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CU-Boulder PHYS 3070 - Units of Mass and Energy

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http://physics.colorado.edu/phys3070Units of Mass and EnergyClicker questionClicker questionStable and unstableTypes of radioactivityTypes of radioactivityTypes of radioactivityHalf-lifeHalf-lifeProperties of UraniumProperties of UraniumFormation of UraniumInduced fissionInduced fissionInduced fissionFirst solution – “Little Boy”Generating powerUsing low-enrichment uraniumEnriched uranium reactorJudah Levine, 3070L21 1http://physics.colorado.edu/phys3070http://physics.colorado.edu/phys3070Judah LevineJudah LevineJILA SJILA [email protected]@colorado.edu303 492303 492--7785 (27785 (2--7785)7785)M,F 11M,F 11--Noon, W 1Noon, W 1--3 pm3 pmalso by appointmentalso by appointmentPower point files for all lectures Power point files for all lectures now on the course web pagenow on the course web pageJudah Levine, 3070L21 2Units of Mass and EnergyUnits of Mass and Energy1 electron-volt= 1 eV= 1.6×10-19joules1 million electron-volts= 1 MeV= 1.6×10-13joules1 atomic mass unit= 1 amu= 1.66×10-27kgE=mc2m in kg, E in joules(c=3×108m/s)Mass is no longer an absolute constantJudah Levine, 3070L21 3Clicker questionClicker question1 million electron-volts= 1 MeV= 1.6×10-13joules1 atomic mass unit= 1 amu= 1.66×10-27kgE=mc2m in kg, E in joules(c=3×108m/s)Suppose I convert 1 amu of mass into energy. How much energy do I get (in MeV)?A: 111 MeVB: 346 MeVC: 521 MeVD: 726 MeVE: 931 MeVJudah Levine, 3070L21 4Clicker questionClicker questionSuppose I convert 1 amu of mass into energy. How much Energy do I get (in MeV)?1 million electron-volts= 1 MeV= 1.6×10-13joules1 atomic mass unit= 1 amu= 1.66×10-27kgE=mc2m in kg, E in joules(c=3×108m/s)MeVjoulesMeVjoulesjoulesmcE931106.111049.11049.11091066.113101016272=××××=×××==−−−−Ans= EJudah Levine, 3070L21 5Stable and unstableStable and unstableAll nuclei with mass > 209 amu are unstableand are “naturally” radioactiveSome nuclei with mass < 209 amu are alsonaturally radioactiveJudah Levine, 3070L21 6Types of radioactivityTypes of radioactivity242242HeYXnaznznaz+=−−−+=Alpha decay:Short range in air, cannot penetrate materialsJudah Levine, 3070L21 7Types of radioactivityTypes of radioactivityBeta decay:npnpXeveHeHyearsdecayTritiumenpepn+−+−++=++=++=000,19:)5.12(......132231Meters in air, 1 cm or less in a materialJudah Levine, 3070L21 8Types of radioactivityTypes of radioactivityGamma decay:Nucleus emits energy, no change inproton, neutron numbers.Energy appears as electromagneticpulse (“photon”)Centimeters of lead, meters of concreteJudah Levine, 3070L21 9HalfHalf--lifelifeThe half life is the time after which one-half of the materialhas reacted to form the product How long must I wait until less than 1% of the initialmaterial is left? (no new initial material is created during the decay)A: 1 half-lifeB: 3 half-livesC: 5 half-livesD: 7 half-livesE: 9 half-livesJudah Levine, 3070L21 10HalfHalf--lifelifeThe half life is the time after which one-half of the materialhas reacted to form the product How long must I wait until less than 1% of the materialis left?A: 1 half-life (1/2) (50%)B: 3 half-lives (1/8) (12.5%)C: 5 half-lives (1/32) (3.1%)D: 7 half-lives (1/128) (0.8%)E: 9 half-lives (1/512) (0.2%)Judah Levine, 3070L21 11Properties of UraniumProperties of UraniumQQHeaviest naturallyHeaviest naturally--occurring atomoccurring atomQQTwo common isotopes:Two common isotopes:yearsdecayalphaUyearsdecayalphaU914623892614323592109.4,%,3.9910713,%,7.0×=×=ττEnd point of decay chain is an isotope of lead (mass < 209):12420682238921252078223592PbUPbU→→Judah Levine, 3070L21 12Properties of UraniumProperties of UraniumQQHeaviest naturallyHeaviest naturally--occurring atomoccurring atomQQTwo common isotopes:Two common isotopes:yearsdecayalphaUyearsdecayalphaU914623892614323592109.4,%,3.9910713,%,7.0×=×=ττIs the ratio of isotopes surprising or not?Judah Levine, 3070L21 13Formation of UraniumFormation of UraniumAge of the Earth is about 4.5×109yearsSuppose initial values were about the sameHow much of each isotope has decayed?yearsdecayalphaUyearsdecayalphaU914623892614323592109.4,%,3.9910713,%,7.0×=×=ττ%)3.1(,3.610713105.4%)53(,92.0109.4105.469235929923892=××=−=××=−lifehalfUageEarthlifehalfUageEarthJudah Levine, 3070L21 14Induced fissionInduced fissionenergyneutronsorBAUUnMeVnBaKrUUn+++==++++==+3222144236921432359285141565793361442369214323592Uranium 235 is the only natural element that willdo thisJudah Levine, 3070L21 15Induced fissionInduced fissionenergyneutronsorBAUUnMeVnBaKrUUn+++==++++==+3222144236921432359285141565793361442369214323592Chain reaction:neutrons from one fission are used to trigger the next eventsNumber of events can double on each generationRapid exponential growthJudah Levine, 3070L21 16Induced fissionInduced fissionenergyneutronsorBAUUnMeVnBaKrUUn+++==++++==+3222144236921432359285141565793361442369214323592Probability of inducing fission much larger wheninput neutron is moving slowlyOutput neutrons are too fast – small probability oftriggering another event using uranium 235Judah Levine, 3070L21 17First solution First solution ––““Little BoyLittle Boy””Neutron initiatorUranium targetUraniumprojectileExtract nearly pure Uranium 235 (90%+)Make density so high that low fission probability is not the limitGunBarrelJudah Levine, 3070L21 18Generating powerGenerating powerQQHighHigh--purity uranium is very expensive purity uranium is very expensive to produce and there isnto produce and there isn’’t a lot of it t a lot of it aroundaroundQQBombs are hard to controlBombs are hard to controlJudah Levine, 3070L21 19Using lowUsing low--enrichment uraniumenrichment uraniumQQEnriched about 4Enriched about 4××––235 isotope about 3%235 isotope about 3%––238 isotope about 97%238 isotope about 97%QQOutput neutrons from each fission Output neutrons from each fission event must be slowed down to increase event must be slowed down to increase the probability of triggering another the probability of triggering another fissionfission––Neutron Neutron ““moderationmoderation””must minimize must minimize absorptionabsorptionJudah Levine, 3070L21 20Enriched uranium reactorEnriched uranium reactorTotal mass of fuel: 200,000 kg3% 235Fuel rodModeratorWater, graphite,


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CU-Boulder PHYS 3070 - Units of Mass and Energy

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