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lecture10 - Physics 126 Lecture 10 March 11 2011 Matter...

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M.Loy, H. B. Chan 1 Physics 126 Lecture 10 March 11 2011 Matter Wave: Dawn before the birth of Quantum Mechanics Reading: Chapter 3 of Text p The two broad themes: (a) nature of radiation (b) nature of matter (atoms) p de Broglie Matter Wave Hypothesis p Davisson-Germer Electron Diffraction: Experimental verification of wave nature of matter p Wave Properties p Fourier Series p Wave Packet p Phase and Group velocity p Uncertainty Principle p Need for the development of a ‘new mechanics’
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H. B. Chan 2 Midterm exam b March 26, Saturday, LTJ (TA’s will send out seating plan) p 2:30 to 5:00 pm b Covers Lectures 1 – 12 b Closed Book p Complicated formulae and physical constants will be provided p Fundamental Equations such as below will NOT be provided. p Lorentz Transform p E 2 = (pc) 2 + (mc 2 ) 2 , β ββ = pc/E p Key Discoveries leading to the new Quantum Mechanics You are expected to know: p How the experiment was done and what were the key observations p What the experiment proved, or disproved p In what ways are that experiment important You will not be tested on the date and the place of the experiments.
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M.Loy 2010 3 WAVE-PARTICLE DUALITY OF LIGHT “ There are therefore now two theories of light, both indispensable, and … without any logical connection.” Einstein 1924 Evidence for wave-nature of light • Diffraction and interference Evidence for particle-nature of light • Photoelectric effect • Compton effect We need both to explain what we observe experimentally.
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M.Loy, H. B. Chan 4 θ λ = 2dsin θ X-ray diffraction Wavelength < 1 nm Use crystals as the “grating” Compton scattering Shift in wavelength of scattered X-ray λ ’ – λ = (h/m e c)(1 - cos θ ).
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M.Loy 2010 5 We need the dual nature of light to understand the COMPTON SCATTERING experiment! X-ray source Target Crystal (selects wavelength) Collimator (selects angle) θ Result: peak in scattered X-ray radiation shifts to lower energy (longer wavelength) than source. Amount depends on θ (but not on the target material). Measurement of the energy of the scattered X-ray requires the scattered X-ray to be wave , and its wavelength satisfy E = hc/ λ Detector Compton With Bragg crystal spectrometer technique, X-ray sources with definite energy can be used for precise experiment. This requires X-ray to be wave to be diffracted by the spectrometer. Yet all these results only make sense when we treat X-ray as particles with energy E = h ν and momentum p = h/ λ .
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M.Loy 2010 6 b Particle-Wave Duality: Bohr’s Principle of Complementarity b If your experiment is designed to measure its particle property, it behaves as particle (the scattering of photon and electron in Compton Scattering); b and if your experiment is designed to measure its wave property, it behaves as wave (Laue Diffraction, or when the X-ray energy was selected or detected using crystal diffraction). But we never measure BOTH properties at the
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This note was uploaded on 03/31/2011 for the course PHY 126 taught by Professor Hobunchan during the Spring '11 term at HKUST.

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lecture10 - Physics 126 Lecture 10 March 11 2011 Matter...

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