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UF PHY 3101 - The Nucleus

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The NucleusRutherford ScatteringRutherford Model of the AtomThe NeutronThe Periodic TableNomenclatureAtomic Mass Units (u)Binding EnergyAtomic Binding EnergiesNuclear Binding EnergiesNuclear Potential WellSize of NucleiThe NucleusPHY 3101D. Acosta01/14/19PHY 3101 -- D. Acosta 2Rutherford ScatteringExperiments by Geiger & Marsden in 190901/14/19PHY 3101 -- D. Acosta 3Rutherford Model of the AtomConclusion: the atom contains a positive nucleus < 10 fm in size (1 fm = 10-15 m)01/14/19PHY 3101 -- D. Acosta 4The NeutronThe neutron was discovered in 1932 by James Chadwick-particles accelerated in a small accelerator and collided with Be nuclei–Neutral, very penetrating radiation–Found by elastic scattering off protons in paraffin waxBy the way, the positron (anti-electron) also was discovered in 1932 by Carl Anderson in cosmic rays–Anti-matter predicted by P.A.M. Dirac in his relativistic version of the Schrodinger Equation01/14/19PHY 3101 -- D. Acosta 5The Periodic TableAll elements composed of just electrons, neutrons, and protons Elements of the same group have nearly the same chemical propertyChemical periodicity depends on the atomic number ZAny other fundamental particles? Next chapter…01/14/19PHY 3101 -- D. Acosta 6NomenclatureX is the elementA is the atomic mass (Z+N)Z is the atomic number (number of protons)N is the number of neutronsAtoms are neutral. Number of electrons equals number of protons = ZChemical properties depend on Z–Ordering of Periodic Table given by valence configuration of electronsIsotopes:–Same Z, different AIsobars:–Same A, different Z Isotones:–Same N, different AZAX24He He2313H He23613C N71401/14/19PHY 3101 -- D. Acosta 7Atomic Mass Units (u)The atomic mass is the mass of an atomic isotope, including electronsNote that mass of 12C is 6 mp + 6mn + 6me = 12.1 u > 12.0 uThe nucleus is bound–Binding energy is 0.1 u = 90 MeV–It takes energy to liberate all particlesShould not think of mass as measuring the number of particles, only the rest energy of the system:–Mass is a measure of inertia (a = F/m)not contentsmass of u1212C 1 1 66054 101 00727647 938 271 00866490 939 575 4858 10 0 51127 2224 2 u kg = 931.49 MeV / u = MeV / u = MeV / u = MeV /  .. .. .. .cm cm cm cpne01/14/19PHY 3101 -- D. Acosta 8Binding EnergyTake the mass of all particles individually, including electrons, and subtract the mass of the combined systemA system is bound if the binding energy is positive.Example: Deuterium–Note that e- mass cancelsIf the binding energy is negative, the system will decay. The energy released isB m m c  separate combineda f2Q m m c B    combined separatea f2B M M M cu u u cu u = H n H = = MeV / = MeV011211 221 007825 1 008665 2 0141020 002388 931 52 224b g bg b g  . . .. ..01/14/19PHY 3101 -- D. Acosta 9Atomic Binding EnergiesThe Coulomb potential for an electron in a hydrogen-like atom can be written in terms of the dimensionless fine structure constantThe energy levels are given byHydrogen:Positronium (e+e-):These are the binding energies!–e.g. mass of H is less than mass of e+pThe Bohr radii areV rc Zrec   2041137E cZnm mne N  FHGIKJ121 12 2221     m Ee eV113 6.  mEe26 81 eV.rcn rn    10 53 102110 m.01/14/19PHY 3101 -- D. Acosta 10Nuclear Binding EnergiesConsider the binding energy of the deuteron –proton–neutron bound state The binding potential is roughly similar to that of the Coulomb potential, but with a dimensionless constant characteristic of the Strong Nuclear Force rather than EMThe energy levels are given byAgrees with measured value of 2.2 MeV 1 million times larger than atomic energies!Nuclear radius is 10,000 times smaller:V rcrqcsssafaf   20401 10.E cnm mmcEn sp np FHGIKJ   1211 1247012470 0 1 2 32 221212  MeV / MeV MeV. .rcn rns    14 2 102115 m.01/14/19PHY 3101 -- D. Acosta 11Nuclear Potential WellRutherford concludes from Geiger and Marsden that the range of the Strong Nuclear Force is < 10-14 m–No deviation in the scattering rate of the highest-energy -particles off nuclei from that predicted by electromagnetic Coulomb scatteringThus, the Strong Nuclear Force is short-ranged, and does not extend to infinityTo probe the size of nuclei, need higher energies than -particles from radioactive decayThe nuclear potential well resembles a semi-infinite potential well-particles inside the nucleus must tunnel to escape! Higher rate for higher energy -particles01/14/19PHY 3101 -- D. Acosta 12Size of NucleiRobert Hofstadter performs experiment at Stanford using a new linear accelerator for electrons in 1950sE = 100 -- 500 MeV = h / p = 2.5 fmThe proton is not a point! (Deviation of elastic scattering rate from Rutherford Scattering prediction)Proton and nuclei have extended charge distributionsNobel prize in 1961nucleusrr R aR r A V R Araafa f     001 3 301514312 100 5exp /../ #nucleons m = 1.2 fm


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UF PHY 3101 - The Nucleus

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