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

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

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3 3 Compton scattering A H Compton, Phys Rev 22 409 (1923) GRAPHITE TARGET 0.711 Å X-RAYS wavelength shift angle 04590135 photon momentum

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

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

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

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

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

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

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

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

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

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13 Wave-particle duality + WHAT SORT OF WAVE? transverse/longitudinal motion? + transverse density density? QUANTUM WAVEFUNCTION amplitude 2 describes probability phase has no classical analogue amplitude and phase combined to form complex number ? phase matters! rate of phase variation defines frequency and wavelength

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

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

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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

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

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18 Atomic clock x/a 0 electron density depends upon relative phase of superposition components atomic wavefunction

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

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20 Quantum mechanics 1.particles behave like waves, and vice-versa 2.energies and momenta can be quantized, ie measurements yield particular results 3.all information about a particle is contained within a complex wavefunction, which determines the probabilities of experimental outcomes 4.80 years of experiments have found no inconsistency with quantum theory 5.explanation of the ‘quantum measurement problem’ – the collapse of the wavefunction upon measurement – remains an unsolved problem

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