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lecture15 - Lecture 15 Notes 07 26 The photoelectric effect...

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Lecture 15 Notes: 07 / 26 The photoelectric effect and the particle nature of light When diffraction of light was discovered, it was assumed that light was purely a wave phenomenon, since waves, but not particles, diffract. However, the discovery of the photoelectric effect changed this. When light strikes the surface of a metal, it will, under certain conditions, eject electrons from the metal. The presence of ejected electrons can be detected when they reach another metal plate, creating a current; the energy of the electrons can be determined by applying a stopping voltage. Electrons ejected with an energy of, say, 1 eV, will be able to get through up to 1 volt of stopping voltage, but increasing the voltage higher than that will stop the photoelectric current. From the wave picture of light, we would expect both the number of electrons ejected and the average energy of the electrons to be simply proportional to the intensity of the wave. However, that's not what we find. Up to a certain frequency of light, no electrons are ejected at all; above that frequency, the number of electrons ejected is in fact proportional to the intensity of light, but the energy of the electrons depends on the frequency of light, and is given by The graph of the electron energy vs. the frequency of incident light looks like this: The slope of this graph is found to be the same in all photoelectric effect experiments, and is given by Planck's constant h = 6.63 x 10 -34 m 2 kg/s = 4.14 x 10 -15 eV s. The quantity φ is known as the work function , and depends on the particular kind of metal used in the experiment.
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The photoelectric effect is readily explained if light consists of particles called photons . These particles are associated with electromagnetic waves, and have an energy equal to Planck's constant times the frequency of the wave: When a photon strikes an electron, it can be absorbed. The electron in the metal is bound to the metal by a binding potential φ ; if the energy of the photon is sufficient, it can liberate the electron from the metal. The leftover kinetic energy of the electron is equal to E = hf - φ , where hf is the energy of the photon (which has nothing to do with the kind of metal or experimental apparatus used, just the frequency of light) and φ is the binding energy of the electrons in the metal. Thus the constant h is expected to be independent of the metal used, while φ is expected to depend on the metal, just as observed. The relationship between the energy and the frequency can be rewritten in terms of the angular frequency: The momentum is similarly related to the wave number: Photons have zero mass, and thus move at the speed of light, as discussed in the previous lecture.
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