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 NucleusSymbol:X is the chemical symbol of the elementExample: Mass number is 27Atomic number is 13Contains 13 protonsContains 14 (27 – 13) neutronsThe Z may be omitted since the element can be used to determine ZXAZAl27135More PropertiesThe nuclei of all atoms of a particular element must contain the same number of protonsThey may contain varying numbers of neutronsIsotopes of an element have the same Z but differing N and A valuesExample: 11 12 13 146 6 6 6C C C CChargeThe proton has a single positive charge, +eThe electron has a single negative charge, -eThe neutron has no chargeMakes it difficult to detecte = 1.602 177 33 x 10-19 CMassIt is convenient to use unified mass units, u, to express masses1 u = 1.660 559 x 10-27 kgBased on definition that the mass of one atom of C-12 is exactly 12 uMass can also be expressed in MeV/c2From ER = m c21 u = 931.494 MeV/c2Summary of Masses101/ 3 150 0, 1.2 10 1.2 fermi=1.2 fmR r A r m-= = � = VAconstantAs 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 NucleiThe volume of the nucleus (assumed to be spherical) is directly proportional to the total number of nucleonsThis suggests that all nuclei have nearly the same densityNucleons combine to form a nucleus as though they were tightly packed spheresIf 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 StabilityThere are very large repulsive electrostatic forces between protonsThe nuclei are stable because of the presence of another, short-range attractive force, called the nuclear forceThis is an attractive force that acts between all nuclear particlesThe nuclear attractive force is stronger than the Coulomb repulsive force at the short ranges within the nucleusLight nuclei are most stable if N = ZHeavy nuclei are most stable when N > ZAs the number of protons increase, the Coulomb force increases and so more nucleons are needed to keep the nucleus stableNo nuclei are stable when Z > 83Radioactivity – Types Three types of radiation can be emittedAlpha particlesThe particles are 4He nucleiBarely penetrate a piece of paperBeta particlesThe particles are either electrons or positronsA positron is the antiparticle of the electronIt is similar to the electron except its charge is +eCan penetrate a few mm of aluminumGamma raysThe “rays” are high energy photonsCan penetrate several cm of leadAlpha DecayWhen a nucleus emits an alpha particle it loses two protons and two neutronsN decreases by 2Z decreases by 2A decreases by 4SymbolicallyX is called the parent nucleusY is called the daughter nucleusHeYX424A2ZAZAlpha Decay – ExampleDecay of 226 RaHalf life for this decay is 1600 yearsExcess mass is converted into kinetic energyMomentum of the two particles is equal and oppositeHeRnRa422228622688Beta DecayDuring beta decay, the daughter nucleus has the same number of nucleons as the parent, but the atomic number is changed by oneThe emission of the electron is from the nucleusThe nucleus contains protons and neutronsThe process occurs when a neutron is transformed into a proton and an electronEnergy must be conservedSymbolically eYXeYXAZAZAZAZ11Beta Decay – Accounting for some missing energy – the neutrino Symbolically is the symbol for the neutrino is the symbol for the antineutrinoTo summarize, in beta decay, the following pairs of particles are emittedAn electron and an antineutrinoA positron and a neutrinoeYXeYXA1ZAZA1ZAZnGamma DecayGamma rays are given off when an excited nucleus “falls” to a lower energy stateSimilar to the process of electron “jumps” to lower energy states and giving off photonsThe photons are called gamma rays, very high energy relative to lightThe excited nuclear states result from “jumps” made by a proton or neutronThe excited nuclear states may be the result of violent collision or more likely of an alpha or beta emissionGamma Decay – ExampleExample of a decay sequenceThe first decay is a beta emissionThe second step is a gamma emissionThe C* indicates the Carbon nucleus is in an excited stateGamma emission doesn’t change either A or ZC*Ce*CB126126126125ExamplesAlphaBetaGammaeYSr903990382 * 6028602860275927NieNiConCoHePP422068221084 b o Decay Series of 232ThSeries starts with 232ThProcesses through a series of alpha and beta decaysEnds with a stable isotope of lead, 208Pb2526The Decay ConstantThe number of particles that decay in a given time is proportional to the total number of particles in a radioactive sampleΔN = -λ N Δtλ is called the decay constant and determines the rate at which the material will decayThe 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 ReactionsStructure of nuclei can be changed by bombarding them with energetic particlesThe
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