2303_-_Spr_2011_-_Week_11_-_Wave_Packets_-_G

2303_-_Spr_2011_-_Week_11_-_Wave_Packets_-_G - Week 11.1...

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1 Week 11.1 Diffraction and Bohr Model Homework Review Testing de Broglie Wavelength Quantization of Energy Bohr Model Reading: 41.1 Review Ch. 15 Quantiki.org, EG
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2 Testing de Br ö glie wavelength In an electron diffraction experiment, the incoming energy can be varied, and then the wavelength measured from We see that the de Bröglie wavelength fits theory. EG
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3 Electron Diffraction: Example Problem (a) The diffraction angle φ for 45-eV electrons from a crystal is φ = 53º . Find the crystal spacing D. (b) Find the diffraction angle φ for 90-eV electrons. EG, Baski
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41-1 The Quantization of Energy Atomic energy levels are discrete and can take on only certain values Atomic electrons can move from one energy level to another by absorbing or emitting photons of the appropriate energy Experimental spectrum of atomic hydrogen shown below
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5 Click to edit Master subtitle style Baski - Fall 2000 PHYS 320 Notes: The Nuclear Atom (Ch. 4) Page 5 Emission spectrum from H shows atomic lines based on energy levels En = -13.6 / n2 eV .
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6 Bohr Model Problem: Classical model of the electron “orbiting” nucleus is unstable. Why? Electron experiences centripetal acceleration. Accelerated electron emits radiation. Radiation leads to energy loss. Electron eventually “crashes” into nucleus. Solution: In 1913, Bohr proposed the quantized model of the H atom to predict the observed spectrum. Baski
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7 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 with quantized frequency f when electron makes a transition between two energy states. hc = 1240 eV nm Baski
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8 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. Baski
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Bohr Model Allowed energies:
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Bohr Model Emission and Absorption of Photons from Atoms This is the Rydberg constant. Agreement with observed spectra is excellent.
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11 Week 11.2 Wave Packets Beats Superposition of waves to produce packets Fourier Series EG
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12 Adding two waves together, one forms beat patterns. See section 15-3 Beats
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13 Wave envelope showing beats
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Pulse moving to the right See section 15-5
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15 Single Cosine Wave (phase velocity) 1 NO LOCALIZATION IN SPACE Solution: Baski vp Wave Equation:
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16 Two Cosine Waves : Pictures (Similar Frequency) Wave #1 k = 11, v = 4 Wave #2 k = 10, v = 1 #1 + #2 Baski
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17 Two Cosine Waves : Pictures (Similar Frequency)
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2303_-_Spr_2011_-_Week_11_-_Wave_Packets_-_G - Week 11.1...

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