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Chapter 45 Applications of Nuclear Physics Processes of Nuclear Energy Fission Fusion A nucleus of large mass number splits into two smaller nuclei Two light nuclei fuse to form a heavier nucleus Large amounts of energy are released in both cases 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 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 to a nucleus For fast neutrons in some materials, elastic collisions dominate These materials are called moderators since they moderate the originally energetic neutrons very efficiently 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 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 1 0 n AZ XAZ1 X*AZ1 X The excited state lasts for a very short time The product nucleus is generally radioactive and decays by beta emission 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 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 Fission Equation: 235U Fission of 235U by a thermal neutron 236 n 235 U 92 92 U* X Y neutrons 1 0 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 Fission Example: 235U A typical fission reaction for uranium is 141 92 1 n 235 U Ba Kr 3 92 56 36 0n 1 0 Distribution of Fission Products The most probable products have mass numbers A 140 and A 95 There are also an average of 2.5 neutrons released per event Energy in a Fission Process Binding energy for heavy nuclei is about 7.2 MeV per nucleon Binding energy for intermediate nuclei is about 8.2 MeV per nucleon Therefore, the fission fragments have less mass than the nucleons in the original nuclei This decrease in mass per nucleon appears as released energy in the fission event Energy, cont. An estimate of the energy released 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 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 Chain Reaction – Diagram Active Figure 45.3 Use the active figure to observe the chain reaction PLAY ACTIVE FIGURE Enrico Fermi 1901 – 1954 Italian physicist Nobel Prize in 1938 for producing transuranic elements by neutron irradiation Other contributions include theory of beta decay, freeelectron theory of metal, development of world’s first fission reactor (1942) 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 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 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 K Values When K = 1, the reactor is said to be critical When K < 1, the reactor is said to be subcritical The chain reaction is self-sustaining The reaction dies out When K > 1, the reactor is said to be supercritical A run-away chain reaction occurs Pressurized Water Reactor – Diagram 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 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 turbinegenerator to create electric power 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 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 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 Reactor Safety – Containment Radiation exposure, and its potential health risks, are controlled by three levels of containment: Reactor vessel Reactor building Contains the fuel and radioactive fission products 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 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 Nuclear Fusion Nuclear fusion occurs when two light nuclei combine to form a heavier nucleus The mass of the final nucleus is less than the masses of the original nuclei This loss of mass is accompanied by a release of energy Fusion: 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 H H H e 1 1 1 1 2 1 H 21H32 He 1 1 Then H 32 He 42 He e 1 1 or 3 2 He 32 He 42 He 11H11H 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 Fusion Reactions, final 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 and two positrons 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 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 H 21H 32 H 01n Q 3.27 MeV 2 1 H H H H Q 403 . MeV 2 1 2 1 3 1 1 1 H 31H 42 He 01n Q 1759 . MeV 2 1 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 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 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 gen lines with the lost line give the Tignit Requirements for Successful Thermonuclear Reactor High temperature ~ 108 K Plasma ion density, n Needed to give nuclei enough energy to overcome Coulomb forces At these temperatures, the atoms are ionized, forming a plasma The number of ions present Plasma confinement time, The time interval during which energy injected into the plasma remains in the plasma 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 Requirements, Summary The plasma temperature must be very high To meet Lawson’s criterion, the product n must be large For a given value of n, the probability of fusion between two particles increases as increases For a given value of , the collision rate increases as n increases Confinement is still a problem Confinement Techniques Magnetic confinement Uses magnetic fields to confine the plasma Inertial confinement Particles’ inertia keeps them confined very close to their initial positions 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 Fusion Reactors Using Magnetic Confinement TFTR – Tokamak Fusion Test Reactor NSTX – National Spherical Torus Experiment Close to values required by Lawson criterion 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 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 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 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) Currently under construction Will include 192 laser beams focused on D-T pellets Fusion ignition tests are planned for 2010 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 Active Figure 45.12 Use the active figure to observe different fusion reactions Measure the energy released PLAY ACTIVE FIGURE Fusion Reactor Design, Particles 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 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 Fusion Reactor Design, Diagram Some Advantages of Fusion Low cost and abundance of fuel Deuterium Impossibility of runaway accidents Decreased radiation hazards 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 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 Radiation Damage, cont. Radiation damage in the metals used in the reactors comes from neutron bombardment They can be weakened by high fluxes of energetic neutrons producing metal fatigue The damage is in the form of atomic displacements, often resulting in major changes in the properties of the material Radiation damage in biological organisms is primarily due to ionization effects in cells Ionization disrupts the normal functioning of the cell Types of Damage in Cells Somatic damage is radiation damage to any cells except reproductive ones Can lead to cancer at high radiation levels Can seriously alter the characteristics of specific organisms Genetic damage affects only reproductive cells Can lead to defective offspring Damage Dependence on Penetration Damage caused by radiation also depends on the radiation’s penetrating power Alpha particles cause extensive damage, but penetrate only to a shallow depth Due to their charge, they will have a strong interaction with other charged particles Neutrons do not interact with material and so penetrate deeper, causing significant damage Gamma rays can cause severe damage, but often pass through the material without interaction Units of Radiation Exposure The roentgen (R) is defined as That amount of ionizing radiation that produces an electric charge of 3.33 x 10-10 C in 1 cm3 of air under standard conditions Equivalently, that amount of radiation that increases the energy of 1 kg of air by 8.76 x 10-3 J One rad (radiation absorbed dose) That amount of radiation that increases the energy of 1 kg of absorbing material by 1 x 10-2 J More Units The RBE (relative biological effectiveness) The number of rads of x-radiation or gamma radiation that produces the same biological damage as 1 rad of the radiation being used Accounts for type of particle which the rad itself does not The rem (radiation equivalent in man) Defined as the product of the dose in rad and the RBE factor Dose in rem = dose in rad x RBE RBE Factors, A Sample Radiation Levels Natural sources – rocks and soil, cosmic rays Upper limit suggested by US government Called background radiation About 0.13 rem/yr 0.50 rem/yr Excludes background Occupational 5 rem/yr for whole-body radiation Certain body parts can withstand higher levels Ingestion or inhalation is most dangerous Radiation Levels, cont. 50% mortality rate About 50% of the people exposed to a dose of 400 to 500 rem will die New SI units of radiation dosages The gray (Gy) replaces the rad The sievert (Sv) replaces the rem SI Units, Table Radiation Detectors, Introduction Radiation detectors exploit the interactions between particles and matter to allow a measurement of the particles’ characteristics Things that can be measured include: Energy Momentum Charge Existence Early Detectors Photographic emulsion The path of the particle corresponds to points at which chemical changes in the emulsion have occurred Cloud chamber Contains a gas that has been supercooled Energetic particles ionize the gas along the particles’ paths Early Detectors, Cont. Bubble chamber Uses a liquid maintained near its boiling point Ions produced by incoming charged particles leave bubble tracks The picture is an artificially colored bubble chamber photograph Contemporary Detectors Ion chamber Electron-ion pairs are generated as radiation passes through a gas and produces an electric signal The current is proportional to the number of pairs produced A proportional counter is an ion chamber that detects the presence of the particle and measures its energy Geiger Counter A Geiger counter is the most common form of an ion chamber used to detect radiation When a gamma ray or particle enters the thin window, the gas is ionized The released electrons trigger a current pulse The current is detected and triggers a counter or speaker Geiger Counter, cont. The Geiger counter easily detects the presence of a particle The energy lost by the particle in the counter is not proportional to the current pulse produced Therefore, the Geiger counter cannot be used to measure the energy of a particle Other Detectors The semiconductor-diode detector A reverse-bias p-n junction As a particle passes through the junction, a brief pulse of current is created and measured The scintillation counter Uses a solid or liquid material whose atoms are easily excited by radiation The excited atoms emit photons as they return to their ground state With a photomultiplier, the photons can be converted into an electrical signal Other Detectors, cont. Track detectors Various devices used to view the tracks or paths of charged particles directly The energy and momentum of these energetic particles are found from the curvature of their path in a magnetic field of known magnitude and direction Other Detectors, Final Spark chamber A counting device that consists of an array of conducting parallel plates and is capable of recording a three-dimensional track record Drift chamber A newer version of the spark chamber Has thousands of high-voltage wires throughout the space of the detector Applications of Radiation Tracing Radioactive particles can be used to trace chemicals participating in various reactions Example, 131I to test thyroid action Also to analyze circulatory system Also useful in agriculture and other applications Materials analysis Neutron activation analysis uses the fact that when a material is irradiated with neutrons, nuclei in the material absorb the neutrons and are changed to different isotopes Applications of Radiation, cont. Radiation therapy Radiation causes the most damage to rapidly dividing cells Therefore, it is useful in cancer treatments Food preservation High levels of radiation can destroy or incapacitate bacteria or mold spores