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Chapter 38B - Quantum Physics A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007

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Objectives: After completing this module, you should be able to: Discuss the meaning of quantum physics and Plancks constant for the description of matter in terms of waves or particles.Discuss the meaning of quantum physics and Plancks constant for the description of matter in terms of waves or particles. Demonstrate your understanding of the photoelectric effect, the stopping potential, and the deBroglie wavelength.Demonstrate your understanding of the photoelectric effect, the stopping potential, and the deBroglie wavelength. Explain and solve problems similar to those presented in this unit.Explain and solve problems similar to those presented in this unit.

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Planks Constant In his studies of black-body radiation, Maxwell Planck discovered that electromagnetic energy is emitted or absorbed in discrete quantities. Plancks Equation: E = hf ( h = x J s) Apparently, light consists of tiny bundles of energy called photons, each having a well- defined quantum of energy. E = hf Photon

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Energy in Electron-volts Photon energies are so small that the energy is better expressed in terms of the electron-volt. One is the energy of an electron when accelerated through a potential difference of one volt. One electron-volt (eV) is the energy of an electron when accelerated through a potential difference of one volt. 1 eV = 1.60 x J1 keV = 1.6 x J 1 MeV = 1.6 x J

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Example 1: What is the energy of a photon of yellow-green light ( = 555 nm)? First we find f from wave equation: First we find f from wave equation: c = f E = 3.58 x J E = 2.24 eV Or Since 1 eV = 1.60 x J

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Useful Energy Conversion Since light is often described by its wavelength in nanometers (nm) and its energy E is given in eV, a conversion formula is useful. (1 nm = 1 x m) If is in nm, the energy in eV is found from: Verify the answer in Example 1...

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The Photo-Electric Effect When light shines on the cathode C of a photocell, electrons are ejected from A and attracted by the positive potential due to battery. CathodeAnode Incident light Ammeter +- A A C There is a certain threshold energy, called the work function W, that must be overcome before any electrons can be emitted.

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Photo-Electric Equation CathodeAnode Incident light Ammeter +- A A C The conservation of energy demands that the energy of the incoming light hc/ be equal to the work function W of the surface plus the kinetic energy of the emitted electrons. The conservation of energy demands that the energy of the incoming light hc/ be equal to the work function W of the surface plus the kinetic energy ½ mv 2 of the emitted electrons. Threshold wavelength

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Example 2: The threshold wavelength of light for a given surface is 600 nm. What is the kinetic energy of emitted electrons if light of wavelength 450 nm shines on the metal? A = 600 nm ; K = 2.76 eV – 2.07 eV K = eV Or K = 1.10 x J

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Stopping Potential A CathodeAnode Incident light Potentiometer +- V A potentiometer is used to vary to the voltage V between the electrodes. K max = eV o Photoelectric equation: The stopping potential is that voltage V o that just stops the emission of electrons, and thus equals their original K.E.

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Slope of a Straight Line (Review) The general equation for a straight line is: y = mx + b The x-intercept x o occurs when line crosses x axis or when y = 0. The slope of the line is the rise over the run: xoxo x y The slope of a line: y x Slope

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Finding Plancks Constant, h Using the apparatus on the previous slide, we determine the stopping potential for a number of incident light frequencies, then plot a graph. Note that the x-intercept f o is the threshold frequency. fofo Stopping potential Frequency V Finding h constant y x Slope

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Example 3: In an experiment to determine Plancks constant, a plot of stopping potential versus frequency is made. The slope of the curve is 4.13 x V/Hz. What is Plancks constant? fofo Stopping potential Frequency V y x Slope h = e(slope) = (1.6 x C)(4.13 x V/Hz) Experimental Plancks h = 6.61 x J/Hz

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Example 4: The threshold frequency for a given surface is 1.09 x Hz. What is the stopping potential for incident light whose photon energy is 8.48 x J? Photoelectric Equation: W = (6.63 x Js)(1.09 x Hz) =7.20 x J Stopping potential: V o = V A Cathode Anode Incident light+- V

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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 m o = 0, but it does have momentum p: E = m o c 2 E = pc

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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:

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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 = K = ½ mv 2 ; p = mv mK = mK = ½ m 2 v 2 = ½ p 2 Multiply first Equation by m: Momentum from K:

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Example 5: What is the de Broglie wavelength of a 90-eV electron? (m e = 9.1 x kg.) - e-e-e-e- 90 eV Next, we find momentum from the kinetic energy: p = 5.12 x kg m/s = nm

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Summary Plancks Equation: E = hf ( h = x J s) Apparently, light consists of tiny bundles of energy called photons, each having a well- defined quantum of energy. E = hf Photon1 eV = 1.60 x J 1 keV = 1.6 x J 1 MeV = 1.6 x J The Electron-volt:

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Summary (Cont.) If is in nm, the energy in eV is found from: Wavelength in nm; Energy in eV CathodeAnode Incident light Ammeter +- A A C Threshold wavelength

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Summary (Cont.) A CathodeAnode Incident light Potentiometer +- V K max = eV o Plancks Experiment: fofo Stopping potential Frequency V y x Slope

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Summary (Cont.) For a particle with zero momentum p = 0: A light photon has m o = 0, but it does have momentum p: E = m o c 2 E = pc Quantum physics works for waves or particles: Wavelength of a photon: de Broglie Wavelength:

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CONCLUSION: Chapter 38B Quantum Physics

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