Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London 1 WORK FUNCTION • threshold for photocurrent • no current above threshold wavelength regardless of intensity A photocurrent Photoelectric effect increasing intensity • applied voltage BIAS VOLTAGE • applied voltage changes threshold • threshold voltage proportional to optical frequency optical frequency h eV voltage electron charge work function optical frequency Planck’s constant 2 wavelength shift Compton scattering GRAPHITE TARGET 0.711 Å X-RAYS 0 45 90 135 angle A H Compton, Phys Rev 22 409 (1923) • photon momentum h p 3 Davisson-Germer experiment NICKEL TARGET C Davisson & L H Germer, Phys Rev 30 705 (1927) ELECTRON DIFFRACTION • electrons behave like waves • electron wavelength h p 4 Light and optics 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 • energy quantized in units of h (h = Planck’s constant) h • momentum quantized in units of h k c h • angular momentum quantized in units of 2 5 Bohr model of the hydrogen atom BOHR MODEL • circular orbits e2 mv 2 2 40 r r + • quantized angular momentum mvr n • de Broglie wavelength • quantized energy levels h p E h • Hydrogen energy level measurements and calculations agree to 15 figures f1S 2 S 2 466 061 413187 074 34 Hz R 10 973 731.568 527 73 m 1 6 Bohr model of the hydrogen atom E me4 1 3 2 2 hc 8h 0 c n R Rydberg 2 constant n energy • allowed energies me4 1 E 2 2 240 n n= 0 n=3 hcR 4 n=2 hcR n=1 • emission wavelengths 1 1 E Ei E j R 2 2 n n hc hc j i 1 R 10 973 731.568 527 73 m 1 7 Atomic line spectra E me4 1 3 2 2 hc 8h 0 c n R Rydberg 2 constant n energy • allowed energies me4 1 E 2 2 240 n n= 0 n=3 hcR 4 n=2 hcR n=1 • emission wavelengths 1 1 E Ei E j R 2 2 n n hc hc j i 1 R 10 973 731.568 527 73 m 1 8 energy Atomic line spectra n= 0 n=3 Paschen n=2 hcR 4 Balmer universe-review.ca scope.pari.edu hcR n=1 Lyman R 10 973 731.568 527 73 m 1 9 Hydrogenic atoms E me4 Z 2 3 2 2 hc 8h 0 c n R 2 Rydberg 2 Z constant n energy • allowed energies Z 2 me4 1 E 2 2 240 n n= 0 n=3 hcR 4 n=2 hcR n=1 • emission wavelengths 1 1 E Ei E j 2 Z R 2 2 n n hc hc j i 1 R 10 973 731.568 527 73 m 1 10 Franck-Hertz experiment 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 singlet triplet Hg G Rapior et al., Am J Phys 74 423 (2006) 11 Quantum theory PHOTONS • energy quantized in units of (h = Planck’s constant) h • blackbody radiation h • momentum quantized in units of h k c h • angular momentum quantized in units of 2 • photoelectric effect • Compton scattering PARTICLES • frequency determined by energy • de Broglie wavelength determined by momentum E h p k • angular momentum quantized in units of • discrete energy levels for bound particles h h 2 • electron diffraction • atomic theory • Stern-Gerlach • atomic theory 12 Wave-particle duality WHAT SORT OF WAVE? • transverse/longitudinal motion? + • density? QUANTUM WAVEFUNCTION • amplitude2 describes probability • phase has no classical analogue • rate of phase variation defines frequency and wavelength transverse ? + • amplitude and phase combined to form complex number ae i density • phase matters! 13 Diffracting molecules S Gerlich et al, Nature Physics 3 711 (2007) MOLECULE DIFFRACTION • molecules behave like waves h • molecule wavelength p ikx • molecular wavefunction ae 14 Ramsauer-Townsend effect Ar A S G Kukolich, Am. J. Phys. 36 701 (1968) • anomalous dip in scattering probability at low energy • proves to be interference from front and rear ‘reflections’ from Ar atom 15 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 Atomic clock energy 2 e i 0 t 0 1 0 2 • Cs atom 1 • = 9.1926 GHz • electron density depends upon relative phase of superposition components 17 Atomic clock 1 x/a0 • atomic wavefunction 2 x/a0 ae i E t • electron density depends upon relative phase of superposition components 18 Quantum measurement • allowed energies energy THE HYDROGEN ATOM me4 1 E 2 2 240 n n= 0 n=3 hcR 4 n=2 hcR n=1 QUANTUM MEASUREMENT 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 19 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 20