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UW-Madison PHYSICS 107 - Phy 107 Lecture 32 Notes

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1Wed, Apr. 12, 2006 Phy107 Lecture 321Exam 3: Wed. Apr. 19Covers Quantum Physics, Solids, Nuclear PhysicsHW11: Griffith Chap 19:Q9, Q11, Q13, E6, E8, E12From last time…• Radioactive decay: alpha, beta, gamma• Radioactive half-life• Decay type understood in terms of numberneutrons, protons.• Understand in terms of weak interaction,Quark internal structure.Wed, Apr. 12, 2006 Phy107 Lecture 32214C to 12C ratio•14C has a half-life of ~6,000 years,continually decaying back into 14N.• Steady-state achieved in atmosphere,with 14C:12C ratio ~ 1:1 trillion (1 part in 1012)As long asbiologicalmaterial alive,atmosphericcarbon mixingested (as CO2),ratio stays fixed.After death, no exchangewith atmosphere. Ratiostarts to change as 14C decaysWed, Apr. 12, 2006 Phy107 Lecture 323Carbon-dating questionThe 14C:12C ratio in a fossil bone is found to be 1/4that of the ratio in the bone of a living animal.The half-life of 14C is 5,730 years.What is the approximate age of the fossil?A. 17,200 yearsB. 7,640 yearsC. 22,900 yearsD. 11,460 yearsSince the ratio has been reducedby a factor of 4, two half-liveshave passed.2 x 5,730 years = 11,460 yearsWed, Apr. 12, 2006 Phy107 Lecture 324Other carbon decays• Lightest isotopes of carbon are observed to emit aparticle like an electron, but has a positive charge!•This is the antiparticle of the electron.•Called the positron.Wed, Apr. 12, 2006 Phy107 Lecture 325Antimatter• Every particle now known to have an antiparticle.• Even antimatter has been generated.Matter and antimatterannihilate when inclose proximity.Photons are created sothat energy isconserved.Wed, Apr. 12, 2006 Phy107 Lecture 326What is going on?•14C has more neutronsthan the most stableform 12C.– So it decays by electronemission, changingneutron into a proton.• Other isotopes of carbonhave fewer neutrons– Decays by emittingpositron, changingproton into neutron.2Wed, Apr. 12, 2006 Phy107 Lecture 327Decay question20Na decays in to 20Ne, a particle is emitted?What particle is it?Na atomic number = 11Ne atomic number = 10A. AlphaB. Electron betaC. Positron betaD. Gamma20Na has 11 protons, 9 neutrons20Ne has 10 protons, 10 neutronsSo one a proton (+ charge ) changed to aneutron (0 charge) in this decay.A positive particle had to be emitted.Wed, Apr. 12, 2006 Phy107 Lecture 328Gamma decay• So far– Alpha decay: alpha particle emitted from nucleus– Beta decay: electron or positron emitted• Both can leave the nucleus in excited state– Just like a hydrogen atom can be in an excited state– Hydrogen emits photon as it drops to lower state.Nucleus also emits photon asit drops to ground stateThis is gamma radiationBut energies much larger,so extremely high energyphotons.Wed, Apr. 12, 2006 Phy107 Lecture 329Radioactive decay summary• Alpha decay– Nucleus emits alpha particle (2 neutrons + 2 protons)– Happens with heavy nuclei only• Beta decay– Nucleus emits electron (beta-) or positron (beta+)– Internally,neutron changes to proton (beta-), orproton changes to neutron (beta+)• Gamma decay– Nucleus starts in internal excited state– Emits photon and drops to lower energy stateWed, Apr. 12, 2006 Phy107 Lecture 3210Energy stored in the nucleusNPThesepulledtogether bystrong forceNPRequires lots ofwork to pullthem apartSo energy of nucleus is LESS than that of isolated nucleons……and energy is released when nucleons bind together.Wed, Apr. 12, 2006 Phy107 Lecture 32112 protons &2 neutronsNuclear Binding Energy• The energy difference between nucleus and isolatednucleons is the binding energy.• From E=mc2, shows up as mass difference.4He nucleus is 0.0305ulighter than isolated2 protons, 2 neutronsHeliumnucleus(12.000u defined as mass of 12C)Wed, Apr. 12, 2006 Phy107 Lecture 3212How much energy?• This doesn’t sound like much.• Mass difference = 0.0305u• 1 u = 1.66 x 10-27 kg• But E=mc2 saysE=(0.0305) x (1.66x10-27 kg) x ( 3x108 m/s)2 = 4.56x10-12 J• Not much, but this is for each nucleus!• 1 gm of Helium has 1.5x1023 nuclei.3Wed, Apr. 12, 2006 Phy107 Lecture 3213Energy production•Coal-burning plant–10,000 tons coal/dayto produce 1,000 MW•Fission reactor–Uses 100 tons uranium/yrto produce 1,000 MW•Hydroelectric plant–Uses 60,000 tons/sec waterto produce 1,000 MWWed, Apr. 12, 2006 Phy107 Lecture 3214Another comparisonHow can we release this energy?Wed, Apr. 12, 2006 Phy107 Lecture 3215Binding energy of different nucleiEnergy of separatednucleonsMass difference / nucleon(MeV/c2)Wed, Apr. 12, 2006 Phy107 Lecture 3216Differences between nuclei• Schematic view ofprevious diagram•56Fe is most stable• Move toward lowerenergies by fission orfusion.• Energy releasedrelated to differencein binding energy.Wed, Apr. 12, 2006 Phy107 Lecture 3217Nuclear fission• A heavy nucleus is split apart into twosmaller ones.• Energy is released because the lighter nucleiare less tightly bound.Wed, Apr. 12, 2006 Phy107 Lecture 3218Nuclear Fusion• ‘Opposite’ processalso occurs, wherenuclei are fused toproduce a heaviernucleus, but requireslarge initial energyinput.• Called nuclear fusion.4Wed, Apr. 12, 2006 Phy107 Lecture 3219Fission and Fusion• Fission:– Heavy nucleus is broken apart– Total mass of pieces less than original nucleus– Missing mass appears as energy E=mc2• Fusion– Light nuclei are fused together into heavier nuclei– Total mass of original nuclei greater than resultingnucleus– Missing mass appears as energy.Wed, Apr. 12, 2006 Phy107 Lecture 3220Fission• Fission occurs when a heavy nucleus breaks apartinto smaller pieces.• Does not occur spontaneously, but is induced bycapture of a neutronWed, Apr. 12, 2006 Phy107 Lecture 3221Neutron capture• When neutron is captured, 235U becomes 236U– Only neutron # changes, same number of protons.Nucleus distorts andoscillate, eventuallybreaking apart(fissioning)Wed, Apr. 12, 2006 Phy107 Lecture 3222Neutron production• Fission fragmentshave too manyneutrons to bestable.• So free neutrons areproduced in additionto the large fissionfragments.• These neutrons caninitiate more fissionevents# protons# neutronsWed, Apr. 12, 2006 Phy107 Lecture 3223Chain reaction• If neutrons produced by fissioncan be captured by othernuclei, fission chain reactioncan proceed.Wed, Apr. 12, 2006 Phy107 Lecture 3224Neutrons• Neutrons may be captured by nuclei that donot undergo fission– Most commonly, neutrons are captured by 238U– The possibility of neutron capture by


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UW-Madison PHYSICS 107 - Phy 107 Lecture 32 Notes

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