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Waves, Light & Quanta

Waves, Light & Quanta. Tim Freegarde. Web Gallery of Art; National Gallery, London. Photoelectric effect. A. photocurrent. increasing intensity. optical frequency. voltage. electron charge. work function. optical frequency. Planck’s constant. WORK FUNCTION. threshold for photocurrent.

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Waves, Light & Quanta

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  1. Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London

  2. Photoelectric effect A photocurrent increasing intensity optical frequency voltage electron charge work function optical frequency Planck’s constant WORK FUNCTION • threshold for photocurrent • no current above threshold wavelength regardless of intensity • applied voltage BIAS VOLTAGE • applied voltage changes threshold • threshold voltage proportional to optical frequency 2

  3. Compton scattering GRAPHITE TARGET wavelength shift 0.711 Å X-RAYS 0 45 90 135 angle • photon momentum A H Compton, Phys Rev 22 409 (1923) 3

  4. Davisson-Germer experiment • electron wavelength NICKEL TARGET C Davisson & L H Germer, Phys Rev 30 705 (1927) ELECTRON DIFFRACTION • electrons behave like waves 4

  5. Light and optics • energy quantized in units of (h = Planck’s constant) • momentum quantized in units of • angular momentum quantized in units of RAYS • straight propagation paths • least time (Fermat’s principle) focus • reflection, refraction, lenses, telescopes, microscopes directrix WAVES • Huygens’ description of propagation, reflection, refraction • polarization, colour (wavelength, frequency) • diffraction, interference, beats, interferometers • Maxwell’s electromagnetism, Einstein’s relativity PHOTONS 5

  6. Bohr model of the hydrogen atom + • circular orbits BOHR MODEL • quantized angular momentum • de Broglie wavelength • quantized energy levels • Hydrogen energy level measurements and calculations agree to 15 figures 6

  7. Bohr model of the hydrogen atom energy • allowed energies 0 n = 3 n = 2 n = 1 n =  Rydberg constant • emission wavelengths 7

  8. Atomic line spectra energy • allowed energies n =  0 n = 3 n = 2 n = 1 Rydberg constant • emission wavelengths 8

  9. Atomic line spectra n =  energy n = 3 0 n = 2 universe-review.ca scope.pari.edu n = 1 Paschen Balmer Lyman 9

  10. Hydrogenic atoms energy • allowed energies 0 n = 3 n = 2 n = 1 n =  Rydberg constant • emission wavelengths 10

  11. Franck-Hertz experiment singlet triplet Hg J Franck & G Hertz, Verh. Dtsch. Phys. Ges. 16 457 (1914) • accelerate electrons through atomic vapour • periodic modulation of measured current • inelastic collisions when electron energy equals atomic transition energy G Rapior et al., Am J Phys 74 423 (2006) 11

  12. Quantum theory • energy quantized in units of (h = Planck’s constant) • momentum quantized in units of • frequency determined by energy • de Broglie wavelength determined by momentum • angular momentum quantized in units of • angular momentum quantized in units of PHOTONS • blackbody radiation • photoelectric effect • Compton scattering PARTICLES • electron diffraction • atomic theory • Stern-Gerlach • discrete energy levels for bound particles • atomic theory 12

  13. Wave-particle duality + + WHAT SORT OF WAVE? • transverse/longitudinal motion? • density? transverse QUANTUM WAVEFUNCTION ? • amplitude2 describes probability • phase has no classical analogue • rate of phase variation defines frequency and wavelength • amplitude and phase combined to form complex number density • phase matters! 13

  14. Diffracting molecules • molecule wavelength • molecular wavefunction S Gerlich et al, Nature Physics 3 711 (2007) MOLECULE DIFFRACTION • molecules behave like waves 14

  15. Ramsauer-Townsend effect A S G Kukolich, Am. J. Phys. 36 701 (1968) Ar • anomalous dip in scattering probability at low energy • proves to be interference from front and rear ‘reflections’ from Ar atom 15

  16. Particle interference MOLECULE DIFFRACTION and RAMSAUER-TOWNSEND • give particle two or more routes through experiment • interference depends upon relative phases of contributions • phase depends upon path difference and wavelength STATIONARY PARTICLES • give particle two or more routes through experiment • interference depends upon relative phases of contributions • phase depends upon frequency difference and duration 16

  17. Atomic clock energy 0 • Cs atom •  = 9.1926 GHz • electron density depends upon relative phase of superposition components 17

  18. Atomic clock • atomic wavefunction x/a0 x/a0 • electron density depends upon relative phase of superposition components 18

  19. Quantum measurement energy • allowed energies 0 n = 3 n = 2 n = 1 THE HYDROGEN ATOM n =  QUANTUM MEASUREMENT • measured energy must be one of allowed values • …but until measurement, any energy possible • after measurement, subsequent measurements will give same value 19

  20. Quantum mechanics • particles behave like waves, and vice-versa • energies and momenta can be quantized, ie measurements yield particular results • all information about a particle is contained within a complex wavefunction, which determines the probabilities of experimental outcomes • 80 years of experiments have found no inconsistency with quantum theory • explanation of the ‘quantum measurement problem’ – the collapse of the wavefunction upon measurement – remains an unsolved problem 20

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