ChapterChapter 3939 -- NuclearNuclear PhysicsPhysics AAA PowerPointPowerPointPowerPoint PresentationPresentationPresentation bybyby PaulPaulPaul E.E.E. Tippens,Tippens,Tippens, ProfessorProfessorProfessor ofofof PhysicsPhysicsPhysics SouthernSouthernSouthern PolytechnicPolytechnicPolytechnic StateStateState UniversityUniversityUniversity © 2007 Objectives:Objectives: AfterAfter completingcompleting thisthis module,module, youyou shouldshould bebe ableable to:to: •• DefineDefine andand applyapply thethe conceptsconcepts ofof massmass numbernumber,, atomicatomic numbernumber,, andand isotopesisotopes.. •• CalculateCalculate thethe massmass defectdefect andand thethe bindingbinding energyenergy perper nucleonnucleon forfor aa particularparticular isotope.isotope. •• DefineDefine andand applyapply conceptsconcepts ofof radioactiveradioactive decaydecay andand nuclearnuclear reactionsreactions.. •• StateState thethe variousvarious conservationconservation lawslaws,, andand discussdiscuss theirtheir applicationapplication forfor nuclearnuclear reactions.reactions. CompositionComposition ofof MatterMatter AllAll ofof mattermatter isis composedcomposed ofof atat leastleast threethree fundamentalfundamental particlesparticles (approximations):(approximations): Particle Fig. Sym Mass Charge Size Electron e- 9.11 x 10-31 kg -1.6 x 10-19 C Proton p 1.673 x 10-27 kg +1.6 x 10-19 C 3 fm Neutron n 1.675 x 10-31 kg 0 3 fm TheThe massmass ofof thethe protonproton andand neutronneutron areare close,close, butbut theythey areare aboutabout 18401840 timestimes thethe massmass ofof anan electron.electron. TheThe AtomicAtomic NucleusNucleus CompactedCompacted nucleus:nucleus: 44 protonsprotons 55 neutronsneutrons SinceSince atomatom isis electrielectri-- callycally neutral,neutral, therethere mustmust bebe 44 electrons.electrons. 44 electronselectrons BerylliumBeryllium AtomAtom ModernModern AtomicAtomic TheoryTheory The Bohr atom, which is sometimes shown with electrons as planetary particles, is no longer a valid representation of an atom, but it is used here to simplify our discussion of energy levels. The uncertain position of an electron is now described as a probability distribution—loosely referred to as an electron cloud. DefinitionsDefinitions AA nucleonnucleon isis aa generalgeneral termterm toto denotedenote aa nuclearnuclear particleparticle -- thatthat is,is, eithereither aa protonproton oror aa neutron.neutron. TheThe atomicatomic numbernumber ZZ ofof anan elementelement isis equalequal toto thethe numbernumber ofof protonsprotons inin thethe nucleusnucleus ofof thatthat element.element. TheThe massmass numbernumber AA ofof anan elementelement isis equalequal toto thethe totaltotal numbernumber ofof nucleonsnucleons (protons(protons ++ neutrons).neutrons). The mass number A of any element is equal to the sum of the atomic number Z and the number of neutrons N : A = N + Z SymbolSymbol NotationNotation AAA convenientconvenientconvenient waywayway ofofof describingdescribingdescribing ananan elementelementelement isisis bybyby givinggivinggiving itsitsits massmassmass numbernumbernumber andandand itsitsits atomicatomicatomic number,number,number, alongalongalong withwithwith thethethe chemicalchemicalchemical symbolsymbolsymbol forforfor thatthatthat element.element.element. A Mass number ZX Atomic numberSymbol 9 For example, consider beryllium (Be): 4 Be ExampleExample 1:1: DescribeDescribe thethe nucleusnucleus ofof aa lithiumlithium atomatom whichwhich hashas aa massmass numbernumber ofof 77 andand anan atomicatomic numbernumber ofof 3.3. AA == 7;7; ZZ == 3;3; NN == ?? NN == AA –– ZZ == 77 -- 33 neutrons:neutrons: NN == 44 Protons:Protons: ZZ == 33 Electrons:Electrons: SameSame asas ZZ 7 Li 3 LithiumLithium AtomAtom IsotopesIsotopes ofof ElementsElements IsotopesIsotopes areare atomsatoms thatthat havehave thethe samesame numbernumber ofof protonsprotons ((ZZ1= = ZZ2), ), butbut aa differentdifferent numbernumber ofof neutronsneutrons (N).(N). ((AA1 AA2) ) 3 4 He 2 He IsotopesIsotopes 2 ofof heliumhelium HeliumHelium -- 33 HeliumHelium -- 44 NuclidesNuclides BecauseBecause ofof thethe existenceexistence ofof soso manymany isotopes,isotopes, thethe termterm elementelement isis sometimessometimes confusing.confusing. TheThe termterm nuclidenuclide isis better.better. A nuclide is an atom that has a definite mass number A and Z-number. A list of nuclides will include isotopes. TheThe followingfollowing areare bestbest describeddescribed asas nuclides:nuclides: 3 4 12 13 2 He 2 He 6 C 6 C AtomicAtomic MassMass Unit,Unit, uu OneOne atomicatomic massmass unitunit (1(1 u)u) isis equalequal toto oneone-- twelfthtwelfth ofof thethe massmass ofof thethe mostmost abundantabundant formform ofof thethe carboncarbon atomatom----carboncarbon--1212.. Atomic mass unit: 1 u = 1.6606 x 10-27 kg Common atomic masses: Proton: 1.007276 u Neutron: 1.008665 u Electron: 0.00055 u Hydrogen: 1.007825 u ExampeExampe 2:2: TheThe averageaverage atomicatomic massmass ofof BoronBoron--1111 isis 11.00930511.009305 u.u. WhatWhat isis thethe massmass ofof thethe nucleusnucleus ofof oneone boronboron atomatom inin kg?kg? 11 = 11.009305 Electron: 0.00055 u 5 B = 11.009305 Electron: 0.00055 u TheThe massmass ofof thethe nucleusnucleus isis thethe atomicatomic massmass lessless thethe massmass ofof ZZ == 55 electrons:electrons: MassMass == 11.00930511.009305 uu –– 5(0.000555(0.00055 u)u) 11 boronboron nucleusnucleus == 11.0065611.00656 uu 1.6606 x 10-27 kg m 11.00656 u mm == 1.831.83 xx 1010-26-26 kgkg 1 u MassMass andand EnergyEnergy RecallRecall EinsteinEinstein’’ss equivalencyequivalency formulaformula forfor mm andand E:E: Emcc28; 3 x 10 m/s TheThe energyenergy ofof aa massmass ofof 11 uu cancan bebe found:found: EE == (1(1 u)u)cc2 == (1.66(1.66 xx 1010-27 kg)(3kg)(3 xx 10108 m/s)m/s)2 E = 1.49 x 10-10 J OrOr E = 931.5 MeV WhenWhen convertingconverting c2 931.5 MeV amuamu toto energy:energy: u ExampleExample 3:3: WhatWhat isis thethe restrest massmass energyenergy ofof aa protonproton (1.007276(1.007276 u)?u)? EE == mcmc2 == (1.00726(1.00726 u)(931.5u)(931.5 MeV/uMeV/u)) Proton:Proton: EE== 938.3938.3 MeVMeV SimilarSimilar conversionsconversions showshow otherother restrest massmass energies:energies: Neutron:Neutron: EE== 939.6939.6 MeVMeV Electron:Electron:Electron: EEE=== 0.5110.5110.511 MeVMeVMeV TheThe MassMass DefectDefect TheTheThe massmassmass defectdefectdefect isisis thethethe differencedifferencedifference betweenbetweenbetween thethethe restrestrest massmassmass ofofof aaa nucleusnucleusnucleus andandand thethethe sumsumsum ofofof thethethe restrestrest massesmassesmasses ofofof itsitsits constituentconstituentconstituent nucleons.nucleons.nucleons. TheThe wholewhole isis lessless thanthan thethe sumsum ofof thethe parts!parts! ConsiderConsider thethe carboncarbon--1212 atomatom (12.00000(12.00000 u):u): NuclearNuclear massmass == MassMass ofof atomatom –– ElectronElectron massesmasses == 12.0000012.00000 uu –– 6(0.000556(0.00055 u)u) == 11.99670611.996706 uu TheThe nucleusnucleus ofof thethe carboncarbon--1212 atomatom hashas thisthis mass.mass. (Continued(Continued .. .. .).) MassMass DefectDefect (Continued)(Continued) MassMass ofof carboncarbon--1212 nucleus:nucleus: 11.99670611.996706 Proton:Proton: 1.0072761.007276 uu Neutron:Neutron: 1.0086651.008665 uu TheThe nucleusnucleus containscontains 66 protonsprotons andand 66 neutrons:neutrons: 66 pp == 6(1.0072766(1.007276 u)u) == 6.0436566.043656 uu 66 nn == 6(1.0086656(1.008665 u)u) == 6.0519906.051990 uu TotalTotal massmass ofof parts:parts: == 12.09564612.095646 uu MassMass defectdefect mmD == 12.09564612.095646 uu –– 11.99670611.996706 uu m = 0.098940 u mDD = 0.098940 u TheThe BindingBinding EnergyEnergy TheThe bindingbinding energyenergy EE ofof aa nucleusnucleus isis thethe The binding energy EBB of a nucleus is the energyenergyenergy requiredrequiredrequired tototo separateseparateseparate aaa nucleusnucleusnucleus intointointo itsitsits constituentconstituentconstituent parts.parts.parts. 2 2 EB = mD c where c = 931.5 MeV/u TheThe bindingbinding energyenergy forfor thethe carboncarbon--1212 exampleexample is:is: EEB == (0.098940( u)(931.5 MeV/u) Binding EB for C-12: EB = 92.2 MeV BindingBinding EnergyEnergy perper NucleonNucleon AnAnAn importantimportantimportant waywayway ofofof comparingcomparingcomparing thethethe nucleinucleinuclei ofofof atomsatomsatoms isisis findingfindingfinding theirtheirtheir bindingbindingbinding energyenergyenergy perperper nucleon:nucleon:nucleon: Binding energy EB MeV = per nucleon A nucleon ForFor ourour CC--1212 exampleexample AA == 1212 and:and: E 92.2 MeV B 7.68 MeV A 12 nucleon FormulaFormula forfor MassMass DefectDefect TheThe followingfollowing formulaformula isis usefuluseful forfor massmass defect:defect: MassMass defectdefect mZmNmMDHn mmD mmH == 1.0078251.007825 u;u; mmn == 1.0086651.008665 uu ZZ isis atomicatomic number;number; NN isis neutronneutron number;number; MM isis massmass ofof atomatom (including(including electrons).electrons). ByBy usingusing thethe massmass ofof thethe hydrogenhydrogen atom,atom, youyou avoidavoid thethe necessitynecessity ofof subtractingsubtracting electronelectron masses.masses. 4 ExampleExample 4:4: FindFind thethe massmass defectdefect forfor thethe 2 He nucleusnucleus ofof heliumhelium--4.4. ((MM == 4.0026034.002603 u)u) MassMass defectdefect mZmNmMDHn mmD ZmZmH == (2)(1.007825(2)(1.007825 u)u) == 2.0156502.015650 uu NmNmn == (2)(1.008665(2)(1.008665 u)u) == 2.0173302.017330 uu MM == 4.0026034.002603 uu