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The Photoelectric Effect Einstein’s Triumph Graphics courtesy of Physics 2000, University of Colorado Quantum Theory – Early Experiments • Cathode rays discovered in late 19th century End of tube near + terminal(anode) glowed • Charge to mass ratio e/m measured = E/B2r evB = mv2/r eE = evB etc “Discovery” of Electron • Cathode rays became known as electrons • Most believed they were atoms • J.J. Thompson believed they were parts of atoms • Millikin measured charge on electron Millikin Oil Drop Experiment • Shows that electron charge is quantized. • qe= integer x 1.6 x 10-19 C Closer Look at Millikan Oil Drop Millikan put a charge on a tiny drop of oil and measured how strong an applied electric field had to be in order to stop the oil drop from falling. Planck Distribution Wavelength distribution of “blackbody” radiation Planck E = hf • Planck postulated that the radiators or oscillators can only emit electromagnetic radiation in finite amounts of energy. • At a given temperature T, there is then not enough thermal energy available to create and emit many large radiation quanta. More large energy quanta can be emitted, however, when the temperature is raised. Do You Know How a Solar Cell Works? Light produces electricity, right? How? The Photoelectric Effect, first explained correctly by Einstein in 1905 Basic Info • When light of high enough frequency strikes a metal, electrons are given off Apparatus Simulations of Photoelectric Effect • Link #1 • Link #2 Planck’s E = hf • Called quantum hypothesis • Needed to explain spectrum of light given off by hot objects • Main idea: energy of atomic oscillators is not continuous but finite number of discrete amounts each related to frequency of oscillation by E =nhf • h = 6.63 x 10-34 J-s (Planck’s Constant) • Photons act like particles Photoelectric Effect Apparatus • When light hits cathode(-) current flows • Electrons move toward anode (+) o Light • If battery is reversed, electrons can be stopped • KEmax = eV0 V0 is stopping voltage What Wave Theory Predicts • If light made brighter – #electrons increases – Maximum KE increases • If change frequency, no effect on KE of electrons WRONG! • Sorry Maxwell What Photon Theory Predicts • Increasing brightness means more photons, not more energy per photon • Increasing frequency increases KEmax (E=hf) • Decreasing frequency below “cutoff” could mean no electrons ejected Two Theories Animated • Link Now for the Math… • Let hf be incoming energy of the photon • Let W0 be the minimum energy required to eject out through the surface(work function) • KEmax is the maximum energy of the ejected electron • then hf = KEmax + W0 by conservation of energy in a collision How to Analyze • KEmax can be easily determined by measuring the stopping potential • KEmax =eV0 ( =qeV) • So let’s plot KEmax vs. f What Happens When Light Frequency Increases? • KEmax = hf - W0 f0 is called threshold frequency KEmax h is the slope W0 f0 f Meaning of Threshold(Cutoff) Frequency • • • • When f is less than f0 KEmax is negative. There can be no photocurrent The bigger f, the bigger is KEmax At cutoff frequency f0 hf0 = W0 Problems 1. What stopping voltage is required to stop an electron with KE of 1electron volt? Ans. 1 volt 2. A stopping voltage of 2.5 volts is just enough to stop all photocurrent. What is KEmax? Ans. 2.5 eV Finding Photon Energy • What is the energy of a photon of blue light with l = 450 nm ? HINT: First find f f = c/l E = hf = hc/l = hc/l = (6.63x10-34 J-s)(3.0x108m/s)/(4.5 x 10-7 m) = 4.42x10-19 J /(1.6)x10-19 J/eV = 2.76 eV Finding KEmax • What is the maximum kinetic energy of electrons ejected from a sodium surface whose work function is W0 = 2.28 eV when illuminated by light of wavelength 410nm? hf = hc/l = 4.85x10-19 J or 3.03 eV (1243/410) KEmax = hf - W0 = 3.03 eV – 2.28 eV = 0.75 eV Finding Cutoff Frequency or h =6.63 x 10 J-s W = 2.28 eV Wavelength -34 0 • What is the cutoff frequency for sodium? hf0 = W0 = 2.28 eV = 3.65 x 10-19 J f0 = 3.65 x 10-19 J / 6.63 x 10-34 J-s = 5.5 x 1014 Hz • What is the longest wavelength for a photo current to flow? l0 = c/f0 = 3.0 x 108 m/s /5.5 x 1014 Hz = 545 nm Shortcut-click Using 1243 Rule • The wavelength corresponding to the work function is just 1243/2.28 eV = 545 nm How Can We Measure h Using the Photoelectric Effect? • Plot KEmax as a function of frequency • h is the slope • KEmax = hf - W0