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The photoelectric effect Contents: •Einstein’s proposed experiment •Solving photoelectric problems •Example 1 | Example 2 •Whiteboard •Photon vs wave theory Light Waves Wavelength Changes Color small = blue Photons Energy per photon changes E = hf Radio waves vs X-rays big = red Amplitude Changes Brightness small = dim big = bright # of photons changes many = bright few = dim CCD Devices, High speed film Photo Electric Effect How it works Einstein’s idea Photon Energy = Work + Kinetic Energy hf = + Emax hf = hfo + eV - Work function (Depends on material) fo - Lowest frequency that ejects e - Electron charge V - The uh stopping potential Ex. 1: = 3.25 eV, V = 7.35 V, = for light? V - + Reverse the voltage Ex. 2: = 70.9 nm, = 5.10 eV, V = for electrons? TOC Photon Energy = Work + Kinetic Energy hf = + Emax hf = hfo + eV - Work function (Depends on material) fo - Lowest frequency that ejects e - Electron charge V - The uh stopping potential Example 1: A certain metal has a work function of 3.25 eV. When light of an unknown wavelength strikes it, the electrons have a stopping potential of 7.35 V. What is the wavelength of the light? Photon energy = Work + Kinetic Energy Photon Energy = 3.25 eV + 7.35 eV = 10.60 eV Convert to J: (10.60 eV)(1.602E-19 J/eV) = 1.69812E-18 J E = hf = hc/ , = hc/E = (6.626E-34 Js)(3.00E8 m/s)/(1.69812E-18 J) = 1.17059E-07 m = 117 nm TOC Photon Energy = Work + Kinetic Energy hf = + Emax hf = hfo + eV - Work function (Depends on material) fo - Lowest frequency that ejects e - Electron charge V - The uh stopping potential Example 2: 70.9 nm light strikes a metal with a work function of 5.10 eV. What is the maximum kinetic energy of the ejected photons in eV? What is the stopping potential? E = hf = hc/ = (6.626E-34 Js)(3.00E8 m/s)/(70.9E-9) = 2.80367E-18 J Convert to eV: (2.80367E-18 J)/(1.602E-19 J/eV) = 17.5 eV Photon Energy = Work + Kinetic Energy 17.5 eV = 5.10 + Kinetic Energy Kinetic Energy = 12.4 eV, so 12.4 V would stop the electrons. TOC Metal Work Function Ag (silver) 4.26 Au (gold) 5.1 Cs (cesium) 2.14 Cu (copper) 4.65 Li (lithium) 2.9 Pb (lead) 4.25 Sn (tin) 4.42 Chromium 4.6 Nickel 4.6 Whiteboards: Photoelectric effect 1|2|3|4 Photons of a certain energy strike a metal with a work function of 2.15 eV. The ejected electrons have a kinetic energy of 3.85 eV. (A stopping potential of 3.85 V) What is the energy of the incoming photons in eV? Photon energy = Work function + Kinetic energy of electron Photon energy = 2.15 eV + 3.85 eV = 6.00 eV 6.00 eV W Another metal has a work function of 3.46 eV. What is the wavelength of light that ejects electrons with a stopping potential of 5.00 V? (2) E = hf = hc/, Photon energy = Work function + Kinetic energy of electron Photon energy = 3.46 eV + 5.00 eV = 8.46 eV E = (8.46 eV)(1.602 x 10-19 J/eV) = 1.3553 x 10-18 J E = hf = hc/, = hc/E = (6.626 x 10-34 Js)(3.00 x 108 m/s)/(1.3553 x 10-18 J) = 1.4667x 10-07 m = 147 nm 147 nm W 112 nm light strikes a metal with a work function of 4.41 eV. What is the stopping potential of the ejected electrons? (2) E = hf = hc/, 1 eV = 1.602 x 10-19 J Photon energy = Work function + Kinetic energy of electron E = hf = hc/ = (6.626 x 10-34 Js)(3.00 x 108 m/s)/(112 x 10-9 m) E = 1.7748 x 10-18 J E = (1.7748 x 10-18 J)/(1.602 x 10-19 J/eV) = 11.079 eV Photon energy = Work function + Kinetic energy of electron 11.079 eV = 4.41 eV + eVs 11.079 eV - 4.41 eV = 6.6688 eV = eVs Vs = 6.67 V 6.67 V W 256 nm light strikes a metal and the ejected electrons have a stopping potential of 1.15 V. What is the work function of the metal in eV? (2) E = hf = hc/, 1 eV = 1.602 x 10-19 J Photon energy = Work function + Kinetic energy of electron E = hf = hc/ = (6.626 x 10-34 Js)(3.00 x 108 m/s)/(256 x 10-9 m) E = 7.7648 x 10-19 J E = (7.7648 x 10-19 J)/(1.602 x 10-19 J/eV) = 4.847 eV Photon energy = Work function + Kinetic energy of electron 4.847 eV = Work function + 1.15 eV 11.079 eV - 1.15 eV = 3.70 eV 3.70 eV W Einstein’s Photon theory predicts: Photon energy = work function + Kinetic energy of electron hf = + Ekmax Ekmax = hf - Photon Theory predicts: •Ekmax rises with frequency •Intensity of light ejects more Wave Theory predicts: •Ekmax rises with Amplitude (Intensity) •Frequency should not matter Survey says Millikan does the experiment 1915 conclusion 1930 conclusion TOC