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Slide 1Lightning 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 enough information to say29.4 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) 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.Beta 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 reactionsSlide 23Threshold EnergyIf the Q value of an endothermic reaction is -2.17 MeV, the minimum kinetic energy needed in the reactant nuclei if the reaction is to occur must be (a) equal to 2.17 MeV, (b) greater than 2.17 MeV, (c) less than 2.17 MeV, or (d) precisely half of 2.17 MeV.1101/14/1901/14/19General Physics (PHY 2140)Lecture 37Lecture 37 Modern PhysicsNuclear PhysicsRadioactivityNuclear reactionsChapter 29http://www.physics.wayne.edu/~apetrov/PHY2140/2201/14/1901/14/19Lightning ReviewLightning ReviewLast lecture: 1.1.Nuclear physicsNuclear physicsProperties of nucleiProperties of nucleiBinding energy, types of radiationBinding energy, types of radiationReview 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?AZX1/ 30r r A=3301/14/1901/14/1929.3 Radioactivity29.3 RadioactivityRadioactivityRadioactivity is 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AlphaAlpha particles particlesThe particles are The particles are 44He nucleiHe nucleiBetaBeta particles particlesThe particles are either electrons or positronsThe particles are either electrons or positronsA positron is the A positron is the antiparticleantiparticle of the electron of the electronIt is similar to the electron except its charge is +eIt is similar to the electron except its charge is +eGammaGamma rays raysThe “rays” are high energy photonsThe “rays” are high energy photons4401/14/1901/14/19The Decay ConstantThe Decay ConstantThe number of particles that decay in a given time is proportional to The number of particles that decay in a given time is proportional to the total number of particles in a radioactive samplethe total number of particles in a radioactive sampleλλ is called the is called the decay constantdecay constant and and determines the rate at which the determines the rate at which the material will decaymaterial will decayThe The decay decay raterate or or activityactivity, R, of a sample is defined as the number , R, of a sample is defined as the number of decays per secondof decays per secondNR NtlD= =D( )N N tlD =- D5501/14/1901/14/19Decay CurveDecay CurveThe decay curve follows the The decay curve follows the equationequationThe The half-lifehalf-life is also a useful is also a useful parameterparameterThe half-life is defined as the The half-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 decaynuclei to decay693.02lnT210tN N el-=6601/14/1901/14/19UnitsUnitsThe 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 101010 decays/second decays/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 101010 Bq BqThe most commonly used units of activity are the mCi The most commonly used units of activity are the mCi and the µCiand the µCi7701/14/1901/14/19QUICK 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:1 1 1 32 2 2 4� �+ =� �� �8801/14/1901/14/1929.4 The Decay Processes – General Rules29.4 The Decay Processes – General RulesWhen one element changes into another element, the process When one element changes into another element, the process is called is called spontaneous decayspontaneous decay or or transmutationtransmutationThe The sum of the mass numberssum of the mass numbers, , AA, must be , must be the samethe same on 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 same on both on both sides of the equationsides of the equationConservation of mass-energy and conservation of momentum Conservation of mass-energy and conservation of momentum must holdmust hold9901/14/1901/14/19Alpha DecayAlpha DecayWhen a nucleus emits an When a nucleus emits an alpha particlealpha particle it 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 nucleusdaughter nucleusHeYX424A2ZAZ101001/14/1901/14/19Alpha Decay -- ExampleAlpha Decay -- ExampleDecay 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111101/14/1901/14/19QUICK


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