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Chapter 45

Chapter 45. Applications of Nuclear Physics. 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 both cases. Introduction.

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Chapter 45

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  1. Chapter 45 Applications of Nuclear Physics

  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 both cases. Introduction

  3. Interactions Involving Neutrons • Because of their charge neutrality, neutrons are not subject to Coulomb forces. • As a result, they do not interact electrically with electrons or the nucleus. • Neutrons can easily penetrate deep into an atom and collide with the nucleus. Section 45.1

  4. Fast Neutrons • A fast neutron has energy greater than approximately 1 MeV. • During its many collisions when traveling through matter, the neutron gives up some of its kinetic energy. • For fast neutrons in some materials, elastic collisions dominate. • These materials are called moderators since they moderate the originally energetic neutrons very efficiently. • Moderator nuclei should be of low mass so that a large amount of kinetic energy is transferred to them in elastic collisions. • Materials such as paraffin and water are good moderators for neutrons. Section 45.1

  5. Thermal Neutrons • Most neutrons bombarding a moderator will become thermal neutrons. • They are in thermal equilibrium with the moderator material. • Their average kinetic energy at room temperature is about 0.04 eV. • This corresponds to a neutron root-mean-square speed of about 2 800 m/s. • Thermal neutrons have a distribution of speeds. Section 45.1

  6. Neutron Capture • Once the energy of a neutron is sufficiently low, there is a high probability that it will be captured by a nucleus. • The neutron capture equation can be written as • The excited state lasts for a very short time. • The product nucleus is generally radioactive and decays by beta emission. Section 45.1

  7. Nuclear Fission • A heavy nucleus splits into two smaller nuclei. • Fission is initiated when a heavy nucleus captures a thermal neutron. • The total mass of the daughter nuclei is less than the original mass of the parent nucleus. • This difference in mass is called the mass defect. • Multiplying the mass defect by c2 gives the numerical value of the released energy. • This energy is in the form of kinetic energy associated with the motion of the neutrons and the daughter nuclei after the fission event. Section 45.2

  8. Short History of Fission • First observed in 1938 by Otto Hahn and Fritz Strassman following basic studies by Fermi. • Bombarding uranium with neutrons produced barium and lanthanum. • Lise Meitner and Otto Frisch soon explained what had happened. • After absorbing a neutron, the uranium nucleus had split into two nearly equal fragments. • About 200 MeV of energy was released. Section 45.2

  9. Fission Equation: 235U • Fission of 235U by a thermal neutron • 236U* is an intermediate, excited state that exists for about 10-12 s before splitting. • X and Y are called fission fragments. • Many combinations of X and Y satisfy the requirements of conservation of energy and charge. Section 45.2

  10. Fission Example: 235U • A typical fission reaction for uranium is Section 45.2

  11. Distribution of Fission Products • The most probable products have mass numbers A  95 and A  140. • There are also 2 to 3 neutrons released per event. Section 45.2

  12. Energy in a Fission Process • Binding energy for heavy nuclei is about 7.2 MeV per nucleon. • Binding energy for intermediate nuclei is about 8.2 MeV per nucleon. • An estimate of the energy released • Releases about 1 MeV per nucleon • 8.2 MeV – 7.2 MeV • Assume a total of 235 nucleons • Total energy released is about 235 MeV • This is the disintegration energy, Q • This is very large compared to the amount of energy released in chemical processes. Section 45.2

  13. Chain Reaction • Neutrons are emitted when 235U undergoes fission. • An average of 2.5 neutrons • 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. • When controlled, the energy can be put to constructive use. Section 45.3

  14. Chain Reaction – Diagram Section 45.3

  15. Enrico Fermi • 1901 – 1954 • Italian physicist • Nobel Prize in 1938 for producing transuranic elements by neutron irradiation and for his discovery of nuclear reactions brought about by thermal neutrons • Other contributions include theory of beta decay, free-electron theory of metal, development of world’s first fission reactor (1942) Section 45.3

  16. 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 average value of K from uranium fission is 2.5. • In practice, K is less than this • A self-sustained reaction has K = 1 Section 45.3

  17. 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 45.3

  18. Moderator • The moderator slows the neutrons. • The slower neutrons are more likely to react with 235U than 238U. • The probability of neutron capture by 238U is high when the neutrons have high kinetic energies. • Conversely, the probability of capture is low when the neutrons have low kinetic energies. • The slowing of the neutrons by the moderator makes them available for reactions with 235U while decreasing their chances of being captured by 238U. Section 45.3

  19. Reactor Fuel • Most reactors today use uranium as fuel. • Naturally occurring uranium is 99.3% 238U and 0.7% 235U • 238U almost never fissions • It tends to absorb neutrons producing neptunium and plutonium. • Fuels are generally enriched to at least a few percent 235U. Section 45.3

  20. Pressurized Water Reactor – Diagram Section 45.3

  21. Pressurized Water Reactor – Notes • This type of reactor is the most common in use in electric power plants in the US. • Fission events in the uranium in the fuel rods raise the temperature of the water contained in the primary loop. • The primary system is a closed system. • This water is maintained at a high pressure to keep it from boiling. • This water is also used as the moderator to slow down the neutrons. Section 45.3

  22. Pressurized Water Reactor – Notes, cont. • The hot water is pumped through a heat exchanger. • The heat is transferred by conduction to the water contained in a secondary system. • This water is converted into steam. • The steam is used to drive a turbine-generator to create electric power. Section 45.3

  23. Pressurized Water Reactor – Notes, final • 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. • A fraction of the neutrons produced in fission leak out before inducing other fission events. • An optimal surface area-to-volume ratio of the fuel elements is a critical design feature. Section 45.3

  24. Basic Design of a Reactor Core • Fuel elements consist of enriched uranium. • The moderator material helps to slow down the neutrons. • The control rods absorb neutrons. • All of these are surrounded by a radiation shield. Section 45.3 Section 45.3

  25. Control Rods • To control the power level, control rods are inserted into the reactor core. • These rods are made of materials that are very efficient in absorbing neutrons. • Cadmium is an example • By adjusting the number and position of the control rods in the reactor core, the K value can be varied and any power level can be achieved. • The power level must be within the design of the reactor. Section 45.3

  26. Reactor Safety – Containment • Radiation exposure, and its potential health risks, are controlled by three levels of containment: • Reactor vessel • Contains the fuel and radioactive fission products • Reactor building • Acts as a second containment structure should the reactor vessel rupture • Prevents radioactive material from contaminating the environment • Location • Reactor facilities are in remote locations Section 45.3

  27. Reactor Safety – Radioactive Materials • Disposal of waste material • Waste material contains long-lived, highly radioactive isotopes. • Must be stored over long periods in ways that protect the environment • At present, the most promising solution seems to be sealing the waste in waterproof containers and burying them in deep geological repositories. • Transportation of fuel and wastes • 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. Section 45.3

  28. 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 45.4

  29. Fusion: 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. • All of the reactions in the proton-proton cycle are exothermic. • An overview of the cycle is that four protons combine to form an alpha particle, positrons, gamma rays and neutrinos. Section 45.4

  30. Fusion in the Sun • These reactions occur in the core of a star and are responsible for the energy released by the stars. • High temperatures are required to drive these reactions. • Therefore, they are known as thermonuclear fusion reactions. Section 45.4

  31. Advantages of a Fusion Reactor • Inexpensive fuel source • Water is the ultimate fuel source. • If deuterium is used as fuel, 0.12 g of it can be extracted from 1 gal of water for about 4 cents. • Comparatively few radioactive by-products are formed. Section 45.4

  32. Considerations for a Fusion Reactor • The proton-proton cycle is not feasible for a fusion reactor. • The high temperature and density required are not suitable for a fusion reactor. • The most promising reactions involve deuterium and tritium. Section 45.4

  33. Considerations for a Fusion Reactor, cont. • Tritium is radioactive and must be produced artificially. • The Coulomb repulsion between two charged nuclei must be overcome before they can fuse. • A major problem in obtaining energy from fusion reactions. Section 45.4

  34. Potential Energy Function • The potential energy is positive in the region r > R, where the Coulomb repulsive force dominates. • It is negative where the nuclear force dominates. • The problem is to give the nuclei enough kinetic energy to overcome this repulsive force. • Can be accomplished raising the temperature of the fuel to approximately 108 K. • At this temperature, the atoms are ionized and the system contains a collection of electrons and nuclei, referred to as a plasma. Section 45.4

  35. Critical Ignition Temperature • The temperature at which the power generation rate in any fusion reaction exceeds the lost rate is called the critical ignition temperature, Tignit. • The intersections of the Pgen lines with the Plost line give the Tignit. Section 45.4

  36. Requirements for Successful Thermonuclear Reactor • High temperature ~ 108 K • Needed to give nuclei enough energy to overcome Coulomb forces • Plasma ion density, n • The number of ions present • Plasma confinement time,  • The time interval during which energy injected into the plasma remains in the plasma. Section 45.4

  37. Lawson’s Criteria • Lawson’s criteria states that a net power output in a fusion reactor is possible under the following conditions. • n≥ 1014 s/cm3 for deuterium-tritium • n≥ 1016 s/cm3 for deuterium-deuterium • These are the minima on the curves. Section 45.4

  38. Requirements, Summary • The plasma temperature must be very high. • To meet Lawson’s criterion, the product nt must be large. • For a given value of n, the probability of fusion between two particles increases as t increases. • For a given value of t, the collision rate increases as n increases. • Confinement is still a problem. Section 45.4

  39. Confinement Techniques • Magnetic confinement • Uses magnetic fields to confine the plasma • Inertial confinement • Particles’ inertia keeps them confined very close to their initial positions. Section 45.4

  40. Magnetic Confinement • One magnetic confinement device is called a tokamak. • Two magnetic fields confine the plasma inside the donut. • A strong magnetic field is produced in the windings. • A weak magnetic field is produced by the toroidal current. • The field lines are helical, they spiral around the plasma, and prevent it from touching the wall of the vacuum chamber. Section 45.4

  41. Fusion Reactors Using Magnetic Confinement • TFTR – Tokamak Fusion Test Reactor • Close to values required by Lawson criterion • JET – Joint European Torus • Reaction rates of 6 x 1017 D-T fusions per second were reached • NSTX – National Spherical Torus Experiment • Produces a spherical plasma with a hole in the center • Is able to confine the plasma with a high pressure • ITER – International Thermonuclear Experimental 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. • Fusion operation is expected to begin in 2018. Section 45.4

  42. Inertial Confinement • Uses a D-T target that has a very high particle density • Confinement time is very short. • Therefore, because of their own inertia, the particles do not have a chance to move from their initial positions. • Lawson’s criterion can be satisfied by combining high particle density with a short confinement time. Section 45.4

  43. Laser Fusion • Laser fusion is the most common form of inertial confinement. • A small D-T pellet is struck simultaneously by several focused, high intensity laser beams. • This large input energy causes the target surface to evaporate. • The third law reaction causes an inward compression shock wave. • This increases the temperature. Section 45.4

  44. Fusion Reactors Using Inertial Confinement • Omega facility • University of Rochester (NY) • Focuses 24 laser beams on the target • National Ignition Facility • Lawrence Livermore National Lab (CA) • Construction was completed in early 2009 • Will include 192 laser beams focused on D-T pellets • The lasers were fired in March 2009 and broke the megajoule record for lasers. • They delivered 1.1 MJ to a target • Fusion ignition tests are planned for 2010. Section 45.4

  45. Fusion Reactor Design – Energy • In the D-T reaction, the alpha particle carries 20% of the energy and the neutron carries 80%. • The neutrons are about 14 MeV. • The alpha particles are primarily absorbed by the plasma, increasing the plasma’s temperature. • The neutrons are absorbed by the surrounding blanket of material where their energy is extracted and used to generate electric power.

  46. Fusion Reactor Design, cont. • One scheme is to use molten lithium to capture the neutrons. • The lithium goes to a heat-exchange loop and eventually produces steam to drive turbines. Section 45.4

  47. Fusion Reactor Design, Diagram Section 45.4

  48. Some Advantages of Fusion • Low cost and abundance of fuel • Deuterium • Impossibility of runaway accidents • Decreased radiation hazards Section 45.4

  49. Some Anticipated Problems with Fusion • Scarcity of lithium • Limited supply of helium • Helium is needed for cooling the superconducting magnets used to produce the confinement fields. • Structural damage and induced radiation from the neutron bombardment Section 45.4

  50. Radiation Damage • Radiation absorbed by matter can cause damage. • The degree and type of damage depend on many factors. • Type and energy of the radiation • Properties of the matter Section 45.5

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