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Particle Properties of Waves Chapter 2 Photoelectric Effect ! Two metal plates in a vacuum ! Shine light on one of them ! Measure current between the plates Photoelectric Effect ! Two metal plates in a vacuum ! Shine light on one of them ! Measure current between the plates ! Can also apply voltage V across the plates and see the effect on the current ! Adjust: (1) frequency & (2) intensity of light and (3) applied voltage. – + Photoelectric Effect: Classical Prediction Electrons gain KE, and “spill out” ! How does changing the applied voltage affect the current? 0 Voltage B 0 Voltage – + Current ! Current Light heats the metal Current A ! C 0 Voltage D 0 Voltage Photoelectric Effect: Classical Prediction ! Light heats the metal ! Electrons gain KE, and “spill out” ! How does changing the applied voltage affect the current? – + C Diode Curve 0 Voltage Photoelectric Effect: Classical Prediction ! Why is the current 0 when the voltage is reversed? ! Electrons are repelled by cathode and attracted to anode + – C 0 Voltage Photoelectric Effect: Classical Prediction ! Why is the current-voltage curve flat for positive voltage? ! Increasing (+) voltage, accelerates electrons to higher speed ! But, # electrons/sec is set by rate at which they are produced, not how fast they travel to other plate. ! – + C 0 Voltage Thus, the current is constant. Photoelectric Effect: Classical Prediction ! Classical Prediction: ! Diode current-voltage curve ! If leave light on longer, plate heat up more, more electrons will be ejected, and higher current ! ! If increase intensity, plate heats up more giving higher current Frequency (color) has no effect. – C 0 Voltage + Photoelectric Effect: Einstein’s Interpretation ! Light comes in small quanta (photons) ! Energy of a photon is E = h! where h is Plank’s constant ! When light strikes the metal, there is a chance that a given photon’s energy will be absorbed by an electron ! In order for an electron to escape the metal, it must acquire a minimum energy !, which is called the work function of the metal ! When electrons escape, their kinetic energy is determined by the energy of the photon and work needed to escape the metal: h! = " + KEmax Photoelectric Effect: Einstein’s Interpretation h! = " + KEmax h! E KEmax ! Potential Energy of Metal KEmax Sodium Calcium Cesium ! Work Functions of Metals Sodium 2.3 eV Potassium 2.3 eV Calcium 2.9 eV Uranium 3.6 eV Copper 4.7 eV Carbon 4.8 eV Gold 5.2 eV Platinum 6.4 eV I I Which graph represents current-voltage curve for low and high intensity light? B A 0 Batt. V D 0 Batt. V I C I I 0 Batt. V 0 Batt. V F 0 Batt. V 13 Which graph represents current-voltage curve for low and high intensity light? HIGH intensity LOW intensity I Fewer electrons pop off metal Current decreases. Current proportional to light intensity. ans. B 0 14 Battery Voltage What happens to the initial KE of the electrons as the frequency of light changes? (Light intensity is constant) Predict shape of the graph Initial KE e s 0 I Frequency of light 16 C 0 Initial KE Frequency 0 Initial KE 0 B D Frequency Frequency Initial KE A Initial KE What happens to the initial KE of the electrons as the frequency of light changes? (Light intensity is constant) 0 Frequency 17 E. something different a. fewer electrons kicked out b. same # of electrons c. more electrons kicked out d. not enough information Electron potential energy You initially have blue light shining on metal. If you change the frequency to violet light (at same # of photons per second), what happens to the number of electrons coming out? Ephot Ephot work function ! Inside metal You initially have blue light shining on metal. If you change the frequency to violet light (at same # of photons per second), what happens to the number of electrons coming out? elect. potential energy Electrons over large range of energy have equal chance of absorbing photons. Ephot work function ! metal c. more electrons come out with violet absorb blue light and have enough energy to leave absorb blue light, but don t come out so the more energy the light has, the more electrons that come out, until so much energy that every electron comes out. 28 (violet and ultraviolet would not be very different in this case) You initially have blue light shining on metal. If you change the frequency to violet light (at same # of photons per second), what happens to the number of electrons coming out? Blue Light E h! h! Violet Light ! A photon at 300 nm will kick out an electron with an amount of kinetic energy, KE300. If the wavelength is halved to 150 nm and the photon hits an electron in the metal with same energy as the previous electron, the energy of the electron coming out is: 300 nm a. < ! KE300. b. ! KE300 c. = KE300 d. 2 KE300 e. > 2 KE300 150 nm A photon at 300 nm will kick out an electron with an amount of kinetic energy, KE300. If the wavelength is halved to 150 nm and the photon hits an electron in the metal with same energy as the previous electron, the energy of the electron coming out is: h! = " + KEmax 2h! E h! KE150 KE300 ! ! e. > 2 KE300 X-Rays Wilhelm Roentgen 1895 X-Ray Tube X-Ray Tube Mr. Roentgen X-Rays Mrs. Roentgen’s Hand X-Ray Production Path of electron Bremsstrahlung Radiation X-rays Normally, deflections off atoms are gradual, and electron KE is transferred to KE of medium (heating it) Large accelerations cause the electron to radiate Bremsstrahlung radiation (X-rays in this case) X-Ray Production Einstein observed that X-ray production is the opposite of the photoelectric effect: photoelectric effect: light electron metal X-ray production electron X-rays metal X-Ray Spectra X-ray spectra can have continuous and emission line features. The minimum wavelength of the continuum is given by the DuaneHunt law: !min = 1240 nm V where V = accelerating voltage The minimum wavelength occurs when all of the electron’s energy is converted to a single photon Derivation of Duane-Hunt Law Since the energy of electrons in an X-ray tube is >> work function ! h! max = " + KEmax # KEmax hc = KEmax !min !min = hc 1240 nm = eV V X-Rays as EM Radiation Initially, X-rays were mysterious: ! They were not bent by magnetic fields (like cathode rays) ! They did not show diffraction or interference effects like light (why?) ! Bragg showed that X-rays actually are waves by diffracting them through planes of atoms in crystals Compton Effect Initially, X-rays were mysterious: ! They were not bent by magnetic fields (like cathode rays) ! They did not show diffraction or interference effects like light (why?) ! Bragg showed that X-rays actually are waves by diffracting them through planes of atoms in crystals Compton Effect Photon scattering off an electron acts like two particles in an elastic collision Energy Conservation scattered photon ! = h# " photon h! " h! # = $KEelectron ! ! = h" " != electron ( pc )2 + ( mc 2 ) 2 Compton Effect Photon scattering off an electron acts like two particles in an elastic collision Momentum Conservation scattered photon p= photon p= h" ! c ! h! c " photon p= h! c p electron electron Compton Effect Momentum Conservation photon p= h! c electron h" ! sin # c ! " p sin ! p h" ! cos# c p cos ! h" ! sin # c ! " p sin ! p h" ! cos# c p cos !