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 235 U by a slow (low energy) neutron 1 235 236 0n 92U 92 U* X Y neutrons 236 U* 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
More About Fission of 235 U About 90 different daughter nuclei can be formed Several neutrons are also produced in each fission event Example: 1 235 141 92 3 1 0 92 56 36 0 n U Ba Kr n The fission fragments and the neutrons have a great deal of KE following the event
Sequence of Events in Fission The 235 U nucleus captures a thermal (slowmoving) neutron This capture results in the formation of 236 U*, and the excess energy of this nucleus causes it to undergo violent oscillations The 236 U* 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 235 U 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 rods absorb 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 238 U The possibility of 238 U capture is lower with slow neutrons The moderator helps minimize the capture of neutrons by 238 U
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 2 1H is deuterium, and may be written as 2 1D H H H e 1 1 2 1 1 1 H H He 1 2 3 1 1 2 Then H He He e 1 3 4 1 2 2 or He He He 2 H 3 3 4 1 2 2 2 1
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 byproducts 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) D D He n Q 3.27 MeV 2 2 3 1 1 1 2 0 D D T H Q 4.03 MeV 2 2 3 1 1 1 1 1 D T He n Q 17.59 MeV 2 3 4 1 1 1 3 0
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 10 8 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 10 14 s/cm 3 for deuterium-tritium n 10 16 s/cm 3 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) Strong Electromagnetic Mediating Field Particle Gluon Photon Weak W ± and Z 0 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 halflife of at least 10 31 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 electronlepton number after the process
Conservation of Lepton Number, cont Assigning electron-lepton numbers L e = 1 for the electron and the electron neutrino L e = -1 for the positron and the electron antineutrino L e = 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 Chamber Example The dashed lines represent neutral particles At the bottom, - + p Λ 0 + K 0 Then Λ 0 and - + p K 0 + 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?