Example 4 The threshold frequency for a given
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Example 4: The threshold frequency for a given surface is 1. 09 x 1015 Hz. What is the stopping potential for incident light whose photon energy is 8. 48 x 10 -19 J? Incident light Photoelectric Equation: Cathod Anode e V A + W = (6. 63 x 10 -34 Js)(1. 09 x 1015 Hz) =7. 20 x 10 -19 J Stopping potential: Vo = 0. 800 V -
Total Relativistic Energy Recall that the formula for the relativistic total energy was given by: Total Energy, E For a particle with zero momentum p = 0: A light photon has mo = 0, but it does have momentum p: E = moc 2 E = pc
Waves and Particles We know that light behaves as both a wave and a particle. The rest mass of a photon is zero, and its wavelength can be found from momentum. Wavelength of a photon: All objects, not just EM waves, have wavelengths which can be found from their momentum de Broglie Wavelength:
Finding Momentum from K. E. In working with particles of momentum p = mv, it is often necessary to find the momentum from the given kinetic energy K. Recall the formulas: K = ½mv 2 ; Multiply first Equation by m: Momentum from K: p = mv m. K = ½m 2 v 2 = ½p 2
Example 5: What is the de Broglie wavelength of a 90 -e. V electron? (me = 9. 1 x 10 -31 kg. ) e- 90 e. V Next, we find momentum from the kinetic energy: p = 5. 12 x 10 -24 kg m/s l = 0. 122 nm
Summary Photon Apparently, light consists of tiny bundles of energy called photons, each having a welldefined quantum of energy. E = hf Planck’s Equation: E = hf The Electron-volt: 1 ke. V = 1. 6 x 10 -16 J (h = 6. 626 x 10 -34 J s) 1 e. V = 1. 60 x 10 -19 J 1 Me. V = 1. 6 x 10 -13 J
Summary (Cont. ) Incident light Cathode Anode A C - + Ammeter A Threshold wavelength lo If l is in nm, the energy in e. V is found from: Wavelength in nm; Energy in e. V
Summary (Cont. ) Planck’s Experiment: Incident light Cathode Anode Stopping potential V Slope fo y x Frequency V A + Potentiometer Kmax = e. Vo -
Summary (Cont. ) Quantum physics works for waves or particles: For a particle with zero momentum p = 0: A light photon has mo = 0, but it does have momentum p: Wavelength of a photon: E = moc 2 E = pc de Broglie Wavelength: