Lightning Review29.3 RadioactivityThe Decay ConstantDecay CurveUnitsWhat fraction of a radioactive sample has decayed after two half-lives have elapsed? (a) 1/4(b) 1/2(c) 3/4 (d) not enoug29.4 The Decay Processes – General RulesAlpha DecayAlpha Decay -- ExampleIf a nucleus such as 226Ra that is initially at rest undergoes alpha decay, which of the following statements is true? (a) TheBeta DecayBeta Decay – Electron EnergyBeta DecayGamma DecayUses of Radioactivity29.5 Natural RadioactivityDecay Series of 232Th29.6 Nuclear ReactionsWhich of the following are possible reactions?Q ValuesProblem: nuclear reactionsThreshold EnergyIf the Q value of an endothermic reaction is -2.17 MeV, the minimum kinetic energy needed in the reactant nuclei if the reacti1112/5/200312/5/2003General Physics (PHY 2140)Lecture 37Lecture 37¾ Modern Physics9Nuclear Physics9Radioactivity9Nuclear reactionsChapter 29http://www.physics.wayne.edu/~apetrov/PHY2140/2212/5/200312/5/2003Lightning ReviewLightning ReviewLast lecture:1.1.Nuclear physicsNuclear physics99Properties of nucleiProperties of nuclei99Binding energy, types of radiationAZXBinding energy, types of radiation1/30rrA=Review Problem: An alpha particle has twice the charge of a beta particle. Why does the former deflect less than the latter when passing between electrically charged plates, assuming that both have the same speed?3312/5/200312/5/200329.3 Radioactivity29.3 RadioactivityRadioactivityRadioactivityis the spontaneous emission of radiation is the spontaneous emission of radiation Experiments suggested that radioactivity was the result Experiments suggested that radioactivity was the result of the decay, or disintegration, of unstable nucleiof the decay, or disintegration, of unstable nucleiThree types of radiation can be emittedThree types of radiation can be emittedAlphaAlphaparticlesparticlesThe particles are The particles are 44He nucleiHe nucleiBetaBetaparticlesparticlesThe particles are either electrons or positronsThe particles are either electrons or positronsA positron is the A positron is the antiparticleantiparticleof the electronof the electronIt is similar to the electron except its charge is +eIt is similar to the electron except its charge is +eGammaGammaraysraysThe “rays” are high energy photonsThe “rays” are high energy photons4412/5/200312/5/2003The Decay ConstantThe Decay ConstantThe number of particles that decay in a given time is proportionThe number of particles that decay in a given time is proportional to al to the total number of particles in a radioactive samplethe total number of particles in a radioactive sampleλλis called the is called the decay constantdecay constantand and determines the rate at which the determines the rate at which the material will decaymaterial will decayThe The decay decay raterateor or activityactivity, R, of a sample is defined as the number , R, of a sample is defined as the number of decays per second()NNtλ∆=− ∆of decays per secondNRNtλ∆==∆5512/5/200312/5/2003Decay CurveDecay CurveThe decay curve follows the The decay curve follows the equationequationThe The halfhalf--lifelifeis also a useful is also a useful parameterparameterThe halfThe half--life is defined as the life is defined as the time it takes for half of any time it takes for half of any given number of radioactive given number of radioactive nuclei to decay0tNNeλ−=nuclei to decayλ=λ=693.02lnT216612/5/200312/5/2003UnitsUnitsThe unit of activity, R, is the The unit of activity, R, is the Curie, CiCurie, Ci1 Ci = 3.7 x 101 Ci = 3.7 x 101010decays/seconddecays/secondThe SI unit of activity is the The SI unit of activity is the Becquerel, BqBecquerel, Bq1 Bq = 1 decay / second1 Bq = 1 decay / secondTherefore, 1 Ci = 3.7 x 10Therefore, 1 Ci = 3.7 x 101010BqBqThe most commonly used units of activity are the mCi The most commonly used units of activity are the mCi and the µCiand the µCi7712/5/200312/5/2003QUICK QUIZWhat fraction of a radioactive sample has decayed after two half-lives have elapsed? (a) 1/4 (b) 1/2 (c) 3/4 (d) not enough information to say(c). At the end of the first half-life interval, half of the original sample has decayed and half remains. During the second half-life interval, half of the remaining portion of the sample decays. The total fraction of the sample that has decayed during the two half-lives is:111 3222 4+=8812/5/200312/5/200329.4 The Decay Processes 29.4 The Decay Processes ––General RulesGeneral RulesWhen one element changes into another element, the process When one element changes into another element, the process is called is called spontaneous decayspontaneous decayor or transmutationtransmutationThe The sum of the mass numberssum of the mass numbers, , AA, must be , must be the samethe sameon both on both sides of the equationsides of the equationThe The sum of the atomic numberssum of the atomic numbers, , ZZ, must be , must be the samethe sameon both on both sides of the equationsides of the equationConservation of massConservation of mass--energy and conservation of momentum energy and conservation of momentum must holdmust hold9912/5/200312/5/2003Alpha DecayAlpha DecayWhen a nucleus emits an When a nucleus emits an alpha particlealpha particleit loses two it loses two protons and two neutronsprotons and two neutronsN decreases by 2N decreases by 2Z decreases by 2Z decreases by 2A decreases by 4A decreases by 4SymbolicallySymbolicallyX is called the X is called the parent nucleusparent nucleusY is called the Y is called the daughter nucleusHeYX424A2ZAZ+→−−daughter nucleus101012/5/200312/5/2003Alpha Decay Alpha Decay ----ExampleExampleDecay of Decay of 226226RaRaHalf life for this decay is 1600 Half life for this decay is 1600 yearsyearsExcess mass is converted into Excess mass is converted into kinetic energykinetic energyMomentum of the two particles Momentum of the two particles is equal and oppositeis equal and oppositeHeRnRa422228622688+→111112/5/200312/5/2003QUICK QUIZIf a nucleus such as226Ra that is initially at rest undergoes alpha decay, which of the following statements is true? (a) The alpha particle has more kinetic energy than the daughter nucleus. (b) The daughter nucleus has more kinetic energy than the alpha particle. (c) The daughter nucleus and the alpha particle have the same kinetic energy.(a). Conservation of momentum requires