PHYS 205 Chapter 29, Fall 2017

Chapter 29 Particles and Waves Outline 1. The Wave-Particle Duality 2. Blackbody Radiation and Planck’s Constant 3. Photons and the Photoelectric Effect 4. The Momentum of a Photon and the Compton Effect 5. The DE Broglie Wavelength and the Wave Nature of Matter 6. The Heisenberg Uncertainty Principle 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. 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. Wein’s Displacement Law max T = 0.2898 x 10-2 m.K max is the wavelength at the curve’s peak T is the absolute temperature of the object emitting the radiation 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 /  h = Planck’s constant = 6.626 x 10-34 J s Ephoton = h.f = difference between 2 adjacent energy levels Quantization of Energy 3- Photons and photoelectric effect When light strikes E, photoelectrons are emitted and generate a current Photoelectric I/V curve (KEmax of e- ) = e VS 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 –  is called the work function of the metal Validity of Einstein’s explanation Experimental observations Photoelectric effect eq: KE = hƒ –  Cut-off frequency f0 below which no effect is detected hf > hf0 =  Otherwise no effect (KE)max is independent of light intensity KE = hf –  I  nb of e-  current (KE)max increases if f is increased KE = f Emission of e- is instantaneous Energy is absorbed and immediately emitted as photons KEmax vs frequency KEmax = hf0 –  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.      1 cos   mc h Conservation of Momentum and energy in the collision Compton wavelength=0.00243 nm 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? 5- The DE Broglie Wavelength and the wave nature of matter Light has a dual nature: 1. Wave: Long  (micro and radio waves) Ex: f = 2,5 MHz , E = hf = 10-8 eV  electromagnetic wave 2. Particles: Short  (UV, X-rays, – rays) Ex:  = 248 nm E = hf = 5 eV  Particle ( mass less) Do particles exhibit Wave Characteristics? De Broglie (1924): For a photon: E = hf = p.c With f = c / p = h /  Therefore, for a particle with a momentum p, Davisson-Germer: Electron diffraction.(1927) De Broglie wavelenght of a particle h h p mv     Frequency of a matter wave E f  h  Recall Young’s double slit experiment: Interference pattern (maxima and minima) Number of Photons striking the screen, N is almost equal to E2 Electron Interference and Diffraction Electron beam The Wave Function Schrödinger’s equation: the quantum mechanical equivalent to Newton’s Law: is the wave function For particles,  rather than E describe the particles so that 2 , at some location and at a given time, is proportional to the probability of finding the particle at that location at that time 2 r a0 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.      m 10 2.1 10 m s 0.6 kg 10 1.9 J s .6 63 10 10 6 31 34           h p       m 10 3.3 15 kg 13m s .0 J s .6 63 10 34 34        h p  6- The Heisenberg uncertainty principle Momentum and position    4 h y py    Uncertainty in y component of the particle’s momentum Uncertainty in particle’s position along the y direction Energy and time    4 h t E    Uncertainty in the energy of a particle when the particle is in a certain state time interval during which the particle is in that state 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