Chapter 30 Nuclear Energy and Elementary Particles

Processes of Nuclear Energy Fission Fission A nucleus of large mass number splits into two smaller nuclei A nucleus of large mass number splits into two smaller nuclei Fusion Fusion Two light nuclei fuse to form a heavier nucleus Two light nuclei fuse to form a heavier nucleus Large amounts of energy are released in either case Large amounts of energy are released in either case

Nuclear Fission A heavy nucleus splits into two smaller nuclei A heavy nucleus splits into two smaller nuclei The total mass of the products is less than the original mass of the heavy nucleus The total mass of the products is less than the original mass of the heavy nucleus First observed in 1939 by Otto Hahn and Fritz Strassman following basic studies by Fermi First observed in 1939 by Otto Hahn and Fritz Strassman following basic studies by Fermi Lisa Meitner and Otto Frisch soon explained what had happened Lisa Meitner and Otto Frisch soon explained what had happened

Fission Equation Fission of 235 U by a slow (low energy) neutron Fission of 235 U by a slow (low energy) neutron 236 U* is an intermediate, short-lived state 236 U* is an intermediate, short-lived state X and Y are called fission fragments X and Y are called fission fragments Many combinations of X and Y satisfy the requirements of conservation of energy and charge Many combinations of X and Y satisfy the requirements of conservation of energy and charge

Sequence of Events in Fission The 235 U nucleus captures a thermal (slow- moving) neutron The 235 U nucleus captures a thermal (slow- moving) neutron This capture results in the formation of 236 U*, and the excess energy of this nucleus causes it to undergo violent oscillations 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 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 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 heavy nuclei is about 7.2 MeV per nucleon Binding energy for intermediate nuclei is about 8.2 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 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 This decrease in mass per nucleon appears as released energy in the fission event

Energy, cont An estimate of the energy released An estimate of the energy released Assume a total of 240 nucleons Assume a total of 240 nucleons Releases about 1 MeV per nucleon Releases about 1 MeV per nucleon 8.2 MeV – 7.2 MeV 8.2 MeV – 7.2 MeV Total energy released is about 240 Mev Total energy released is about 240 Mev This is very large compared to the amount of energy released in chemical processes This is very large compared to the amount of energy released in chemical processes

Chain Reaction Neutrons are emitted when 235 U undergoes fission Neutrons are emitted when 235 U undergoes fission These neutrons are then available to trigger fission in other nuclei These neutrons are then available to trigger fission in other nuclei This process is called a chain reaction This process is called a chain reaction If uncontrolled, a violent explosion can occur If uncontrolled, a violent explosion can occur The principle behind the nuclear bomb, where 1 g of U can release energy equal to about tons of TNT The principle behind the nuclear bomb, where 1 g of U can release energy equal to about tons of TNT

Chain Reaction – Diagram

Nuclear Fusion Nuclear fusion occurs when two light nuclei combine to form a heavier nucleus 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 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 This loss of mass is accompanied by a release of energy

Fusion in the Sun All stars generate energy through fusion All stars generate energy through fusion The Sun, along with about 90% of other stars, fuses hydrogen The Sun, along with about 90% of other stars, fuses hydrogen Some stars fuse heavier elements Some stars fuse heavier elements Two conditions must be met before fusion can occur in a star Two conditions must be met before fusion can occur in a star The temperature must be high enough The temperature must be high enough The density of the nuclei must be high enough to ensure a high rate of collisions 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 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 Energy liberated is primarily in the form of gamma rays, positrons and neutrinos

Elementary Particles Atoms Atoms From the Greek for “indivisible” From the Greek for “indivisible” Were once thought to the elementary particles Were once thought to the elementary particles Atom constituents Atom constituents Proton, neutron, and electron Proton, neutron, and electron Were viewed as elementary because they are very stable Were viewed as elementary because they are very stable

Discovery of New Particles New particles New particles Beginning in 1937, many new particles were discovered in experiments involving high-energy collisions Beginning in 1937, many new particles were discovered in experiments involving high-energy collisions Characteristically unstable with short lifetimes Characteristically unstable with short lifetimes Over 300 have been cataloged Over 300 have been cataloged A pattern was needed to understand all these new particles A pattern was needed to understand all these new particles

Quarks Physicists recognize that most particles are made up of quarks Physicists recognize that most particles are made up of quarks Exceptions include photons, electrons and a few others 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 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 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 All particles in nature are subject to four fundamental forces Strong force Strong force Electromagnetic force Electromagnetic force Weak force Weak force Gravitational force Gravitational force

Strong Force Is responsible for the tight binding of the quarks to form neutrons and protons 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 Also responsible for the nuclear force binding the neutrons and the protons together in the nucleus Strongest of all the fundamental forces Strongest of all the fundamental forces Very short-ranged Very short-ranged Less than m Less than m

Electromagnetic Force Is responsible for the binding of atoms and molecules Is responsible for the binding of atoms and molecules About times the strength of the strong force About 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 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 instability in certain nuclei Is responsible for beta decay Is responsible for beta decay A short-ranged force A short-ranged force Its strength is about times that of the strong force Its strength is about times that of the strong force Scientists now believe the weak and electromagnetic forces are two manifestions of a single force, the electroweak force Scientists now believe the weak and electromagnetic forces are two manifestions of a single force, the electroweak force

Gravitational Force A familiar force that holds the planets, stars and galaxies together A familiar force that holds the planets, stars and galaxies together Its effect on elementary particles is negligible Its effect on elementary particles is negligible A long-range force A long-range force It is about times the strength of the strong force It is about times the strength of the strong force Weakest of the four fundamental forces 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 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 For electromagnetic force, the photon is the field particle The electromagnetic force is mediated, or carried, by photons The electromagnetic force is mediated, or carried, by photons

Forces and Mediating Particles (also see table 30.1) Interaction (force) Mediating Field Particle StrongGluon ElectromagneticPhoton Weak W  and Z 0 GravitationalGravitons

Antiparticles For every particle, there is an antiparticle For every particle, there is an antiparticle From Dirac’s version of quantum mechanics that incorporated special relativity From Dirac’s version of quantum mechanics that incorporated special relativity An antiparticle has the same mass as the particle, but the opposite charge An antiparticle has the same mass as the particle, but the opposite charge The positron (electron’s antiparticle) was discovered by Anderson in 1932 The positron (electron’s antiparticle) was discovered by Anderson in 1932 Since then, it has been observed in numerous experiments Since then, it has been observed in numerous experiments Practically every known elementary particle has a distinct antiparticle Practically every known elementary particle has a distinct antiparticle Exceptions – the photon and the neutral pi particles are their own antiparticles Exceptions – the photon and the neutral pi particles are their own antiparticles

Feynman Diagrams A graphical representation of the interaction between two particles A graphical representation of the interaction between two particles Feynman diagrams are named for Richard Feynman who developed them 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 is the field particle that mediates the interaction The photon transfers energy and momentum from one electron to the other The photon transfers energy and momentum from one electron to the other The photon is called a virtual photon 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 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 existance of the virtual photon would violate the law of conservation of energy The existance of the virtual photon would 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 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 The virtual photon can exist for short time intervals, such that ΔE~  / Δt

Feynman Diagram – Proton and Neutron The exchange is via the nuclear force The exchange is via the nuclear force The existance of the pion is allowed in spite of conservation of energy if this energy is surrendered in a short enough time The existance of the pion is allowed in spite of conservation of energy if this energy is surrendered in a short enough time Analysis predicts the rest energy of the pion to be 130 MeV / c 2 Analysis predicts the rest energy of the pion to be 130 MeV / c 2 This is in close agreement with experimental results This is in close agreement with experimental results

Classification of Particles Two board categories Two board categories Classified by interactions Classified by interactions Hadrons – interact through strong force Hadrons – interact through strong force Leptons – interact through weak force Leptons – interact through weak force

Hadrons Interact through the strong force Interact through the strong force Two subclasses Two subclasses Mesons Mesons Decay finally into electrons, positrons, neutrinos and photons Decay finally into electrons, positrons, neutrinos and photons Integer spins Integer spins Baryons Baryons Masses equal to or greater than a proton Masses equal to or greater than a proton Noninteger spin values Noninteger spin values Decay into end products that include a proton (except for the proton) Decay into end products that include a proton (except for the proton) Composed of quarks Composed of quarks

Leptons Interact through weak force Interact through weak force All have spin of ½ All have spin of ½ Leptons appear truly elementary Leptons appear truly elementary No substructure No substructure Point-like particles Point-like particles Scientists currently believe only six leptons exist, along with their antiparticles Scientists currently believe only six leptons exist, along with their antiparticles Electron and electron neutrino Electron and electron neutrino Muon and its neutrino Muon and its neutrino Tau and its neutrino Tau and its neutrino

Conservation Laws A number of conservation laws are important in the study of elementary particles A number of conservation laws are important in the study of elementary particles Two new ones are Two new ones are Conservation of Baryon Number Conservation of Baryon Number Conservation of Lepton Number Conservation of Lepton Number

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 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 Peculiar features include Always produced in pairs 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 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 They decay much more slowly than particles decaying via strong interactions

Strangeness To explain these unusual properties, a new law, the conservation of strangeness was introduced To explain these unusual properties, a new law, the conservation of strangeness was introduced Also needed a new quantum number, S 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 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 interaction does not Strong and electromagnetic interactions obey the law of conservation of strangeness, but the weak interaction does not

Bubble Chamber Example The dashed lines represent neutral particles The dashed lines represent neutral particles At the bottom, At the bottom,  - + p  Λ 0 + K 0  - + p  Λ 0 + K 0  Then Λ 0   - + p and  K 0   + µ - + µ

Quarks Hadrons are complex particles with size and structure Hadrons are complex particles with size and structure Hadrons decay into other hadrons Hadrons decay into other hadrons There are many different hadrons There are many different hadrons Quarks are proposed as the elementary particles that constitute the hadrons Quarks are proposed as the elementary particles that constitute the hadrons Originally proposed independently by Gell- Mann and Zweig Originally proposed independently by Gell- Mann and Zweig

Original Quark Model Three types Three types u – up u – up d – down d – down s – originally sideways, now strange s – originally sideways, now strange Associated with each quark is an antiquark Associated with each quark is an antiquark The antiquark has opposite charge, baryon number and strangeness The antiquark has opposite charge, baryon number and strangeness Quarks have fractional electrical charges Quarks have fractional electrical charges +1/3 e and –2/3 e +1/3 e and –2/3 e All ordinary matter consists of just u and d quarks All ordinary matter consists of just u and d quarks

Original Quark Model – Rules All the hadrons at the time of the original proposal were explained by three rules All the hadrons at the time of the original proposal were explained by three rules Mesons consist of one quark and one antiquark Mesons consist of one quark and one antiquark This gives them a baryon number of 0 This gives them a baryon number of 0 Baryons consist of three quarks Baryons consist of three quarks Antibaryons consist of three antiquarks Antibaryons consist of three antiquarks

Additions to the Original Quark Model – Charm Another quark was needed to account for some discrepencies between predictions of the model and experimental results Another quark was needed to account for some discrepencies between predictions of the model and experimental results Charm would be conserved in strong and electromagnetic interactions, but not in weak interactions Charm would be conserved in strong and electromagnetic interactions, but not in weak interactions In 1974, a new meson, the J/Ψ was discovered that was shown to be a charm quark and charm antiquark pair In 1974, a new meson, the J/Ψ was discovered that was shown to be a charm quark and charm antiquark pair

More Additions – Top and Bottom Discovery led to the need for a more elaborate quark model Discovery led to the need for a more elaborate quark model This need led to the proposal of two new quarks This need led to the proposal of two new quarks t – top (or truth) t – top (or truth) b – bottom (or beauty) b – bottom (or beauty) Added quantum numbers of topness and bottomness Added quantum numbers of topness and bottomness Verification Verification b quark was found in a Y meson in 1977 b quark was found in a Y meson in 1977 t quark was found in 1995 at Fermilab t quark was found in 1995 at Fermilab

Numbers of Particles At the present, physicists believe the “building blocks” of matter are complete At the present, physicists believe the “building blocks” of matter are complete Six quarks with their antiparticles Six quarks with their antiparticles Six leptons with their antiparticles Six leptons with their antiparticles

Color Isolated quarks Isolated quarks Physicist now believe that quarks are permanently confined inside ordinary particles Physicist now believe that quarks are permanently confined inside ordinary particles No isolated quarks have been observed experimentally No isolated quarks have been observed experimentally The explanation is a force called the color force The explanation is a force called the color force Color force increases with increasing distance Color force increases with increasing distance This prevents the quarks from becoming isolated particles This prevents the quarks from becoming isolated particles

Colored Quarks Color “charge” occurs in red, blue, or green Color “charge” occurs in red, blue, or green Antiquarks have colors of antired, antiblue, or antigreen Antiquarks have colors of antired, antiblue, or antigreen Color obeys the Exclusion Principle Color obeys the Exclusion Principle A combination of quarks of each color produces white (or colorless) A combination of quarks of each color produces white (or colorless) Baryons and mesons are always colorless Baryons and mesons are always colorless

Quantum Chromodynamics (QCD) QCD gave a new theory of how quarks interact with each other by means of color charge 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 often called the color force The strong force between quarks is carried by gluons The strong force between quarks is carried by gluons Gluons are massless particles Gluons are massless particles There are 8 gluons, all with color charge There are 8 gluons, all with color charge When a quark emits or absorbs a gluon, its color changes When a quark emits or absorbs a gluon, its color changes

More About Color Charge Like colors repel and unlike colors attract Like colors repel and unlike colors attract Different colors attract, but not as strongly as a color and its anticolor Different colors attract, but not as strongly as a color and its anticolor The color force between color-neutral hadrons is negligible at large separations 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 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 This residual strong force is the nuclear force that binds the protons and neutrons to form nuclei

QCD Explanation of a Neutron-Proton Interaction Each quark within the proton and neutron is continually emitting and absorbing virtual gluons Each quark within the proton and neutron is continually emitting and absorbing virtual gluons Also creating and annihilating virtual quark-antiquark pairs Also creating and annihilating virtual quark-antiquark pairs When close enough, these virtual gluons and quarks can be exchanged, producing the strong force When close enough, these virtual gluons and quarks can be exchanged, producing the strong force

Grand Unification Theory (GUT) Builds on the success of the electroweak theory Builds on the success of the electroweak theory Attempted to combine electroweak and strong interactions Attempted to combine electroweak and strong interactions One version considers leptons and quarks as members of the same family 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 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 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 All matter was contained in a quark soup As time increased and temperature decreased, the forces broke apart 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 Starting as a radiation dominated universe, as the universe cooled it changed to a matter dominated universe

A Brief History of the Universe

Cosmic Background Radiation (CBR) CBR is represents the cosmic “glow” left over from the Big Bang CBR is represents the cosmic “glow” left over from the Big Bang The radiation had equal strengths in all directions The radiation had equal strengths in all directions The curve fits a blackbody at ~3K The curve fits a blackbody at ~3K There are small irregularities that allowed for the formation of galaxies and other objects 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 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 There are many common goals between the two fields

Some Questions Why so little antimatter in the Universe? Why so little antimatter in the Universe? Do neutrinos have mass? Do neutrinos have mass? Is it possible to unify electroweak and strong forces? Is it possible to unify electroweak and strong forces? Why do quark and leptons form similar but distinct families? Why do quark and leptons form similar but distinct families? Why do quarks carry fractional charge? Why do quarks carry fractional charge? What determines the masses of fundamental particles? What determines the masses of fundamental particles? Do leptons and quarks have a substructure? Do leptons and quarks have a substructure?