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. Acosta1/5/2005PHY 3101 -- D. Acosta 2Rutherford ScatteringExperiments by Geiger & Marsden in 19091/5/2005PHY 3101 -- D. Acosta 3Rutherford Model of the AtomConclusion: the atom contains a positive nucleus < 10 fm in size (1 fm = 10-15m)1/5/2005PHY 3101 -- D. Acosta 4The Neutron The neutron was discovered in 1932 by James Chadwick– α-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 Equation1/5/2005PHY 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…1/5/2005PHY 3101 -- D. Acosta 6NomenclatureZAXXis 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 A24He He2313H He23613C N7141/5/2005PHY 3101 -- D. Acosta 7Atomic Mass Units (u)mass of u1212C≡ 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 contents1 166054 10100727647 938 27100866490 939 5754858 10 051127 22242 u kg = 931.49 MeV / u = MeV / u = MeV / u = MeV /=×===×−−.......cmcmcmcpne1/5/2005PHY 3101 -- D. Acosta 8Binding EnergyBm m c=−()×separate combinedaf2 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 isQm m c B=()−×=−combined separateaf2BM M M cuu ucuu = H n H = = MeV / = MeV011211221007825 1008665 2 0141020 002388 93152224bgbgbg+−+−⋅......1/5/2005PHY 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 areVrcZrec()=−()=≈ααπε== 2041137EcZnmmneN=− = +FHGIKJ−121122221αµ µ µ=⇒=−mEe eV113 6.µ=⇒=−mEe2681 eV.rcnrn=⇒=×−=µα1053 102110 m.1/5/2005PHY 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:Vrcrqcsssafaf=−=≈>ααπεα== 20401 10.EcnmmmcEnspnp=−=+FHGIKJ≈==−()()≈−12111247012470 01 2 32221212αµµ MeV / MeV MeV..rcnrns=⇒=×−=µα142 102115 m.1/5/2005PHY 3101 -- D. Acosta 11Nuclear Potential Well Rutherford concludes from Geiger and Marsden that the range of the Strong Nuclear Force is < 10-14m– No deviation in the scattering rate of the highest-energy α-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 α-particles from radioactive decay The nuclear potential well resembles a semi-infinite potential well α-particles inside the nucleus must tunnel to escape! Higher rate for higher energy α-particles1/5/2005PHY 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 λ = h / p = 2.5 fm The proton is not a point! (Deviation of elasticscattering rate from Rutherford Scattering prediction) Proton and nuclei have extended charge distributions Nobel prize in 1961nucleusρρπrrRaRrA V R Araafaf=+−≈=∝==×=−0013 301514312 1005exp /../ #nucleons m = 1.2 fm