaseous
atoms, with the energy bands of the semiconductor taken into account.
An electron in the conduction band can recombine with a hole in the valance
band and emit a photon.
An electron in the valance band can absorb a photon and be promoted to the
conduction band, leaving behind a hole.
Section 43.7
Transistors
A junction transistor is formed from two p-n junctions.
 A narrow n region sandwiched between two p regions or a narrow p region
between two n regions.
The transistor can be used as
 An amplifier
 A switch
Section 43.7
Integrated Circuits
An integrated circuit is a collection of interconnected transistors, diodes,
resistors and capacitors fabricated on a single piece of silicon known as a chip.
Integrated circuits
 Solved the interconnectedness problem posed by transistors
 Possess the advantages of miniaturization and fast response
Section 43.7
Superconductivity
A superconductor expels magnetic fields from its interior by forming surface
currents.
Surface currents induced on the superconductor’s surface produce a magnetic
field that exactly cancels the externally applied field.
The surface currents disappear when the external magnetic field is removed.
Under the action of an applied electric field, the Cooper pairs experience an
electric force and move through the metal.
There is no resistance to the movement of the Cooper pairs.
 They are in the lowest possible energy state.
 There are no energy states above that of the Cooper pairs because of the
energy gap.
Section 43.8
Section 43.8
Superconductivity and Cooper Pairs
Two electrons are bound into a Cooper pair when they interact via distortions in
the array of lattice atoms so that there is a net attractive force between them.
Cooper pairs act like bosons and do not obey the exclusion principle.
 Bosons are particles with integral spins.
The entire collection of Cooper pairs in a metal can be described by a single
wave function.
Under the action of an applied electric field, the Cooper pairs experience an
electric force and move through the metal.
There is no resistance to the movement of the Cooper pairs.
 They are in the lowest possible energy state.
 There are no energy states above that of the Cooper pairs because of the
energy gap.
Section 43.8
Superconductivity - Critical Temperatures
The critical temperature is the temperature at which the electrical resistance of
the material decreases to virtually zero.
A new family of compounds was found that was superconducting at “high”
temperatures.
 First discovered in 1986
 Strong evidence for superconductivity at 30 K
 Found materials that are superconductive up to temperatures of 150 K in
oxides containing mercury
 In 2006 scientists found superconductivity in iron-based materials.
 Temperatures up to 55 K so far
 Currently no widely accepted theory for high-temperature superconductivity
Section 43.8