PHYS 3446 – Lecture #2Why do Physics? Structure of MatterQuantum MechanicsEvolution of Atomic ModelsRutherford ScatteringPlanetary Model Bohr ModelElectron Cloud ModelRutherford ScatteringElastic ScatteringAnalysis Case 1Analysis Case 2HW 1 AssignmentWednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 1PHYS 3446 – Lecture #2Wednesday, Sep. 1 2010Dr. Brandt1. Introduction2. History of Atomic Models3. Rutherford Scattering4. Rutherford Scattering with Coulomb forceWednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 2Why 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⇒Understanding leads to applications (electricity, computers, etc.)Exp.{Theory {Wednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 3High Energy PhysicsStructure of Matter10-10m10-14m10-15m<10-18m10-9mMatter Molecule Atom NucleusuQuark<10-19mprotons, neutrons,mesons, etc.π,Ω,Λ...top, bottom,charm, strange,up, downCondensed matter/Nano-Science/ChemistryAtomic PhysicsNuclearPhysicsBaryon(Hadron)Electron(Lepton)10-2mWednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 4Quantum 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:– The Coulomb force is attractive only for oppositely charged particles, yet a nucleus 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, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 5Evolution 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 charge to mass 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 tubespersonally I prefer chocolate chip cookie modelWednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 6Rutherford Scattering• 1911: Geiger and Marsden with Rutherford performed a scattering experiment firing alpha particles at a thin gold foilWednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 7Planetary Model • 1912: Rutherford’s planetary model, an atomic model with a positively charged heavy core surrounded by circling electrons – Unstable Why?• The electrons will eventually get pulled in to the nucleus, destroying the atomWednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 8Bohr Model• 1913: Neils Bohr proposed the Orbit Model, where electrons occupy well quantified orbits– Electrons can only transition to pre-defined orbitsWednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 9Electron Cloud Model• 1926: Schrödinger and de Broglie proposed the Electron Cloud Model based on quantum mechanicsWednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 10Rutherford 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 type of scattering?)• Conservation vs. InvariantWednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 11Elastic Scattering• From momentum conservation• From kinetic energy conservation• From these, we obtainmtmαθφAfter Collision0vvαtv0v =20v =21ttmvmα−=ttm v mvmααα+=ttmvvmαα+22ttmvvmαα+2tvvα⋅***Eq. 1.3***Eq. 1.2Wednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 12Analysis Case 1• If mt<<mα, – left-hand side is positive– vαand vtmust be in the same direction (both positively or negatively directed)– Using the actual masses– and– We obtain – If mt=me, then mt/mα~10-4. (Eq. 1.2)– Thus, pe/pα0<10-4. – Change of momentum of alpha particle is negligible 212tttmv vvmαα−=⋅20.5 /em MeV c≈0vvα≈2etvv vα= ≤324 10 /m MeV cα≈×Wednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 13Analysis Case 2• If mt>>mα, – left-hand side of the above becomes negative– vαand vtin opposite direction– Using the actual masses– and – We obtain– If mt=mAu, then mt/mα~50. (Eq 1.2)– Thus, pAu<2pα0– alpha particle deflected backwards 212tttmv vvmαα−=⋅522 10 /t Aum m MeV c≈ ≈×0vvα≈±324 10 /m MeV cα≈×2ttv mv mαα≤Wednesday, Sep. 1, 2010 PHYS 3446, Fall 2010 Andrew Brandt 14HW 1 Assignment1. Compute the masses of electron, proton and alpha particles in MeV/c2,using E=mc2.• Need to look up masses of electrons, protons and alpha particles in kg.2. Compute the gravitational and the Coulomb force for a Hydrogen atom with the electron and proton separated by 10-10m and calculate the ratio Fcoul/Fgrav.3. Derive the following equations in your book:• Eq. # 1.3, 1.17, 1.32• Show detailed work and any necessary explanation • Due next Wednesday, Sept. 8. (no class Sep.
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