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Chapter 30 Nuclear Energy and Elementary Particles.

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1 Chapter 30 Nuclear Energy and Elementary Particles

2 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

3 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

4 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

5 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

6 Sequence of Events in Fission – Diagram

7 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

8 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

9 QUICK QUIZ 30.1 In the first atomic bomb, the energy released was equivalent to about 30 kilotons of TNT, where a ton of TNT releases an energy of 4.0 × 10 9 J. The amount of mass converted into energy in this event is nearest to: (a) 1  g, (b) 1 mg, (c) 1 g, (d) 1 kg, (e) 20 kilotons

10 QUICK QUIZ 30.1 ANSWER (c). The total energy released was E = (30 ×10 3 ton)(4.0 × 10 9 J/ton) = 1.2 × J. The mass equivalent of this quantity of energy is:

11 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

12 Chain Reaction – Diagram

13 Nuclear Reactor A nuclear reactor is a system designed to maintain a self-sustained chain reaction 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 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 The maximum value of K from uranium fission is 2.5 In practice, K is less than this In practice, K is less than this A self-sustained reaction has K = 1 A self-sustained reaction has K = 1

14 K Values When K = 1, the reactor is said to be critical When K = 1, the reactor is said to be critical The chain reaction is self-sustaining The chain reaction is self-sustaining When K < 1, the reactor is said to be subcritical When K < 1, the reactor is said to be subcritical The reaction dies out The reaction dies out When K > 1, the reactor is said to be supercritical When K > 1, the reactor is said to be supercritical A run-away chain reaction occurs A run-away chain reaction occurs

15 Basic Reactor Design Fuel elements consist of enriched uranium Fuel elements consist of enriched uranium The moderator material helps to slow down the neutrons The moderator material helps to slow down the neutrons The control rods absorb neutrons The control rods absorb neutrons

16 Reactor Design Considerations – Neutron Leakage Loss (or “leakage”) of neutrons from the core Loss (or “leakage”) of neutrons from the core These are not available to cause fission events These are not available to cause fission events The fraction lost is a function of the ratio of surface area to volume The fraction lost is a function of the ratio of surface area to volume Small reactors have larger percentages lost Small reactors have larger percentages lost If too many neutrons are lost, the reactor will not be able to operate If too many neutrons are lost, the reactor will not be able to operate

17 Reactor Design Considerations – Neutron Energies Slow neutrons are more likely to cause fission events Slow neutrons are more likely to cause fission events Most neutrons released in the fission process have energies of about 2 MeV 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 In order to sustain the chain reaction, the neutrons must be slowed down A moderator surrounds the fuel A moderator surrounds the fuel Collisions with the atoms of the moderator slow the neutrons down as some kinetic energy is transferred 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 Most modern reactors use heavy water as the moderator

18 Reactor Design Considerations – Neutron Capture Neutrons may be captured by nuclei that do not undergo fission Neutrons may be captured by nuclei that do not undergo fission Most commonly, neutrons are captured by 238 U Most commonly, neutrons are captured by 238 U The possibility of 238 U capture is lower with slow neutrons The possibility of 238 U capture is lower with slow neutrons The moderator helps minimize the capture of neutrons by 238 U The moderator helps minimize the capture of neutrons by 238 U

19 Reactor Design Considerations – Power Level Control A method of control is needed to adjust the value of K to near 1 A method of control is needed to adjust the value of K to near 1 If K >1, the heat produced in the runaway reaction can melt the reactor If K >1, the heat produced in the runaway reaction can melt the reactor Control rods are inserted into the core to control the power level Control rods are inserted into the core to control the power level Control rods are made of materials that are very efficient at absorbing neutrons Control rods are made of materials that are very efficient at absorbing neutrons Cadmium is an example Cadmium is an example By adjusting the number and position of the control rods, various power levels can be maintained By adjusting the number and position of the control rods, various power levels can be maintained

20 Pressurized Water Reactor – Diagram

21 Pressurized Water Reactor – Notes This type of reactor is commonly used in electric power plants in the US This type of reactor is commonly used in electric power plants in the US Fission events in the reactor core supply heat to the water contained in the primary system Fission events in the reactor core supply heat to the water contained in the primary system The primary system is a closed system The primary system is a closed system This water is maintained at a high pressure to keep it from boiling This water is maintained at a high pressure to keep it from boiling The hot water is pumped through a heat exchanger The hot water is pumped through a heat exchanger

22 Pressurized Water Reactor – Notes, cont The heat is transferred to the water contained in a secondary system The heat is transferred to the water contained in a secondary system This water is converted into steam This water is converted into steam The steam is used to drive a turbine- generator to create electric power The steam is used to drive a turbine- generator to create electric power The water in the secondary system is isolated from the water in the primary system The water in the secondary system is isolated from the water in the primary system This prevents contamination of the secondary water and steam by the radioactive nuclei in the core This prevents contamination of the secondary water and steam by the radioactive nuclei in the core

23 Reactor Safety – Containment Radiation exposure, and its potential health risks, are controlled by three levels of containment Radiation exposure, and its potential health risks, are controlled by three levels of containment Reactor vessel Reactor vessel Contains the fuel and radioactive fission products Contains the fuel and radioactive fission products Reactor building Reactor building Acts as a second containment structure should the reactor vessel rupture Acts as a second containment structure should the reactor vessel rupture Location Location Reactor facilities are in remote locations Reactor facilities are in remote locations

24 Reactor Safety – Loss of Water If the water flow was interrupted, the nuclear reaction could stop immediately If the water flow was interrupted, the nuclear reaction could stop immediately However, there could be enough residual heat to build up and melt the fuel elements However, there could be enough residual heat to build up and melt the fuel elements The molten core could also melt through the containment vessel and into the ground The molten core could also melt through the containment vessel and into the ground Called the China Syndrome Called the China Syndrome If the molten core struck ground water, a steam explosion could spread the radioactive material to areas surrounding the power plant If the molten core struck ground water, a steam explosion could spread the radioactive material to areas surrounding the power plant Reactors are built with emergency cooling systems that automatically flood the core if coolant is lost Reactors are built with emergency cooling systems that automatically flood the core if coolant is lost

25 Reactor Safety – Radioactive Materials Disposal of waste material Disposal of waste material Waste material contains long-lived, highly radioactive isotopes Waste material contains long-lived, highly radioactive isotopes Must be stored over long periods in ways that protect the environment Must be stored over long periods in ways that protect the environment Present solution is sealing the waste in waterproof containers and burying them in deep salt mines Present solution is sealing the waste in waterproof containers and burying them in deep salt mines Transportation of fuel and wastes Transportation of fuel and wastes Accidents during transportation could expose the public to harmful levels of radiation Accidents during transportation could expose the public to harmful levels of radiation Department of Energy requires crash tests and manufacturers must demonstrate that their containers will not rupture during high speed collisions Department of Energy requires crash tests and manufacturers must demonstrate that their containers will not rupture during high speed collisions

26 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

27 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

28 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

29 Fusion Reactors Energy releasing fusion reactions are called thermonuclear fusion reactions 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 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 A thermonuclear reactor that can deliver a net power output over a reasonable time interval is not yet a reality

30 Advantages of a Fusion Reactor Inexpensive fuel source Inexpensive fuel source Water is the ultimate 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 If deuterium is used as fuel, 0.06 g of it can be extracted from 1 gal of water for about 4 cents Comparitively few radioactive by- products are formed Comparitively few radioactive by- products are formed

31 Considerations for a Fusion Reactor The proton-proton cycle is not feasible 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 high temperature and density required are not suitable for a fusion reactor The most promising reactions involve deutrium and tritium The most promising reactions involve deutrium and tritium

32 Considerations for a Fusion Reactor, cont Tritium is radioactive and must be produced artifically Tritium is radioactive and must be produced artifically The Coulomb repulsion between two charged nuclei must be overcome before they can fuse The Coulomb repulsion between two charged nuclei must be overcome before they can fuse

33 Requirements for Successful Thermonuclear Reactor High temperature ~ 10 8 K High temperature ~ 10 8 K Needed to give nuclei enough energy to overcome Coulomb forces Needed to give nuclei enough energy to overcome Coulomb forces At these temperatures, the atoms are ionized, forming a plasma At these temperatures, the atoms are ionized, forming a plasma Plasma ion density, n Plasma ion density, n The number of ions present The number of ions present Plasma confinement time,  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 The time the interacting ions are maintained at a temperature equal to or greater than that required for the reaction to proceed successfully

34 Lawson’s Criteria Lawson’s criteria states that a net power output in a fusion reactor is possible under the following conditions Lawson’s criteria states that a net power output in a fusion reactor is possible under the following conditions n   s/cm 3 for deuterium-tritium n   s/cm 3 for deuterium-tritium n   s/cm 3 for deuterium-deuterium n   s/cm 3 for deuterium-deuterium The plasma confinement time is still a problem The plasma confinement time is still a problem

35 Magnetic Confinement  One magnetic confinement device is called a tokamak Two magnetic fields confine the plasma inside the doughnut Two magnetic fields confine the plasma inside the doughnut A strong magnetic field is produced in the windings A strong magnetic field is produced in the windings A weak magnetic field is produced in the toroid 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 The field lines are helical, spiral around the plasma, and prevent it from touching the wall of the vacuum chamber

36 Current Research in Fusion Reactors NSTX – National Spherical Torus Experiment NSTX – National Spherical Torus Experiment Produces a spherical plasma with a hole in the center Produces a spherical plasma with a hole in the center Is able to confine the plasma with a high pressure Is able to confine the plasma with a high pressure ITER – International Thermonuclear Experimental Reactor ITER – International Thermonuclear Experimental Reactor An international collaboration involving four major fusion programs is working on building this reactor An international collaboration involving four major fusion programs is working on building this reactor It will address remaining technological and scientific issues concerning the feasibility of fusion power It will address remaining technological and scientific issues concerning the feasibility of fusion power

37 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

38 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

39 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

40 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

41 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

42 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

43 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

44 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

45 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

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

47 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

48 Mesons Developed from a theory to explain the strong nuclear force Developed from a theory to explain the strong nuclear force Background notes Background notes Two atoms can form a covalent bond by the exchange of electrons Two atoms can form a covalent bond by the exchange of electrons In electromagnetic interactions, charged particles interact by exchanging a photon In electromagnetic interactions, charged particles interact by exchanging a photon A new particle was proposed to explain the strong nuclear force A new particle was proposed to explain the strong nuclear force It was called a meson It was called a meson

49 Mesons, cont The proposed particle would have a mass about 200 times that of the electron The proposed particle would have a mass about 200 times that of the electron Efforts to establish the existance of the particle were done by studying cosmic rays in the 1930’s Efforts to establish the existance of the particle were done by studying cosmic rays in the 1930’s Actually discovered multiple particles Actually discovered multiple particles Pi meson (pion) Pi meson (pion) Muon Muon Not a meson Not a meson

50 Pion There are three varieties of pions There are three varieties of pions  + and  -  + and  - Mass of MeV/c 2 Mass of MeV/c 2  0  0 Mass of MeV/c 2 Mass of MeV/c 2 Pions are very unstable Pions are very unstable  - decays into a muon and an antineutrino with a lifetime of about 2.6 x10 -8 s  - decays into a muon and an antineutrino with a lifetime of about 2.6 x10 -8 s

51 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

52 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

53 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

54 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

55 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

56 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

57 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

58 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

59 Conservation of Baryon Number Whenever a baryon is created in a reaction or a decay, an antibaryon is also created Whenever a baryon is created in a reaction or a decay, an antibaryon is also created B is the Baryon Number B is the Baryon Number B = +1 for baryons B = +1 for baryons B = -1 for antibaryons B = -1 for antibaryons B = 0 for all other particles 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 The sum of the baryon numbers before a reaction or a decay must equal the sum of baryon numbers after the process

60 Conservation of Lepton Number There are three conservation laws, one for each variety of lepton 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 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

61 Conservation of Lepton Number, cont Assigning electron-lepton numbers Assigning electron-lepton numbers L e = 1 for the electron and the electron neutrino L e = 1 for the electron and the electron neutrino L e = -1 for the positron and the electron antineutrino L e = -1 for the positron and the electron antineutrino L e = 0 for all other particles 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 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 Muon- and tau-lepton numbers are assigned similarly to electron-lepton numbers

62 QUICK QUIZ 30.2 Which of the following reactions cannot occur?

63 QUICK QUIZ 30.2 ANSWER (a). This reaction fails to conserve charge and cannot occur.

64 QUICK QUIZ 30.3 Which of the following reactions cannot occur?

65 QUICK QUIZ 30.3 ANSWER (b). This reaction fails to conserve charge and cannot occur.

66 QUICK QUIZ 30.4 Suppose a claim is made that the decay of a neutron is given by n  p + + e _. Which of the following conservation laws are violated by this proposed decay scheme? (a) energy, (b) linear momentum, (c) spin angular momentum, (d) electric charge, (e) lepton number, (f) baryon number.

67 QUICK QUIZ 30.4 ANSWER (c), (e). The proton and the electron each have spin s = ½. The two possible resultant spins after decay are 1 (spins aligned) or 0 (spins anti-aligned). Neither equal the spin of a neutron, s = ½, so spin angular momentum is not conserved. The are no leptons present before the proposed decay and one lepton (the electron) present after decay. Thus, the decay also fails to conserve lepton number.

68 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

69 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

70 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

71 The Eightfold Way Many classification schemes have been proposed to group particles into families Many classification schemes have been proposed to group particles into families These schemes are based on spin, baryon number, strangeness, etc. These schemes are based on spin, baryon number, strangeness, etc. The eightfold way is a symmetic pattern proposed by Gell-Mann and Ne’eman The eightfold way is a symmetic pattern proposed by Gell-Mann and Ne’eman There are many symmetrical patterns that can be developed There are many symmetrical patterns that can be developed The patterns of the eightfold way have much in common with the periodic table The patterns of the eightfold way have much in common with the periodic table Including predicting missing particles Including predicting missing particles

72 An Eightfold Way for Baryons A hexagonal pattern for the eight spin ½ baryons A hexagonal pattern for the eight spin ½ baryons Stangeness vs. charge is plotted on a sloping coordinate system Stangeness vs. charge is plotted on a sloping coordinate system Six of the baryons form a hexagon with the other two particles at its center Six of the baryons form a hexagon with the other two particles at its center

73 An Eightfold Way for Mesons The mesons with spins of 0 can be plotted The mesons with spins of 0 can be plotted Strangeness vs. charge on a sloping coordinate system is plotted Strangeness vs. charge on a sloping coordinate system is plotted A hexagonal pattern emerges A hexagonal pattern emerges The particles and their antiparticles are on opposite sides on the perimeter of the hexagon The particles and their antiparticles are on opposite sides on the perimeter of the hexagon The remaining three mesons are at the center The remaining three mesons are at the center

74 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

75 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

76 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

77 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

78 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

79 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

80 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

81 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

82 Quark Structure of a Meson A red quark is attracted to an antired quark A red quark is attracted to an antired quark The quark – antiquark pair forms a meson The quark – antiquark pair forms a meson The resulting meson is colorless The resulting meson is colorless

83 Quark Structure of a Baryon Quarks of different colors attract each other Quarks of different colors attract each other The quark triplet forms a baryon The quark triplet forms a baryon The baryon is colorless The baryon is colorless

84 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

85 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

86 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

87 Weak Interaction The weak interaction is an extremely short- ranged force The weak interaction is an extremely short- ranged force This short range implies the mediating particles are very massive 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 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 Also responsible for the decay of  and  leptons into electrons

88 Weak Interaction, cont The weak interaction is very important because it governs the stability of the basic matter particles The weak interaction is very important because it governs the stability of the basic matter particles The weak interaction is not symmetrical The weak interaction is not symmetrical Not symmetrical under mirror reflection Not symmetrical under mirror reflection Not symmetrical under charge exchange Not symmetrical under charge exchange

89 Electroweak Theory The electroweak theory unifies electromagnetic and weak interactions 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 The theory postulates that the weak and electromagnetic interactions have the strength at very high particle energies Viewed as two different manifestions of a single interaction Viewed as two different manifestions of a single interaction

90 The Standard Model A combination of the electroweak theory and QCD form the standard model A combination of the electroweak theory and QCD form the standard model Essential ingredients of the standard model Essential ingredients of the standard model The strong force, mediated by gluons, holds the quarks together to form composite particles The strong force, mediated by gluons, holds the quarks together to form composite particles Leptons participate only in electromagnetic and weak interactions Leptons participate only in electromagnetic and weak interactions The electromagnetic force is mediated by photons The electromagnetic force is mediated by photons The weak force is mediated by W and Z bosons The weak force is mediated by W and Z bosons

91 The Standard Model – Chart

92 Mediator Masses Why does the photon have no mass while the W and Z bosons do have mass? Why does the photon have no mass while the W and Z bosons do have mass? Not answered by the Standard Model Not answered by the Standard Model The difference in behavior between low and high energies is called symmetry breaking The difference in behavior between low and high energies is called symmetry breaking The Higgs boson has been proposed to account for the masses 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 Large colliders are necessary to achieve the energy needed to find the Higgs boson

93 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

94 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

95 A Brief History of the Universe

96 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

97 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

98 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?


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