PHYS 3446 – Lecture #2Why do Physics?Structure of MatterQuantum MechanicsEvolution of Atomic ModelsHistory of Atomic Models cnt’dSlide 7Slide 8Slide 9Rutherford ScatteringElastic ScatteringAnalysis Case 1Analysis Case 2Rutherford 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 7HW 1 AssignmentWednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt1PHYS 3446 – Lecture #2Wednesday, Aug. 28 2007Dr. Brandt1. Introduction2. History of Atomic Models3. Rutherford Scattering4. Rutherford Scattering with Coulomb forceWednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt2Why do Physics?•To understand nature through experimental observations and measurements (Research)•Establish limited number of fundamental laws, usually with mathematical expressions•Predict nature⇒Theory and Experiment work hand-in-hand⇒Theory works generally under restricted conditions⇒Discrepancies between experimental measurements and theory presents opportunities to improve understanding⇒Improves our everyday livesExp.{Theory {Wednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt3High 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. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt4Quantum Mechanics•Cannot adequately describe small scale phenomena with classical mechanics and E&M•The study of atomic structure led to quantum mechanics (QM)–Long range E&M force is responsible for holding atoms together –Yet it is sufficiently weak that QM can be used to reliably predict properties of atoms •The Coulomb force cannot account for the existence of nuclei-- how do we know?–The Coulomb force is attractive only for oppositely charged particles, yet a necleus consisting totally of protons and neutrons can be stable? This implies a force that holds positively charged particles together•The known forces in nature (not just gravity and E&M!)–Strong ~ 1 –Electro-magnetic ~ 10-2 –Weak ~ 10-5 –Gravitational ~ 10-38Wednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt5Evolution of Atomic Models•1803: Dalton’s billiard ball model•1897: J.J. Thompson Discovered electrons–Built on all 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 tubespersonnally I prefer chocolate chip cookie modelWednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt6History of Atomic Models cnt’d•1911: Geiger and Marsden with Rutherford performed a scattering experiment firing alpha particles at a thin gold foilWednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt7History 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 in to the nucleus, destroying the atomWednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt8History 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. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt9History of Atomic Models cnt’d•1926: Schrödinger and de Broglie proposed the Electron Cloud Model based on quantum mechanicsWednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt10Rutherford Scattering•A fixed target experiment with alpha particle as a projectile fired at a thin gold foil–Alpha particle’s energy is low Speed is well below 0.1c (non-relativistic)•Assume an elastic scattering of the particles•What are the conserved quantities in an elastic scattering?–Momentum–Kinetic Energy (is K.E. conserved in any scattering?)Wednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt11Elastic Scattering•From momentum conservation•From kinetic energy conservation•From these, we obtainmtmmmtAfter Collisions0vrvartvr0v =r20v =21ttmvma� �- =� �� �ttm v m vmaaa+=r rttmv vmaa+r r2 2ttmv vmaa+2tv va�r rEq. 1.3Eq. 1.2Wednesday, Aug. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt12Analysis Case 1•If mt<<m, –left-hand side is 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. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt13Analysis Case 2•If mt>>m, –left-hand side of the above becomes negative–v and vt in opposite direction–Using the actual masses– and –We obtain–If mt=mAu, then mt/m~50. –Thus, pAu<2p0–alpha particle deflected backwards 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. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt14Rutherford Scattering with EM Force 1•Need to take into account 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. 28, 2008 PHYS 3446, Fall 2008Andrew Brandt15•From the energy relation, we obtain•From the definition of angular momentum, we obtain an equation of motion •From energy conservation, we obtain another equation of motionRutherford Scattering with EM Force 2•The distance vector r is always the same direction as the force throughout the entire motion, so the net torque (rxF) is 0.•Since there is no net torque, the angular momentum (l=rxp) is conserved. The magnitude of the angular momentum is
View Full Document
Unlocking...