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Particles and Waves: Exploring the Quantum Realm

This chapter delves into the fascinating concepts of wave-particle duality, blackbody radiation, photons, the photoelectric effect, de Broglie wavelength, and Heisenberg's uncertainty principle. Discover the dual nature of matter and light, including how particles can exhibit wave characteristics. Dive into models like Planck's constant and Einstein's quantization of light, and explore phenomena like the Compton effect and electron diffraction. Embrace the intriguing interplay between particles and waves in the quantum world.

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Particles and Waves: Exploring the Quantum Realm

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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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