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Chapter 29

Chapter 29. Particles and Waves. The Wave-Particle Duality Blackbody Radiation and Planck’s Constant Photons and the Photoelectric Effect The Momentum of a Photon and the Compton Effect The DE Broglie Wavelength and the Wave Nature of Matter The Heisenberg Uncertainty Principle. Outline.

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Chapter 29

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  1. Chapter 29 Particles and Waves

  2. The Wave-Particle Duality Blackbody Radiation and Planck’s Constant Photons and the Photoelectric Effect The Momentum of a Photon and the Compton Effect The DE Broglie Wavelength and the Wave Nature of Matter The Heisenberg Uncertainty Principle Outline

  3. 1- The wave-particle duality When a beam of electrons is used in a Young’s double slit experiment, a fringe pattern occurs, indicating interference effects. Waves can exhibit particle-like characteristics, and particles can exhibit wave-like characteristics.

  4. 2-Blackbody radiation and Planck’s constant • Black Body = ideal system that absorbs all incident radiation. • Emission of radiation over a certain range of wavelengths / frequencies.

  5. Wein’s Displacement Law • lmax T = 0.2898 x 10-2 m.K • lmax is the wavelength at the curve’s peak • T is the absolute temperature of the object emitting the radiation

  6. Models for Black Body Radiation Planck’s theory: • Emission is due to submicroscopic charged oscillators having discrete energies En: En = n h ƒ • n = quantum number (integer) • ƒ is the frequency of vibration = c / l • h = Planck’s constant = 6.626 x 10-34 J s

  7. Quantization of Energy Ephoton = h.f = difference between 2 adjacent energy levels

  8. 3- Photons and photoelectric effect When light strikes E, photoelectrons are emitted and generate a current

  9. Photoelectric I/V curve (KEmax of e- ) = e DVS

  10. Einstein (1905): Quantization of light • A photon, would be emitted when a quantized oscillator jumped from one energy level to the next lower one • The photon’s energy would be E = hƒ • Each photon can give all its energy to an electron in the metal • The maximum kinetic energy of the liberated photoelectron is: KE = hƒ – F • F is called the work function of the metal

  11. Validity of Einstein’s explanation

  12. KEmax vs frequency KEmax = hf0 – F

  13. 4- The momentum of a photon and the Compton effect The scattered photon and the recoil electron depart the collision in different directions. Due to conservation of energy, the scattered photon must have a smaller frequency. This is called the Compton effect.

  14. Conservation of Momentum and energy in the collision Compton wavelength=0.00243 nm

  15. Conceptual Example 4 Solar Sails and the Propulsion of Spaceships One propulsion method that is currently being studied for interstellar travel uses a large sail. The intent is that sunlight striking the sail creates a force that pushes the ship away from the sun, much as wind propels a sailboat. Does such a design have any hope of working and, if so, should the surface facing the sun be shiny like a mirror or black, in order to produce the greatest force?

  16. 5- The DE Broglie Wavelength and the wave nature of matter • Light has a dual nature: • Wave: Long l (micro and radio waves) Ex: f = 2,5 MHz , E = hf = 10-8 eV electromagnetic wave • Particles: Short l (UV, X-rays, g – rays) Ex: l = 248 nm E = hf = 5 eV Particle ( mass less)

  17. Do particles exhibit Wave Characteristics? De Broglie (1924): • For a photon: E = hf = p.c • With f = c / l  p = h / l • Therefore, for a particle with a momentum p, • Davisson-Germer: Electron diffraction.(1927)

  18. Interference pattern (maxima and minima) • Recall Young’s double slit experiment: Number of Photons striking the screen, N is almost equal to E2

  19. Electron Interference and Diffraction Electron beam

  20. The Wave Function • Schrödinger’s equation: the quantum mechanical equivalent to Newton’s Law: Y is the wave function

  21. Y2 a0 r • For particles, Y rather than E describe the particles so that Y2 , at some location and at a given time, is proportional to the probability of finding the particle at that location at that time

  22. Example 5 The de Broglie Wavelength of an Electron and a Baseball Determine the de Broglie wavelength of (a) an electron moving at a speed of 6.0x106 m/s and (b) a baseball (mass = 0.15 kg) moving at a speed of 13 m/s.

  23. 6- The Heisenberg uncertainty principle Momentum and position Uncertainty in particle’s position along the y direction Uncertainty in y component of the particle’s momentum

  24. Energy and time time interval during which the particle is in that state Uncertainty in the energy of a particle when the particle is in a certain state

  25. Wave Particle Duality It is like a struggle between a tiger and a shark, each supreme in his own element, each utterly helpless in the other. J.J. Thompson

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