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UK PHY 213 - Nuclear Physics

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Physics 213 General PhysicsSlide 1Slide 2Properties of the NucleusSlide 4More PropertiesChargeMassSummary of MassesSlide 9Density of NucleiSlide 11Slide 12Slide 13Nuclear StabilityRadioactivity – TypesAlpha DecayAlpha Decay – ExampleBeta DecayBeta Decay – Accounting for some missing energy – the neutrinoGamma DecayGamma Decay – ExampleExamplesDecay Series of 232ThSlide 24The Decay ConstantSlide 26Slide 27Slide 28Nuclear ReactionsNuclear Reactions – ExamplePhysics 213General PhysicsLecture 242Last Meeting: Atomic PhysicsToday: Nuclear Physics3A= Mass NumberProperties of the NucleusSymbol:X is the chemical symbol of the elementExample: Mass number is 27Atomic number is 13Contains 13 protonsContains 14 (27 – 13) neutronsThe Z may be omitted since the element can be used to determine ZXAZAl27135More PropertiesThe nuclei of all atoms of a particular element must contain the same number of protonsThey may contain varying numbers of neutronsIsotopes of an element have the same Z but differing N and A valuesExample: 11 12 13 146 6 6 6C C C CChargeThe proton has a single positive charge, +eThe electron has a single negative charge, -eThe neutron has no chargeMakes it difficult to detecte = 1.602 177 33 x 10-19 CMassIt is convenient to use unified mass units, u, to express masses1 u = 1.660 559 x 10-27 kgBased on definition that the mass of one atom of C-12 is exactly 12 uMass can also be expressed in MeV/c2From ER = m c21 u = 931.494 MeV/c2Summary of Masses101/ 3 150 0, 1.2 10 1.2 fermi=1.2 fmR r A r m-= = � = VAconstantAs an example consider helium (Z=2, A=4). The coulomb force on the protons isThis is equivalent to gravitational force on a 15 pound dumbbell !!! But its mass is only 1.7 x 10-27kg !!! Compare the coulomb force for the electrons in helium.     NkFNkFee721021921521910 m100.5 C101.6 64 m101.9 C101.6 Density of NucleiThe volume of the nucleus (assumed to be spherical) is directly proportional to the total number of nucleonsThis suggests that all nuclei have nearly the same densityNucleons combine to form a nucleus as though they were tightly packed spheresIf we were to squeeze all humans on earth to a single nucleus, how large will the size of the giant nucleus be?33 1/3 30.138 fm4 / 3 4 / 3(1.2 fm)A A AV R Arp p-= = = =938271/3 126.7 10 100kg4.01 10 ,1.67 10 kg1.20 fm=8.85 10 fm=0.885cmAR A-� �= = ��= �12epmm 13E(binding) = Z mc2 (prot) +N mc2 (neut) – mN c2 (nucleus)14Nuclear StabilityThere are very large repulsive electrostatic forces between protonsThe nuclei are stable because of the presence of another, short-range attractive force, called the nuclear forceThis is an attractive force that acts between all nuclear particlesThe nuclear attractive force is stronger than the Coulomb repulsive force at the short ranges within the nucleusLight nuclei are most stable if N = ZHeavy nuclei are most stable when N > ZAs the number of protons increase, the Coulomb force increases and so more nucleons are needed to keep the nucleus stableNo nuclei are stable when Z > 83Radioactivity – Types Three types of radiation can be emittedAlpha particlesThe particles are 4He nucleiBarely penetrate a piece of paperBeta particlesThe particles are either electrons or positronsA positron is the antiparticle of the electronIt is similar to the electron except its charge is +eCan penetrate a few mm of aluminumGamma raysThe “rays” are high energy photonsCan penetrate several cm of leadAlpha DecayWhen a nucleus emits an alpha particle it loses two protons and two neutronsN decreases by 2Z decreases by 2A decreases by 4SymbolicallyX is called the parent nucleusY is called the daughter nucleusHeYX424A2ZAZAlpha Decay – ExampleDecay of 226 RaHalf life for this decay is 1600 yearsExcess mass is converted into kinetic energyMomentum of the two particles is equal and oppositeHeRnRa422228622688Beta DecayDuring beta decay, the daughter nucleus has the same number of nucleons as the parent, but the atomic number is changed by oneThe emission of the electron is from the nucleusThe nucleus contains protons and neutronsThe process occurs when a neutron is transformed into a proton and an electronEnergy must be conservedSymbolically eYXeYXAZAZAZAZ11Beta Decay – Accounting for some missing energy – the neutrino Symbolically is the symbol for the neutrino is the symbol for the antineutrinoTo summarize, in beta decay, the following pairs of particles are emittedAn electron and an antineutrinoA positron and a neutrinoeYXeYXA1ZAZA1ZAZnGamma DecayGamma rays are given off when an excited nucleus “falls” to a lower energy stateSimilar to the process of electron “jumps” to lower energy states and giving off photonsThe photons are called gamma rays, very high energy relative to lightThe excited nuclear states result from “jumps” made by a proton or neutronThe excited nuclear states may be the result of violent collision or more likely of an alpha or beta emissionGamma Decay – ExampleExample of a decay sequenceThe first decay is a beta emissionThe second step is a gamma emissionThe C* indicates the Carbon nucleus is in an excited stateGamma emission doesn’t change either A or ZC*Ce*CB126126126125ExamplesAlphaBetaGammaeYSr903990382 * 6028602860275927NieNiConCoHePP422068221084 b o Decay Series of 232ThSeries starts with 232ThProcesses through a series of alpha and beta decaysEnds with a stable isotope of lead, 208Pb2526The Decay ConstantThe number of particles that decay in a given time is proportional to the total number of particles in a radioactive sampleΔN = -λ N Δtλ is called the decay constant and determines the rate at which the material will decayThe decay rate or activity, R, of a sample is defined as the number of decays per secondNR Nt 2728(Roentgen equivalent man – same biological effectiveness as 1 Rad of x-ray)29Nuclear ReactionsStructure of nuclei can be changed by bombarding them with energetic particlesThe


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UK PHY 213 - Nuclear Physics

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