Chapter 30
Nuclear Energy
and
Elementary Particles
Processes of Nuclear Energy
Fission
A nucleus of large mass number splits into two smaller nuclei
Fusion
Two light nuclei fuse to form a heavier nucleus
Large amounts of energy are released in either case
Nuclear Fission
A heavy nucleus splits into two smaller nuclei
The total mass of the products is less than the original mass of the heavy nucleus
Fission Equation
Fission of 235U by a slow (low energy) neutron
236U* is an intermediate, short-lived state
Lasts about 10-12 s
X and Y are called fission fragments
Many combinations of X and Y satisfy the requirements of conservation of energy and charge
1 235 236
0 92 92 *n U U X Y neutrons
More About Fission of 235U
About 90 different daughter nuclei can be formed
Several neutrons are also produced in each fission event
Example:
The fission fragments and the neutrons have a great deal of KE following the event
1 235 141 92 1
0 92 56 36 03n U Ba Kr n
Sequence of Events in Fission
The 235U nucleus captures a thermal (slow-moving) neutron
This capture results in the formation of 236U*, and the excess energy of this nucleus causes it to undergo violent oscillations
The 236U* nucleus becomes highly elongated, and the force of repulsion between the protons tends to increase the distortion
The nucleus splits into two fragments, emitting several neutrons in the process
Sequence of Events in Fission – Diagram
Energy in a Fission Process
Binding energy for heavy nuclei is about 7.2 MeV per nucleon
Binding energy for intermediate nuclei is about 8.2 MeV per nucleon
Therefore, the fission fragments have less mass than the nucleons in the original nuclei
This decrease in mass per nucleon appears as released energy in the fission event
Energy, cont
An estimate of the energy released
Assume a total of 240 nucleons
Releases about 1 MeV per nucleon
8.2 MeV – 7.2 MeV
Total energy released is about 240 Mev
This is very large compared to the amount of energy released in chemical processes
Chain Reaction
Neutrons are emitted when 235U undergoes fission
These neutrons are then available to trigger fission in other nuclei
This process is called a chain reaction If uncontrolled, a violent explosion can
occur
The principle behind the nuclear bomb, where 1 kg of U can release energy equal to about 20 000 tons of TNT
Chain Reaction – Diagram
Nuclear Reactor
A nuclear reactor is a system designed to maintain a self-sustained chain reaction
The reproduction constant, K, is defined as the average number of neutrons from each fission event that will cause another fission event The maximum value of K from uranium
fission is 2.5 In practice, K is less than this
A self-sustained reaction has K = 1
K Values
When K = 1, the reactor is said to be critical The chain reaction is self-sustaining
When K < 1, the reactor is said to be subcritical The reaction dies out
When K > 1, the reactor is said to be supercritical A run-away chain reaction occurs
Basic Reactor Design
Fuel elements consist of enriched uranium
The moderator material helps to slow down the neutrons
The control rodsabsorb neutrons
Reactor Design Considerations – Neutron Leakage
Loss (or “leakage”) of neutrons from the core
These are not available to cause fission events
The fraction lost is a function of the ratio of surface area to volume
Small reactors have larger percentages lost
If too many neutrons are lost, the reactor will not be able to operate
Reactor Design Considerations – Neutron Energies
Slow neutrons are more likely to cause fission events
Most neutrons released in the fission process have energies of about 2 MeV
In order to sustain the chain reaction, the neutrons must be slowed down
A moderator surrounds the fuel
Collisions with the atoms of the moderator slow the neutrons down as some kinetic energy is transferred
Most modern reactors use heavy water as the moderator
Reactor Design Considerations – Neutron Capture
Neutrons may be captured by nuclei that do not undergo fission
Most commonly, neutrons are captured by 238U
The possibility of 238U capture is lower with slow neutrons
The moderator helps minimize the capture of neutrons by 238U
Nuclear Fusion
Nuclear fusion occurs when two light nuclei combine to form a heavier nucleus
The mass of the final nucleus is less than the masses of the original nuclei
This loss of mass is accompanied by a release of energy
Fusion in the Sun
All stars generate energy through fusion
The Sun, along with about 90% of other stars, fuses hydrogen
Some stars fuse heavier elements
Two conditions must be met before fusion can occur in a star
The temperature must be high enough
The density of the nuclei must be high enough to ensure a high rate of collisions
Proton-Proton Cycle
The proton-proton cycle is a series of three nuclear reactions believed to operate in the Sun
Energy liberated is primarily in the form of gamma rays, positrons and neutrinos
21H is deuterium, and
may be written as 21D
1 1 2
1 1 1
1 2 3
1 1 2
1 3 4
1 2 2
3 3 4 1
2 2 2 12
H H H e
H H He
Then
H He He e
or
He He He H
Fusion Reactors
Energy releasing fusion reactions are called thermonuclear fusion reactions
A great deal of effort is being directed at developing a sustained and controllable thermonuclear reaction
A thermonuclear reactor that can deliver a net power output over a reasonable time interval is not yet a reality
Advantages of a Fusion Reactor
Inexpensive fuel source
Water is the ultimate fuel source
If deuterium is used as fuel, 0.06 g of it can be extracted from 1 gal of water for about 4 cents
Comparatively few radioactive by-products are formed
Considerations for a Fusion Reactor
The proton-proton cycle is not feasible for a fusion reactor
The high temperature and density required are not suitable for a fusion reactor
The most promising reactions involve deuterium (D) and tritium (T)
2 2 3 1
1 1 2 0
2 2 3 1
1 1 1 1
2 3 4 1
1 1 3 0
3.27
4.03
17.59
D D He n Q MeV
D D T H Q MeV
D T He n Q MeV
Considerations for a Fusion Reactor, cont
Deuterium is available in almost unlimited quantities in water and is inexpensive to extract
Tritium is radioactive and must be produced artificially
The Coulomb repulsion between two charged nuclei must be overcome before they can fuse
Requirements for Successful Thermonuclear Reactor
High temperature 108 K Needed to give nuclei enough energy to
overcome Coulomb forces
At these temperatures, the atoms are ionized, forming a plasma
Plasma ion density, n The number of ions present
Plasma confinement time, The time the interacting ions are
maintained at a temperature equal to or greater than that required for the reaction to proceed successfully
Lawson’s Criteria
Lawson’s criteria states that a net power output in a fusion reactor is possible under the following conditions
n 1014 s/cm3 for deuterium-tritium
n 1016 s/cm3 for deuterium-deuterium
The plasma confinement time is still a problem
Magnetic Confinement One magnetic
confinement device is called a tokamak
Two magnetic fields confine the plasma inside the doughnut A strong magnetic field is
produced in the windings
A weak magnetic field is produced in the toroid
The field lines are helical, spiral around the plasma, and prevent it from touching the wall of the vacuum chamber
Other Methods of Creating Fusion Events
Inertial laser confinement
Fuel is put into the form of a small pellet
It is collapsed by ultrahigh power lasers
Inertial electrostatic confinement
Positively charged particles are rapidly attracted toward an negatively charged grid
Some of the positive particles collide and fuse
Elementary Particles
Atoms
From the Greek for “indivisible”
Were once thought to be the elementary particles
Atom constituents
Proton, neutron, and electron
Were viewed as elementary because they are very stable
Quarks
Physicists recognize that most particles are made up of quarks Exceptions include photons, electrons and a
few others
The quark model has reduced the array of particles to a manageable few
The quark model has successfully predicted new quark combinations that were subsequently found in many experiments
Fundamental Forces
All particles in nature are subject to four fundamental forces
Strong force
Electromagnetic force
Weak force
Gravitational force
Strong Force
Is responsible for the tight binding of the quarks to form neutrons and protons
Also responsible for the nuclear force binding the neutrons and the protons together in the nucleus
Strongest of all the fundamental forces
Very short-ranged Less than 10-15 m
Electromagnetic Force
Is responsible for the binding of atoms and molecules
About 10-2 times the strength of the strong force
A long-range force that decreases in strength as the inverse square of the separation between interacting particles
Weak Force
Is responsible for instability in certain nuclei Is responsible for beta decay
A short-ranged force
Its strength is about 10-6 times that of the strong force
Scientists now believe the weak and electromagnetic forces are two manifestations of a single force, the electroweak force
Gravitational Force
A familiar force that holds the planets, stars and galaxies together
Its effect on elementary particles is negligible
A long-range force
It is about 10-43 times the strength of the strong force
Weakest of the four fundamental forces
Explanation of Forces
Forces between particles are often described in terms of the actions of field particles or quanta
For electromagnetic force, the photon is the field particle
The electromagnetic force is mediated, or carried, by photons
Forces and Mediating Particles (also see table 30.1)
Interaction (force)Mediating Field Particle
Strong Gluon
Electromagnetic Photon
Weak W± and Z0
Gravitational Gravitons
Richard Feynmann
1918 – 1988
Contributions include Work on the Manhattan
Project
Invention of diagrams to represent particle interactions
Theory of weak interactions
Reformation of quantum mechanics
Superfluid helium
Challenger investigation
Shared Nobel Prize in 1965
Feynman Diagrams
A graphical representation of the interaction between two particles
Feynman diagrams are named for Richard Feynman who developed them
Feynman Diagram – Two Electrons
The photon is the field particle that mediates the interaction
The photon transfers energy and momentum from one electron to the other
The photon is called a virtual photon It can never be detected
directly because it is absorbed by the second electron very shortly after being emitted by the first electron
The Virtual Photon
The existence of the virtual photon would be expected to violate the law of conservation of energy But, due to the uncertainty principle
and its very short lifetime, the photon’s excess energy is less than the uncertainty in its energy
The virtual photon can exist for short time intervals, such that ΔE Δt ħ
Paul Adrien Maurice Dirac
1902 – 1984
Instrumental in understanding antimatter
Aided in the unification of quantum mechanics and relativity
Contributions to quantum physics and cosmology
Nobel Prize in 1933
Antiparticles
For every particle, there is an antiparticle From Dirac’s version of quantum mechanics that
incorporated special relativity
An antiparticle has the same mass as the particle, but the opposite charge
The positron (electron’s antiparticle) was discovered by Anderson in 1932 Since then, it has been observed in numerous
experiments
Practically every known elementary particle has a distinct antiparticle Exceptions – the photon and the neutral pi particles
are their own antiparticles
Classification of Particles
Two broad categories
Classified by interactions
Hadrons
Interact through strong force
Composed of quarks
Leptons
Interact through weak force
Thought to be truly elementary
Some suggestions they may have some internal structure
Hadrons
Interact through the strong force
Two subclasses Mesons
Decay finally into electrons, positrons, neutrinos and photons
Integer spins
Baryons Masses equal to or greater than a proton
Noninteger spin values
Decay into end products that include a proton (except for the proton)
Composed of quarks
Leptons
Interact through weak force
All have spin of ½
Leptons appear truly elementary No substructure
Point-like particles
Scientists currently believe only six leptons exist, along with their antiparticles Electron and electron neutrino
Muon and its neutrino
Tau and its neutrino
Conservation Laws
A number of conservation laws are important in the study of elementary particles
Two new ones are
Conservation of Baryon Number
Conservation of Lepton Number
Conservation of Baryon Number
Whenever a baryon is created in a reaction or a decay, an antibaryon is also created
B is the Baryon Number B = +1 for baryons
B = -1 for antibaryons
B = 0 for all other particles
The sum of the baryon numbers before a reaction or a decay must equal the sum of baryon numbers after the process
Proton Stability
Absolute conservation of baryon number indicates the proton must be absolutely stable Otherwise, it could decay into a
positron and a neutral pion Never been observed
Currently can say the proton has a half-life of at least 1031 years
Some theories indicate the proton can decay
Conservation of Lepton Number
There are three conservation laws, one for each variety of lepton
Law of Conservation of Electron-Lepton Number states that the sum of electron-lepton numbers before a reaction or a decay must equal the sum of the electron-lepton number after the process
Conservation of Lepton Number, cont
Assigning electron-lepton numbers Le = 1 for the electron and the electron neutrino
Le = -1 for the positron and the electron antineutrino
Le = 0 for all other particles
Similarly, when a process involves muons, muon-lepton number must be conserved and when a process involves tau particles, tau-lepton numbers must be conserved Muon- and tau-lepton numbers are assigned
similarly to electron-lepton numbers
Strange Particles
Some particles discovered in the 1950’s were found to exhibit unusual properties in their production and decay and were given the name strange particles
Peculiar features include Always produced in pairs
Although produced by the strong interaction, they do not decay into particles that interact via the strong interaction, but instead into particles that interact via weak interactions
They decay much more slowly than particles decaying via strong interactions
Strangeness
To explain these unusual properties, a new law, conservation of strangeness, was introduced Also needed a new quantum number, S
The Law of Conservation of Strangeness states that the sum of strangeness numbers before a reaction or a decay must equal the sum of the strangeness numbers after the process
Strong and electromagnetic interactions obey the law of conservation of strangeness, but the weak interactions do not
Bubble ChamberExample
The dashed lines represent neutral particles
At the bottom,- + p Λ0 + K0
Then Λ0 - + p and
K0 + µ- + µ
Murray Gell-Mann
1929 –
Worked on theoretical studies of subatomic particles
Nobel Prize in 1969
The Eightfold Way
Many classification schemes have been proposed to group particles into families
These schemes are based on spin, baryon number, strangeness, etc.
The eightfold way is a symmetric pattern proposed by Gell-Mann and Ne’eman
There are many symmetrical patterns that can be developed
The patterns of the eightfold way have much in common with the periodic table
Including predicting missing particles
An Eightfold Way for Baryons
A hexagonal pattern for the eight spin ½ baryons
Strangeness vs. charge is plotted on a sloping coordinate system
Six of the baryons form a hexagon with the other two particles at its center
An Eightfold Way for Mesons
The mesons with spins of 0 can be plotted
Strangeness vs. charge on a sloping coordinate system is plotted
A hexagonal pattern emerges
The particles and their antiparticles are on opposite sides on the perimeter of the hexagon
The remaining three mesons are at the center
Quarks
Hadrons are complex particles with size and structure
Hadrons decay into other hadrons
There are many different hadrons
Quarks are proposed as the elementary particles that constitute the hadrons
Originally proposed independently by Gell-Mann and Zweig
Quark Model
Three types u – up d – down s – strange c – charmed t – top b – bottom
Associated with each quark is an antiquark The antiquark has opposite charge, baryon
number and strangeness
Quark Model, cont
Quarks have fractional electrical charges
+1/3 e and –2/3 e
All ordinary matter consists of just u and d quarks
Quark Model – Rules
All the hadrons at the time of the original proposal were explained by three rules Mesons consist of one quark and one
antiquark This gives them a baryon number of 0
Baryons consist of three quarks
Antibaryons consist of three antiquarks
Numbers of Particles
At the present, physicists believe the “building blocks” of matter are complete
Six quarks with their antiparticles
Six leptons with their antiparticles
See table 30.3 for quark summary
Color
Isolated quarks
Physicist now believe that quarks are permanently confined inside ordinary particles
No isolated quarks have been observed experimentally
The explanation is a force called the color force
Color force increases with increasing distance
This prevents the quarks from becoming isolated particles
Colored Quarks
Color “charge” occurs in red, blue, or green Antiquarks have colors of antired,
antiblue, or antigreen
Color obeys the Exclusion Principle
A combination of quarks of each color produces white (or colorless)
Baryons and mesons are always colorless
Quark Structure of a Meson
A green quark is attracted to an antigreen quark
The quark –antiquark pair forms a meson
The resulting meson is colorless
Quark Structure of a Baryon
Quarks of different colors attract each other
The quark triplet forms a baryon
The baryon is colorless
Quantum Chromodynamics (QCD)
QCD gave a new theory of how quarks interact with each other by means of color charge
The strong force between quarks is often called the color force
The strong force between quarks is carried by gluons Gluons are massless particles
There are 8 gluons, all with color charge
When a quark emits or absorbs a gluon, its color changes
More About Color Charge
Like colors repel and opposite colors attract Different colors also attract, but not as strongly
as a color and its anticolor
The color force between color-neutral hadrons is negligible at large separations The strong color force between the constituent
quarks does not exactly cancel at small separations
This residual strong force is the nuclear force that binds the protons and neutrons to form nuclei
Weak Interaction
The weak interaction is an extremely short-ranged force
This short range implies the mediating particles are very massive
The weak interaction is responsible for the decay of c, s, b, and t quarks into u and d quarks
Also responsible for the decay of and leptons into electrons
Weak Interaction, cont
The weak interaction is very important because it governs the stability of the basic particles of matter
The weak interaction is not symmetrical
Not symmetrical under mirror reflection
Not symmetrical under charge exchange
Electroweak Theory
The electroweak theory unifies electromagnetic and weak interactions
The theory postulates that the weak and electromagnetic interactions have the strength at very high particle energies Viewed as two different
manifestations of a single interaction
The Standard Model
A combination of the electroweak theory and QCD form the standard model
Essential ingredients of the standard model The strong force, mediated by gluons, holds the
quarks together to form composite particles
Leptons participate only in electromagnetic and weak interactions
The electromagnetic force is mediated by photons
The weak force is mediated by W and Z bosons
The Standard Model –Chart
Mediator Masses
Why does the photon have no mass while the W and Z bosons do have mass? Not answered by the Standard Model
The difference in behavior between low and high energies is called symmetry breaking
The Higgs boson has been proposed to account for the masses Large colliders are necessary to achieve the
energy needed to find the Higgs boson
Grand Unification Theory (GUT)
Builds on the success of the electroweak theory
Attempted to combine electroweak and strong interactions One version considers leptons and
quarks as members of the same family They are able to change into each other
by exchanging an appropriate particle
The Big Bang
This theory of cosmology states that during the first few minutes after the creation of the universe all four interactions were unified All matter was contained in a quark soup
As time increased and temperature decreased, the forces broke apart
Starting as a radiation dominated universe, as the universe cooled it changed to a matter dominated universe
A Brief History of the Universe
George Gamow
1904 – 1968
Among the first to look at the first half hour of the universe
Predicted: Abundances of
hydrogen and helium
Radiation should still be present and have an apparent temperature of about 5 K
Cosmic Background Radiation (CBR)
CBR represents the cosmic “glow” left over from the Big Bang
The radiation had equal strengths in all directions
The curve fits a blackbody at 2.9 K
There are small irregularities that allowed for the formation of galaxies and other objects
Connection Between Particle Physics and Cosmology
Observations of events that occur when two particles collide in an accelerator are essential to understanding the early moments of cosmic history
There are many common goals between the two fields
Some Questions
Why so little antimatter in the Universe?
Do neutrinos have mass? How do they contribute to the dark mass in the
universe?
Explanation of why the expansion of the universe is accelerating?
Is there a kind of antigravity force acting between widely separated galaxies?
Is it possible to unify electroweak and strong forces?
Why do quark and leptons form similar but distinct families?
More Questions
Are muons the same as electrons, except for their mass?
Why are some particles charged and others neutral?
Why do quarks carry fractional charge?
What determines the masses of fundamental particles?
Do leptons and quarks have a substructure?