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 NeutronThe 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 waxBy 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 TableAll elements composed of just electrons, neutrons, and protons Elements of the same group have nearly the same chemical propertyChemical periodicity depends on the atomic number ZAny other fundamental particles? Next chapter…01/14/19PHY 3101 -- D. Acosta 6NomenclatureX is the elementA is the atomic mass (Z+N)Z is the atomic number (number of protons)N is the number of neutronsAtoms are neutral. Number of electrons equals number of protons = ZChemical properties depend on Z–Ordering of Periodic Table given by valence configuration of electronsIsotopes:–Same Z, different AIsobars:–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 electronsNote that mass of 12C is 6 mp + 6mn + 6me = 12.1 u > 12.0 uThe nucleus is bound–Binding energy is 0.1 u = 90 MeV–It takes energy to liberate all particlesShould 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 EnergyTake the mass of all particles individually, including electrons, and subtract the mass of the combined systemA system is bound if the binding energy is positive.Example: Deuterium–Note that e- mass cancelsIf 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 EnergiesThe Coulomb potential for an electron in a hydrogen-like atom can be written in terms of the dimensionless fine structure constantThe energy levels are given byHydrogen:Positronium (e+e-):These are the binding energies!–e.g. mass of H is less than mass of e+pThe Bohr radii areV rc Zrec 2041137E cZnm mne N FHGIKJ121 12 2221 m Ee eV113 6. mEe26 81 eV.rcn rn 10 53 102110 m.01/14/19PHY 3101 -- D. Acosta 10Nuclear Binding EnergiesConsider 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 EMThe energy levels are given byAgrees 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 WellRutherford 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 scatteringThus, the Strong Nuclear Force is short-ranged, and does not extend to infinityTo probe the size of nuclei, need higher energies than -particles from radioactive decayThe 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 NucleiRobert Hofstadter performs experiment at Stanford using a new linear accelerator for electrons in 1950sE = 100 -- 500 MeV = h / p = 2.5 fmThe proton is not a point! (Deviation of elastic scattering rate from Rutherford Scattering prediction)Proton and nuclei have extended charge distributionsNobel prize in 1961nucleusrr R aR r A V R Araafa f 001 3 301514312 100 5exp /../ #nucleons m = 1.2 fm
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