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PHYS 3313 – Section 001 Lecture #10 Monday, Feb. 17, 2014 Dr. Jaehoon Yu • • • Photoelectric Effect Compton Effect Pair production/Pair annihilation Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 1 Announcements • Reminder: Homework #2 – CH3 end of the chapter problems: 2, 19, 27, 36, 41, 47 and 57 – Due this Wednesday, Feb. 19 • Reminder: Quiz #2 Wednesday, Feb. 19 – Beginning of the class – Covers CH1.1 – what we finish Monday, Feb. 17 – BYOF: You may bring a one 8.5x11.5 sheet (front and back) of handwritten formulae and values of constants for the exam – No derivations or solutions of any problems allowed! – No additional formulae or values of constants will be provided! • Colloquium this Wednesday: Dr. Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 2 Special Project #3 • • • • A total of Ni incident projectile particle of atomic number Z1 kinetic energy KE scatter on a target of thickness t and atomic number Z2 and has n atoms per volume. What is the total number of scattered projectile particles at an angle ? (20 points) Please be sure to clearly define all the variables used in your derivation! Points will be deducted for missing variable definitions. This derivation must be done on your own. Please do not copy the book, internet or your friends’. Due is Wednesday, Feb.26 . Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 3 Photoelectric Effect Definition: Incident electromagnetic radiation shining on a metal transfers energy to the electrons, allowing them to escape the surface of the metal. Ejected electrons are called photoelectrons. Other methods of electron emission: • Thermionic emission: Application of heat allows electrons to gain enough energy to escape. • Secondary emission: The electron gains enough energy by transfer from another high-speed particle that strikes the material from outside. • Field emission: A strong external electric field pulls the electron out of the material. (an example?) Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 4 Classical Interpretation of Photoelectric Effect Classical theory allows EM radiation to eject photoelectrons from matter • Classical theory predicts the energy of the photoelectrons increase in proportion to the radiation intensity • Thus, KE of the photoelectrons must be proportional to the intensity of light not the current • Time for an experiment! • Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 5 Photoelectric Effect Experimental Setup Hmm.. Something does not make sense!! Anode Photocathode V increased reverse direction to stop I Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 6 Experimental Observations KE proportional to frequency!! The same V0 but higher current The same current!! Number of photoelectrons proportional to light intensity!! Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 7 Summary of Experimental Observations • • • • • Light intensity does not affect the KE of the photoelectrons The max KE of the photoelectrons for a given emitter material depends only on the frequency of the light The smaller the work function of the emitter material, the smaller is the threshold frequency of the light that can eject photoelectrons. When the photoelectrons are produced, their number is proportional to the intensity of light. The photoelectrons are emitted almost instantly following illumination of the photocathode, independent of the intensity of the light. Totally unexplained by classical physics Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 8 Einstein’s Theory of Photoelectric Effect • Einstein suggested that the electromagnetic radiation field is quantized into particles called photons. Each photon has the energy quantum: E =hf • where f is the frequency of the light and h is Planck’s constant. • The photon travels at the speed of light in a vacuum, and its wavelength is given by lf =c Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 9 Einstein’s Theory • Conservation of energy yields: Energy Before(photon)=Energy After (electron) hf = f + KE( photoelectron) where is the work function of the metal The photon energy can then be written 1 2 hf = f + mvmax 2 • The retarding potentials measured the KE of the most energetic photoelectrons. 1 2 eV0 = mvmax 2 Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 10 Quantum Interpretation • • • KE of the electron depends only on the light frequency and the work function of the material not the light intensity at all 1 2 mvmax = eV0 = hf - f 2 Einstein in 1905 predicted that the stopping potential was linearly proportional to the light frequency, with a slope h, the same constant found by Planck. 1 2 eV0 = mvmax = hf - hf0 = h ( f - f0 ) 2 From this, Einstein concluded that light is a particle with energy: hc hf = E= l Was he already thinking about particle/wave duality? Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 11 Ex 3.11: Photoelectric Effect • Light of wavelength 400nm is incident upon lithium ( =2.93eV). Calculate (a) the photon energy (eV) and (b) the stopping potential V0. • Since the wavelength is known, we use plank’s formula: E = hf = hc l 1.626 ´10 ( = -34 J × s ) ( 3 ´10 m s ) 8 -9 400 ´10 m = 3.10eV • The stopping potential can be obtained using Einstein’s formula for photoelectron energy eV0 = hf - f = E - f E - f ( 3.10 - 2.93) eV V0 = = 0.17V = e e Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 12 X-Ray Production • Bremsstrahlung (German word for braking radiation): Radiation of a photon from an energetic electron passing through matter due to an acceleration Since linear momentum must be conserved, the nucleus absorbs very little energy, and it is ignored. The final energy of the electron is determined from the conservation of energy • E f = Ei - hf • An electron that loses a large amount of energy will produce an X-ray photon. – – – Current passing through a filament produces copious numbers of electrons by thermionic emission. These electrons are focused by the cathode structure into a beam and are accelerated by potential differences of thousands of volts until they impinge on a metal anode surface, producing x rays by bremsstrahlung as they stop in the anode material X-ray wavelengths range 0.01 – 10nm. What is the minimum energy of an electron to produce X-ray? Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 13 Inverse Photoelectric Effect. Conservation of energy requires that the electron KE equal the maximum photon energy Work function neglected since it’s small compared to the potential energy of the electron. This is the Duane-Hunt limit The photon wavelength depends only on the accelerating voltage The same for all targets. eV0 = hfmax = lmin hc lmin hc 1.24 ´10 -6 V × m = = V0 eV0 Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 14 Compton Effect When a photon enters matter, it is likely to interact with one of the atomic electrons. The photon is scattered from only one electron. The laws of conservation of energy and momentum apply as in any elastic collisions between two particles. The momentum of a particle moving at the speed of light is E hf h p= = = c c l The electron energy can be written as E = ( mec 2 e ) 2 2 +p c 2 2 e Change of the scattered photon wavelength is known as the Compton effect: h (1- cosq ) Dl = l - l = mec ' Monday, Feb. 17, 2014 PHYS 3313-001, Spring 2014 Dr. Jaehoon Yu 15