1. Chapter 30 Nuclear Energy and Elementary Particles

2. 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. Introduction

3. Forces and Particles Fundamental interactions govern the behavior of subatomic particles. The current theory of elementary particles states that all particles come from only two families – Quarks – Leptons Introduction

4. 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. Section 30.1

5. Fission Equation Fission of 235 U by a slow (low energy) neutron – 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. Section 30.1

6. More About Fission of 235 U About 90 different daughter nuclei can be formed. Several neutrons are also produced in each fission event. Example: The fission fragments and the neutrons have a great deal of KE following the event. Section 30.1

7. Sequence of Events in Fission 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. 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. Section 30.1

8. Sequence of Events in Fission – Diagram Section 30.1

9. 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 235 U can release energy equal to about 20000 tons of TNT Section 30.1

10. Chain Reaction – Diagram Section 30.1

11. 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 Section 30.1

12. 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. Section 30.1

13. Basic Reactor Design Fuel elements consist of enriched uranium. The moderator material helps to slow down the neutrons. The control rods absorb neutrons. Section 30.1

14. 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. Section 30.1

15. Reactor Design Considerations – Neutron Energies Slow neutrons are more likely to cause fission events. Slow neutrons are not captured by 235 U The moderator slows the neutron. – 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. Section 30.1

16. 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 Section 30.1

17. 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. Section 30.2

18. 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. Section 30.2

19. 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 1 H is deuterium, and may be written as 2 1 D Section 30.2

20. 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. Section 30.2

21. Advantages of a Fusion Reactor Inexpensive fuel source – Water is the ultimate fuel source. – If deuterium is used as fuel, 0.06 g of it can be extracted from 1 gal of water for about 4 cents. Comparatively few radioactive by-products are formed. Section 30.2

22. Considerations for a Fusion Reactor The most promising reactions involve deuterium (D) and tritium (T). Section 30.2

23. 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. Section 30.2

24. 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 Section 30.2

25. Lawson’s Criterion Lawson’s criterion 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. Section 30.2

26. 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. Section 30.2

27. 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. Section 30.2

28. Elementary Particles Atom constituents – Proton, neutron, and electron – Were viewed as elementary because they are very stable Other particles – Numerous other particles have been found. – These particles decay rapidly. Section 30.3

29. Fundamental Particles Quarks – Make up protons and neutrons for example Leptons – Electron is an example Particles that convey forces – Photon is an example Section 30.3

30. Fundamental Forces All particles in nature are subject to four fundamental forces. – Strong force – Electromagnetic force – Weak force – Gravitational force Section 30.3

31. 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 Section 30.3

32. 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 Section 30.3

33. 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. Section 30.3

34. 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 Section 30.3

35. 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. Section 30.3

36. Forces and Mediating Particles Interaction (force) Mediating Field Particle StrongGluon ElectromagneticPhoton WeakW ± and Z 0 GravitationalGravitons Section 30.3

37. 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 Section 30.3

38. Feynman Diagrams A graphical representation of the interaction between two particles Feynman diagrams are named for Richard Feynman who developed them. Section 30.3

39. 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 Section 30.3

40. 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 Section 30.3

41. Field Quanta All the field quanta have been discovered except for the graviton. Section 30.3

42. 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 Section 30.4

43. 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 Section 30.4

44. Classification of Particles Two broad categories – Excluding those that transmit forces 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 Section 30.5

45. 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 Section 30.5

46. Leptons Participate in the weak interaction All have spin of ½ Leptons appear truly elementary. – No substructure (to the limit of current experiments) – 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 Section 30.5

47. Conservation Laws A number of conservation laws are important in the study of elementary particles. The new ones are – Conservation of Baryon Number – Conservation of Lepton Number – Conservation of Strangeness Section 30.6

48. 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 Law of Conservation of Baryon Number states the sum of the baryon numbers before a reaction or a decay must equal the sum of baryon numbers after the process. Section 30.6

49. Proton Stability Absolute conservation of baryon number indicates the proton must be absolutely stable – Otherwise, it could decay into a positron and a neutral pion Never been observed Currently can say the proton has a half-life of at least 10 31 years Some theories indicate the proton can decay. – If so, baryon number would not be absolutely conserved Section 30.6

50. Conservation of Lepton Number There are three conservation laws, one for each variety of lepton. Law of Conservation of Electron-Lepton Number states that the sum of electron- lepton numbers before a reaction or a decay must equal the sum of the electron-lepton number after the process. Section 30.6

51. 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. Section 30.6

52. 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. Section 30.6

53. Strangeness To explain these unusual properties, a new law, conservation of strangeness, was introduced. – Also needed a new quantum number, S S = ±1 for strange particles, S = 0 for nonstrange particles – 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. Section 30.6

54. Bubble Chamber Example The dashed lines represent neutral particles. At the bottom,  - + p  Λ 0 + K 0 Then Λ 0   + p and K 0   + µ - + µ Section 30.6

55. Murray Gell-Mann 1929 – Worked on theoretical studies of subatomic particles Nobel Prize in 1969 Section 30.7

56. 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 Section 30.7

57. 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. Particles with spin 1/2 and 3/2 are called fermions. Section 30.7

58. 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. Particles with spin 0 or 1 are called bosons. Section 30.7

59. Eightfold Way Patterns The patterns of the eightfold way have much in common with the periodic table. – Whenever a vacancy occurs in the pattern, experimentalists have a guide for their investigations. Example: Ω - was predicted to have a spin 3/2, a charge - 1, a strangeness -3, and a mass of about 1680 MeV/c 2 A short time later, experimenters at Brookhaven found the particle and confirmed all its properties. Section 30.7

60. Quarks Hadrons are complex particles with size and structure. There are many different hadrons. Quarks are proposed as the elementary particles that constitute the hadrons. Section 30.8

61. Quark Model Six quarks – 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. Section 30.8

62. 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. Section 30.8

63. Quark Model – Particle Make-up All the hadrons at the time of the original proposal were explained by these rules. – Mesons consist of one quark and one antiquark. This gives them a baryon number of 0. – Baryons consist of three quarks. See table 30.3 for quark summary. Section 30.8

64. Quark Model – Particle Examples Section 30.8

65. Colored Quarks Color “charge” occurs in red, blue, or green. – Antiquarks have colors of antired, antiblue, or antigreen. – Color with quarks has nothing to do with visual sensation from light. – It is a convenient name for a property analogous to electric charge. Color obeys the Exclusion Principle. A combination of quarks of each color produces white (or colorless). Baryons and mesons are always colorless. Section 30.8

66. 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. Section 30.8

67. Quark Structure of a Baryon Quarks of different colors attract each other. The quark triplet forms a baryon. The baryon is colorless. Section 30.8

68. 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. Section 30.8

69. 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. Section 30.8

70. 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 Section 30.9

71. 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 Section 30.9

72. Electroweak Theory The electroweak theory unifies electromagnetic and weak interactions. The theory postulates that the weak and electromagnetic interactions have the same strength at very high particle energies. – Viewed as two different manifestations of a single interaction Section 30.9

73. 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. Section 30.9

74. The Standard Model – Chart Section 30.9

75. 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. Section 30.9

76. 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. – Most GUT theories predict that protons are unstable and will decay. Section 30.9

77. 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. Section 30.10

78. A Brief History of the Universe Section 30.10

79. 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 Section 30.10

80. 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. Section 30.10

81. Questions in Cosmology – Dark Matter When the velocities of stars in our galaxy are measured, the mass of the galaxy necessary to keep the stars orbiting does not match the mass found in luminous stars. From the velocity profile of stars, about 90% of the matter in the galaxy would consist of dark matter. Section 30.11

82. Candidates for Dark Matter Neutrinos – Since neutrinos oscillate, they are now thought to have mass. – Since stars produce enormous numbers of neutrinos, even having a small mass could account for dark matter. WIMPs – Weakly Interacting Massive Particle Left over from the Big Bang Section 30.11

83. Alternative Explanations MOND – Modified Newtonian Dynamics – Newton’s Law of Gravitation doesn’t hold over large distances. – So far it hasn’t worked well enough to gain widespread acceptance General Relativity – Used instead of Newton’s Law of Gravitation Some combination of new kinds of matter and a modification of gravity theory? Section 30.11

84. Dark Energy Observations indicated that the universe was expanding and accelerating The accelerated expansion could not be caused by normal matter nor dark matter. – Both would exert attractive gravitational forces. It is thought that a new type of energy, called dark energy, exerts a repulsive force. – This causes the universe to expand at a rate greater than that predicted by general relativity. Section 30.11

85. Composition of the Universe The theorized composition of the universe – 4% normal matter – 23% dark matter Causes the increased gravitation attraction on the galactic scale – 73% dark energy Causes the accelerated expansion of the universe Section 30.11

86. Unanswered Questions About the Universe Horizon problem – The universe seems too uniform – How can equilibrium be achieved when the parts of the universe are so far apart they can’t exchange energy? Flatness problem – Cosmic microwave background radiation suggests a flat universe. – A flat universe is in unstable equilibrium. – Unlikely the universe was so finely tuned early in its evolution Section 30.11

87. Possible Fates of the Universe A closed universe would expand, but then collapse back on itself. – The Big Crunch A flat universe could expand forever. – The expansion would eventually slow to zero as cosmic time approached infinity. An open universe would accelerate forever. Section 30.11

88. Another Unanswered Question Monopole problem – Studies of the standard model in the early universe show that large numbers of magnetic monopoles should have been created. – Monopoles have never been observed. Section 30.11

89. Possible Answer to the Questions Inflationary model of the universe – The inflation field caused the universe to enter a very rapid expansion phase. – Answers the previously posed questions Monopoles would be dilute enough that few would exist in the observable universe. Just prior to expansion, the universe was very small, so it would be in thermal equilibrium. The rapid expansion would cause the curvature to flatten out. Section 30.11

90. 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. Section 30.12

91. Some Questions Why so little antimatter in the Universe? Do neutrinos have mass? – How do they contribute to the dark matter in the universe? Explanation of why the expansion of the universe is accelerating? Is there a kind of antigravity force (or dark energy) acting between widely separated galaxies? Is it possible to unify electroweak and strong forces? Why do quarks and leptons form similar but distinct families? Section 30.12

92. 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? Section 30.12

93. Strings? Many physicists believe leptons and quarks have a substructure. These are not infinitesimal points, but tiny vibrating strings. The final Theory of Everything has not been found. Section 30.12