PHYS 3446 – Lecture #2AnnouncementsWhy do Physics?Structure of MatterTheory for Microscopic Scale, QMEvolution of Atomic ModelsHistory of Atomic Models cnt’dSlide 8Slide 9Slide 10Rutherford ScatteringElastic ScatteringAnalysis Case IAnalysis Case IIRutherford Scattering with EM Force 1Rutherford Scattering with EM Force 2Rutherford Scattering with EM Force 3Rutherford Scattering with EM Force 4Rutherford Scattering with EM Force 5Rutherford Scattering with EM Force 6Rutherford Scattering with EM Force 7AssignmentsWednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu1PHYS 3446 – Lecture #2Wednesday, Aug. 30, 2006Dr. Jae Yu1. Introduction2. History on Atomic Models3. Rutherford Scattering4. Rutherford Scattering with Coulomb force5. Scattering Cross Section6. Measurement of Cross SectionsWednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu2Announcements•Mail distribution list is ready. Go ahead and subscribe! –5 points extra credit if done by next Wednesday, Sept. 6–3 points extra credit if done by next Friday, Sept. 8•Extra credit opportunities–Obtain a particle data booklet and a pocket diary •http://pdg.lbl.gov/pdgmail/–Subscribe to the Symmetry Magazine (free!)•http://www.symmetrymagazine.org •Request for printed copies–Subscribe to the printed copies of CERN Courier Magazine•http://www.cerncourier.com/ •Send e-mail to Janice Voss at [email protected] –3 points each if done by Wednesday, Sept. 6.Wednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu3Why do Physics?•To understand nature through experimental observations and measurements (Research)•Establish limited number of fundamental laws, usually with mathematical expressions•Predict nature’s courses⇒Theory and Experiment work hand-in-hand⇒Theory works generally under restricted conditions⇒Discrepancies between experimental measurements and theory presents opportunities to quantum leap⇒Improves our everyday lives, though some laws can take a while till we see amongst usExp.{Theory {Wednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu4High Energy Physics Structure of Matter10-10m10-14m10-15m<10-18m10-9mMatter Molecule Atom NucleusuQuark<10-19mprotons, neutrons,mesons, etc.top, bottom,charm, strange,up, downCondensed matter/Nano-Science/ChemistryAtomic PhysicsNuclearPhysicsBaryon(Hadron)Electron(Lepton)10-2mWednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu5Theory for Microscopic Scale, QM•Difficult to describe Small scale phenom. w/ just CM and EM•The study of atomic structure led to quantum mechanics–Long range EM force is responsible for holding atoms together (why ?)–Yet sufficiently weak for QM to estimate properties of atoms reliably•In Nucleus regime, the simple Coulomb force does not work. Why?–The force in nucleus holds positively charged particles together•The known forces in nature–Strong ~ 1 –Electro-magnetic ~ 10-2 –Weak ~ 10-5 –Gravitational ~ 10-38Wednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu6Evolution of Atomic Models•1803: Dalton’s billiard ball model•1897: J.J. Thompson Discovered electrons–Built on all the work w/ cathode tubes–Called corpuscles–Made a bold claim that these make up atoms–Measured m/e ratio•1904: J.J. Thompson Proposed a “plum pudding” model of atoms –Negatively charged electrons embedded in a uniformly distributed positive chargeCathode ray tubeThompson’s tubesWednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu7History of Atomic Models cnt’d•1911: Geiger and Marsden with Rutherford performed a scattering experiment with alpha particles shot on a thin gold foilWednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu8History of Atomic Models cnt’d•1912: Rutherford’s planetary model, an atomic model with a positively charged heavy core surrounded by circling electrons –Deficiency of instability. Why?•The electrons will eventually get pulled onto the nucleus, destroying the atomWednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu9History of Atomic Models cnt’d•1913: Neils Bohr proposed the Orbit Model, where electrons occupy well quantified orbits–Electrons can only transition to pre-defined orbitsWednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu10History of Atomic Models cnt’d•1926: Schrödinger and de Broglie proposed the Electron Cloud Model based on quantum mechanicsWednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu11Rutherford Scattering•A fixed target experiment with alpha particle as projectile shot on thin gold foil–Alpha particle’s energy is low Speed is well below 0.1c (non-relativistic)•An elastic scattering of the particles•What are the conserved quantities in an elastic scattering?–Momentum–Kinetic EnergyWednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu12Elastic Scattering•From momentum conservation•From kinetic energy conservation•From these two, we obtainmtmmmtAfter Collisions0vrvartvr0v =r20v =21ttmvma� �- =� �� �ttm v m vmaaa+=r rttmv vmaa+r r2 2ttmv vmaa+2tv va�r rWednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu13Analysis Case I•If mt<<m, –left-hand side becomes positive–v and vt must be in the same direction–Using the actual masses– and–We obtain –If mt=me, then mt/m~10-4. –Thus, pe/p0<10-4. –Change of momentum of alpha particle is negligible 21 2tttmv v vmaa� �- = �� �� �r r20.5 /em MeV c�0v va�2e tv v va= �3 24 10 /m MeV ca� �Wednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu14Analysis Case II•If mt>>m, –left-hand side of the above becomes negative–v and vt is opposite direction–Using the actual masses– and –We obtain–If mt=mAu, then mt/m~50. –Thus, pe/p0~2p0. –Change of momentum of alpha particle is large• particle can even recoil 21 2tttmv v vmaa� �- = �� �� �r r5 22 10 /t Aum m MeV c� � �0v va�3 24 10 /m MeV ca� �2t tv m v ma a�Wednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu15Rutherford Scattering with EM Force 1•Let’s take into account only the EM force between the and the atom •Coulomb force is a central force, so a conservative force•Coulomb potential between particles with Ze and Z’e electrical charge separated by distance r is•Since the total energy is conserved, ( )2'ZZ eV rr=201constant>02E mv= =02 vEm� =Wednesday, Aug. 30, 2006 PHYS 3446, Fall 2006Jae Yu16•From the energy relation, we
View Full Document
Unlocking...