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What is Modern Physics?

What is Modern Physics?. Modern physics only came of age in the 1900’s. Physicists discovered that Newtonian mechanics did not apply when objects were very small or moved very fast ! If things are confined to very small dimensions (nanometer-scale), then QUANTUM mechanics is necessary.

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What is Modern Physics?

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  1. What is Modern Physics? • Modern physics only came of age in the 1900’s. • Physicists discovered that Newtonian mechanics did not apply when objects were very small or moved very fast! • If things are confined to very small dimensions (nanometer-scale), then QUANTUM mechanicsis necessary. • Atomic orbitals, quantum heterostructures. • If things move very fast (close to the speed of light), then RELATIVISTIC mechanics is necessary. • Cosmic particles, atomic clocks (GPS), synchrotrons. • Plan for Physics 320. • Test #1: Nuclear Atom, Wave/Particle Duality, Wave Packets • Test #2: Schroedinger Equation, Atomic & Solid-state Physics • Nuclear Physics, Relativity Topic 1: Nuclear Atomic Model

  2. Topic 1: Nuclear Atomic Model • Optical (Atomic) Spectra • Lower-energy optical absorption/emission lines from materials indicate quantized electron energy levels. • Bohr model predicts energy transitions for one-electron atoms. • X-ray Spectra • Analogous to optical spectra, but for higher-energy x-ray transitions of heavier, multi-electron elements. • Franck-Hertz Experiment • Quantized inelastic scattering of electrons in Hg gas provide evidence for atomic energy levels. • Rutherford Scattering Experiment • Large scattering angles of alpha particles from atoms in a metal foil indicate a “hard” nuclear model. Topic 1: Nuclear Atomic Model

  3. Atomic Spectra • In 1885, Balmer observed Hydrogen spectrum and saw colored lines. • Found empirical formula for discrete wavelengths of lines. • Formula generalized by Rydberg for all one-electronatoms. Q: Where is Red vs. Blue line? Prism separates wavelengths Topic 1: Nuclear Atomic Model

  4. Atomic Spectra: Modern Physics Lab High Voltage Supply (to “excite” atoms) Neon Tube Diffraction Grating (to separate light) Eyepiece (to observe lines) Topic 1: Nuclear Atomic Model

  5. Atomic Spectra: Hydrogen Energy Levels E = 0 eV Paschen Series (IR) n = 3 Balmer Series (visible) n = 2 Energy Lyman Series (ultraviolet) E1 = -13.6 eV n = 1 Lyman Balmer Paschen Example Data Topic 1: Nuclear Atomic Model

  6. Atomic Spectra: Rydberg Formula for H • Rydberg constant R ~ 1.097 × 107 m-1 • nfinal = 1 (Lyman), 2 (Balmer), 3 (Paschen) For Hydrogen: • Example forn = 2 to 1transition: Topic 1: Nuclear Atomic Model

  7. Bohr Model • Problem:Classical model of the electron “orbiting” nucleus is unstable. Why unstable? • Electron experiences centripetal acceleration. • Accelerated electron emits radiation. • Radiation leads to energy loss. • Electron eventually “crashes” into nucleus. • Solution:In 1913, Bohr proposed quantized model of the H atom to predict the observed spectrum. Topic 1: Nuclear Atomic Model

  8. Bohr Model: Quantization of L, f • Bohr proposed two “quantum” postulates: • Postulate #1: Electrons exist in stationary orbits (no radiation) with quantized angular momentum. • Postulate #2: Atom radiates withquantized frequency f (or energy E) when electron makes a transition between two energy states. • Note: The product hc of Planck’s constant h and the speed of light c gives: hc = 1240 eV nm in “Modern Physics” units. Topic 1: Nuclear Atomic Model

  9. Bohr Model: Quantization of r, E • Quantized angular momentum L leads to quantized radii and energies for an electron in a hydrogen atom or any ionized, one-electron atom. • Derivation uses the following: Topic 1: Nuclear Atomic Model

  10. Bohr Model: IMPORTANTEnergyFormula • Energy transitionsyieldgeneral Rutherford formula. • Applicable to ionized atoms of nuclear charge Z with only one electron. • where hc = 1240 eV nm in “Modern Physics” units. Topic 1: Nuclear Atomic Model

  11. Bohr Model: Transition Energy Problem Find the energy E , frequency f , and wavelength l of the series limit (i.e., highest energy transition) for the Brackettspectral series (nf = 4) of Be3+. Topic 1: Nuclear Atomic Model

  12. Bohr Model : Unknown Transition Problem If the energy of a particular transition in the Helium Paschenseries is 2.644 eV, find the corresponding transition, i.e. initial and final n values. Topic 1: Nuclear Atomic Model

  13. Bohr Model: Ionization Energy Problem Suppose that a He atom (Z=2) in its ground state(n = 1) absorbs a photon whose wavelength is l= 41.3 nm. Will the electron beionized? • Find the energy of the incoming photon and compare it to the ground state ionization energy of helium, or E0 from n=1 to . • The photon energy (30 eV) is less than the ionization energy (54 eV), so the electron will NOT be ionized. Topic 1: Nuclear Atomic Model

  14. Bohr Model: Rotational Energies for Diatomic Molecule • In addition to quantized electronic energy levels, there are quantized rotational energy levels due to “rotating” nuclei. n = 5 n = 4 Energy n = 3 n = 2 n = 1 Diatomic Molecule Topic 1: Nuclear Atomic Model

  15. Bohr Model : Rotational Energy Problem Calculate the energy difference between the first excited rotational state and the ground state for a bromine (80 amu) diatomic molecule (R~ 0.2 nm). Use only “modern physics” units of nm and eV (amu = 931.5 MeV/c2). Topic 1: Nuclear Atomic Model

  16. Bohr Model: “Vibrational” SHO Energy Levels • There are also quantized vibrational energy levels due to “oscillating” nuclei. n = 5 n = 4 Energy n = 3 n = 2 n = 1 Topic 1: Nuclear Atomic Model

  17. X-Ray Spectra • In 1913, Moseley measured characteristic x-ray spectra of 40 elements (energy ~ keV). • Observed “series” of x-ray energy levels called K, L, M, etc. • Analogous to optical series for hydrogen (e.g. Lyman, Balmer, Paschen) • X-rays vs. optical light • Higher-energy x-ray transitions for heavier elements. • Lower-energy optical transitions for lighter elements. • Moseley Plot gives equation with similarities to Rydberg equation. Topic 1: Nuclear Atomic Model

  18. X-ray Spectra: “Stylized” Diagram of Atomic Levels Mafor n = 4to3 Lafor n = 3to2 Kaforn = 2to1 n = 1 n = 2 afor n+1 to n bfor n+2 to n gfor n+3 to n n = 3 Topic 1: Nuclear Atomic Model

  19. X-ray Spectra: Moseley Plot and Energy Formulas K Series n = 2,3,etc. to n = 1 Wavelength l (Å) L Series Lan = 3 to 2 • Derived from Bohr’s formula with Z-1 “effective” charge instead of Z due to shielding of nucleus. Kan = 2 to 1 L Series n = 3,4,etc. to n = 2 K Series Kbn = 3 to 1 Topic 1: Nuclear Atomic Model

  20. X-ray Spectra: Transition Energy Problem Find the energy of the Kbx-ray line for Al. Topic 1: Nuclear Atomic Model

  21. X-ray Spectra: Unknown Z Problem If the wavelength of the La x-ray line for an unknown element is l = 0.3617 nm, find the element number Z. Topic 1: Nuclear Atomic Model

  22. Franck-Hertz Experiment • In 1914, Franck and Hertz directly measured the energy quantization of atoms via the inelastic scattering of electrons. • Electron IN and Electron OUT (same electrons) • Summary of Experiment • Measure current of electron beam (I) vs. accelerating grid voltage (V) inside a glass tube filled with Hg gas (5 eV transition). Topic 1: Nuclear Atomic Model

  23. Franck-Hertz Experiment: Modern Physics Lab Franck-Hertz Tube Electron Beam Acceleration Voltage Collector Voltage Sensor #2: Collector Current Voltage Sensor #1: Acceleration Voltage Topic 1: Nuclear Atomic Model

  24. Franck-Hertz Experiment: I-V Data • At 4V: e- reaches collector. • EK = 4 eV: Observe maximum current I. • At 5V: e-excites (1) Hg atom. • Promote Hg e- to excited state. • EK = 5eV - 5eV (to excite Hg) = 0e- does not reach collector. • Observe minimum current I. • At 6V: e- excites (1) Hg atom & reaches collector. • Ek = 6eV - 5eV = 1eVe- barely reaches collector. • Current starts to rise again. • At 10V: e- excites (2) Hg atoms. • Ek = 10eV - 2(5eV) = 0e- does not reach collector. • Observe 2ndminimum in current I. • Continue with same logic to explain multiple minima in IV curve. IV Data Topic 1: Nuclear Atomic Model

  25. Rutherford Scattering: Nuclear Model • Rutherford scattering probes the atom. (Hit it with something!) • Beam of a particles (He2+) strikes a thin gold metal foil. • Atoms in the foil scatter the alpha particles through various scattering angles q that are detected with a scintillation screen. • 180º scattering can occur (“back bounce”), indicating a “hard core” interaction between the a particles and atoms in the foil. • “Nuclear” modelby Rutherford explains large scattering angles. Topic 1: Nuclear Atomic Model

  26. Rutherford Scattering: Nuclear Model • Atomic Model must include: 10-10 m dia., electrons, neutral atom. • Model #1 - Thomson’s “Plum Pudding” Model. • Model #2 - Rutherford’s Hard Core “Nuclear” Model.  Nuclear Model proven correct by Rutherford’s experiment. “Plum Pudding” Model “Nuclear” Model electrons + sphere a Failure (q too small) +Ze (nucleus) Success (large q possible) Topic 1: Nuclear Atomic Model

  27. Rutherford Scattering: Schematic with Parameters • Scattering occurs due to coulombic electric repulsion FE between incoming +a particles and +nuclei in metal foil. • b= impact parameter (distance of closest approach, b gives q) • s = pb2= scattering cross section q1 q1 Hyperbolic path q2 b2 a2 a1 b1 +Ze Topic 1: Nuclear Atomic Model

  28. Rutherford Scattering: Other Quantities • Scattering fractionf=fraction of particles scattered through angles > q for given b. • Radius of closest approach rd • Derive using conservation of kinetic and potential energy. Topic 1: Nuclear Atomic Model

  29. Rutherford Scattering: Fraction f Problem A gold foil(Z = 79, n = 5.9×1028 atoms/m3) of thickness 2 mm is used in a Rutherford experiment to scatter aparticles with energy7 MeV. Find the fraction fof particles scattered at anglesq > 10°. • First, find the impact parameter b for q= 10° and then solve for f. Topic 1: Nuclear Atomic Model

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