Announcements. Lecture 8 Chapter. 3 Wave & Particles I. EM- Waves behaving like Particles. The Compton effect (Arthur Compton 1927) Hypothesis:

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1 Announcements HW3: Ch.3-13, 17, 23, 25, 28, 31, 37, 38, 41, 44 HW3 due: 2/16 ** Lab manual is posted on the course web *** Course Web Page *** Lecture Notes, HW Assignments, Schedule for thephysics Colloquium, etc.. Outline: Lecture 8 Chapter. 3 Wave & Particles I EM- Waves behaving like Particles! Blackbody Radiation (Plank; 1900; 1918*)! The Photoelectric Effect (Einstein; 1905; 1921*)! The Production of X-Rays (Rontgen;1901; 1901*)! The Compton Effect (Compton; 1927; 1927*)! Pair Production (Anderson; 1932; 1936*)! Is It a Wave or a Particle?! Duality? The Compton effect (Arthur Compton 1927) Momentum & Energy when a photon strike a free electron Is this true? Compton provided the 1 st experimental evidence!! momentum energy Hypothesis: Experiment? Before Collision: A photon approaches an electron at rest

2 Momentum & Energy when a photon strike a free electron Momentum & Energy when a photon strike a free electron After Collision: The electron scatters at speed u, angle!. A photon of wavelength " scatters at angle # Energy and Momentum Conservation X-ray detector The Compton Effect X-ray tube target (light atoms, e.g. graphite) Photons carry momentum like particles and scatter individually with other particles indeed, the wavelength shift is independent of the target material and the initial photon wavelength. e -

3 Problem An X-ray photon with "=60nm is scattered over by a target electron. (a)! Find the change of its wavelength. (b)! Find the angle between the directions of motion of the recoil electron and the incident photon. (c)! Find the energy of the recoil electron. (a) (b) momentum conservation: along y axis: along x axis: The photoelectric effect and the Compton effect are two important ways in which EM radiation interacts as a particle with matter. We now discuss a third! (c) Particle-Antiparticle Pair Creation Bubble Chamber

4 Electromagnetic Waves behaving like Particles (Chapter 2) PHOTONS Black Body Radiation The Photoelectric Effect The Production of X-Rays The Compton Effect PHOTONS E = hf PHOTONS p = hf/c = h/! Particle-Antiparticle Pair Production Is It a Wave or a Particles? Duality Ch.3:: EM-Waves behaving like Particles Ch.4:: Particles behaving like Waves! > D Wave! << D Particle

5 Double-slit Diffraction Experiment light INDIVIDUAL PHOTON HITS Although diffraction of light is a wave phenomenon, there is no smooth distribution of light in the diffraction pattern, but the pattern is rather formed of many individual hits of particles the photons A single photon DOES NOT get disintegrated in the Diffraction process to make a smooth diffraction pattern

6 Electromagnetic waves (light) Particles (photons) Coming back to that soon Waves? Massive Particles Outline: Chapter. 4 Wave & Particles II Matter behaving as Waves! A Double-Slit Experiment (watch video )! Properties of Matter Waves! The Free-Particle Schrödinger Equation! Uncertainty Principle! The Bohr Model of the Atom! Mathematical Basis of the Uncertainty Principle The Fourier Transform Electron passing through a wide slit arrive at a screen one by one and produce a bright region essentially the same width as the slit

7 Very strange But when 2 slits are open, there are certain points at which no electron ever arrives. Very strange With a single narrow slit, Electrons arrive one by one all over the screen. They don t avoid any points Each electron wave is destructively interfering with itself. Like a Wave Electrons producing a double-slit interference pattern-one particle at a time electrons Waves? Massive Particles

8 Bragg s Law! Bragg's law states that when X-rays hit an atom (in a x-tal), they make the electronic cloud move as does any EM-wave. The movement of these charges re-radiates waves with the same frequency; this phenomenon is known as the Rayleigh scattering.! These re-emitted wave fields interfere with each other either constructively or destructively, producing a diffraction pattern on a detector or film. The resulting wave interference pattern is the basis of diffraction analysis. [..excellent probe for small length scale] Actual double-slit pattern produced by electrons Diffraction of a beam from multiple atomic planes Bragg s Law! The interference is constructive when the phase shift is a multiple of 2!; this condition can be expressed by Bragg's law,! n is an integer determined by the order given,! is the wavelength of the X-rays, d is the spacing between the planes in the atomic lattice, and " is the angle between the incident ray and the scattering planes.! Bragg's Law is the result of experiments into the diffraction of X-rays off crystal surfaces at certain angles. Bragg's law confirmed the existence of real particles at the atomic scale, as well as providing a powerful new tool for studying crystals in the form of X-ray diffraction.

9 Electron wave diffracted by AlMn quasicrystal De Broglie Hypothesis The EM waves can be described using the language of quantum particles (photons). Q:: Can particles behave as waves? De Broglie (1923) suggested that a plane mono-energetic wave is associated with a freely moving particle: This is a solution of the wave equation in one dimension: This wave travels with the phase velocity We ll apply the same logic which helped us to establish the relationship between p and " for photons: for photon, E = pc and E = h$% h$ = pc = p"v, h = p"! " = h/p De Broglie wavelength p - the object s momentum