Nuclear PhysicsThis Lecture: Nuclear structure, Strong Force, RadioactivityPrevious lecture: More on Atomic PhysicsElectron Spin and Exclusion PrincipleEmission and absorption spectra for atoms with more electrons LasersFinalMon. May 12, 12:25-2:25, Ingraham B10New material: Particle in a box (Ch 40.4-5, 40.10)Hydrogen Atom quantum numbers, wave functions, probability(Ch 41.1-2)Electron Spin and Pauli exclusion principle (Ch 41.3-6)Lasers (Ch 41.8)Nuclear Physics: nuclear structure (Ch 42.1-3) and Radioactivity (Ch 42.5-7) MTE1-3 material (see past lecture notes and Exam web page)Final Exam• Final is 25% of final grade• In the final about 30% on new material, rest is material in MTE1-3• 2 sheets allowed (HAND WRITTEN!)Notify NOW any potential and VERY serious problem you have with this time From last lecture: building atoms4http://eclipse.gsfc.nasa.gov/SEhelp/ApolloLaser.htmlMeasuring the Moon-Earth distance with a laser5NASA Apollo Laser Ranging Experiment: begun 25 yrs ago when Apollo 11 deployed a reflector in the Sea of tranquillityLunar ranging involves sending a laser beam through an optical telescopeAt the Moon's surface the beam is roughly four miles wideHighly collimated beam from stimulated emission, almost monochromaticNeutronProtonNuclear Structure6Size of electron orbit is 5x10-11 mNucleus is 5,000 times smaller than the atom!Neutron: zero charge (neutral)Proton: positive charge(equal and opposite to electron)Nucleus size ~10-14 mSpacing betweennucleons 10-15 m1 fermi = 10-15mNucleons are not building blocks of matter7• We now know thatprotons and neutronsare not fundamentalparticles.• They are composedof quarks, whichinteract byexchanging gluons.• Zero net charge -># protons in nucleus = # electrons orbiting.• The number of electrons determines which element.– 1 electron ! Hydrogen– 2 electrons ! Helium– 6 electrons ! Carbon• How many neutrons?Li63AZNucleus =Protons+ NeutronsnucleonsA=N+ZNotation for nuclei8A = # of nucleons=atomic mass numberZ = atomic number (# of protons or # of electrons)N = # of neutrons•Carbon has 6 electrons (Z=6)•Zero net charge => 6 protons in the nucleus.•Most common form of carbon has 6 neutrons in the nucleus.Example: Carbon9C126Another form of Carbon has6 protons, 8 neutrons in the nucleus. This is 14C.different massTritum is an isotope of hydrogen with threetotal nucleons: two neutrons and oneproton. How many electrons does it have?A. OneB. TwoC. ThreeQuiz10Isotopes of Hydrogen11D2O has 20 nucleons and H2O has 18. So heavy water is heavier than water by (20-18)/18= 10%Number of nucleons determines the mass of atomsWomen Nobel PrizesThe only 2 female Nobel Prizes in Nuclear Physics! (we need more!!!)Maria Goeppert-Mayer 1963 Shell Model of Nucleus1903 Marie Curie (with Pierre)in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel• So what holds the nucleus together?• Coulomb force? Gravity?• Coulomb force only acts oncharged particles– Repulsive between protons,and doesn’t affect neutrons at all.• Gravitational force is much too weak.Showed before that gravitational force ismuch weaker than Coulomb force.Nuclear Force (Strong Interaction)Gravitational effects are negligible at atomic and nuclear level• New attractive force.• Dramatically stronger than Coulomb force atshort distances.• Doesn’t depend on sign of charge.• This is the ‘strong interaction’, one of the fourfundamental interactions:electromagnetic interactionstrong interactionweak interactiongravitational interactionThe Strong Nuclear Force14The Coulomb attraction energy (~10 eV) binds thehydrogen atom together.Protons in nucleus are 50,000 times closer togetherthan electron and proton in hydrogen atom.Attractive energy must be larger than the Coulomb repulsion, so nuclear binding energies are at leastA. 5000 eVB. 500,000 eVC. 5,000,000 eVExperimentally, nucleons bound by ~ 8 MeV / nucleon(8,000,000 eV / nucleon)Estimating the Strong Force15=0.5 MeV• It is convenient to use atomic mass units, u, toexpress masses– 1 u = 1.660 539 x 10-27 kg– mass of one atom of 12C = 12 u ! 1 u = 1.66 x 10-27 kg• Mass can also be expressed in MeV/c2– From rest energy of a particle ER = mc2– 1 u = 931.494 MeV/c2A convenient unit of Mass16• Experimentally,– radius of nucleus r = roA1/3 (A=mass # = # nucleons)– says that volume V proportional to A.– says that nucleon density is constant• Nuclear matter is ~ incompressible– More nucleons -> larger nucleus– Nucleons ~ same distance apart in all nucleiNuclear densityr0=1.2 fm! "nuc=mV=Au43#r3=Au43#r03A=u43#r03=1.66 $10%27kg43#(1.2 $10%15)= 2.3 $1017kg /m3Nuclear Binding Energy18mp=1.6726 x 10-27kg/1.66 x 10-27 kg/u= 1.0078u2 protons &2 neutrons• Mass of nucleus is less thanmass of isolated constituents!• Helium nucleus energy < energy isolated nucleons.Arises from E=mc2Equivalence of massand energy.Heliumnucleus• Energy difference isbinding energy.1.0078u1.0078umn=1.6749 x 10-27kg/1.66 x 10-27 kg/u= 1.0087uBinding energy• Binding energy: energy you would need to supply to disassemble the nucleus into nucleons: Ebinding = (Zmp+Nmn-mnucleus)c2 • Example: deuteron = 1 proton and 1 neutron bounded together• Free particles: mp = 1.0078u, mn= 1.0087u, mp+mn=2.01649u• Atomic mass of deuteron 2H = 2.01410u• Binding energy =0.002388u x 931.494MeV/u = 2.224MeV• Binding energy/nucleon = 2.224/219Nucles massmnucleusMass of Z protons and N neutrons: Zmp + NmnExperiment says:mnucleus < Zmp + NmnBinding energy of different nuclei20For nuclei smaller than Fe the binding energy increases with A: you have to supply more energy to win nuclear bounds.Fe with A = 56 nucleons has 8.79 MeV/nucleon (amount of energy to remove one nucleon from Fe nuclei)Peaks at 4He, 12C and 16O because these nuclei are more tightly bond.Nuclear force is short range: as nucleus grows nuclear bonds are saturated and nuclei interact only with neighbors => Ebinding almost constantBinding energy released: fusion and fission21Combine p and n to form 4He7MeV/nucleonbinding energy is releasedsmaller energyis released in fission of a heavy nuclei into 2 lighter nucleifusionof 2 light nuclei ina heavier oneStable and Unstable IsotopesIsotope = same ZIsotone = same NIsobar = same AStability of nuclei• Dots: naturally occurring isotopes.• Shaded region: isotopes created in the laboratory.•
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