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2.The Particle-like Properties Of Electromagnetic Radiation 2.1Photoelectric effect and Einstein’s theory 2.2Black body radiation 2.3Compton effect 2.4Bremsstrahlung and pair production 2.5The photon

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Photoelectric effect and Einstein’s theory V A light electron collector emitter i

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The voltage V is increased gradually until no current pass through the outer circuit. The voltage in this case called stopping potential V S. The energy used to stop this electron is eV S. This value is equal to K max the maximum energy required to overcome the electric potential energy acquired by an electron.

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Classical Postulates Electrons are released from the metal surface if the energy of the incident light exceeds the binding energy of the electron to the metal surface. This value is called work function . The maximum kinetic energy K max should be proportional to the intensity of the radiation I. (it is thought that as the intensity of the incident light increased more energy is delivered to the surface of the metal).

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Classical Postulates (continued) The photoelectric effect should occur for light of any frequency or wavelength. ( as long as light intensity is enough) The first electrons should be emitted in a time interval of the order of seconds after radiation first strikes the surface.

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Experimental Results Comparison to the classical postulates 1.The maximum kinetic energy is totally independent of the intensity of the light source. 2.The photoelectric effect does not occur at all if the frequency of the light source is below a certain value (the cutoff frequency C ) any light source of frequency above this value may cause emission of photoelectrons. 3.The first photoelectrons are emitted virtually instantaneously (within s) after the light source is turned on.

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K max (V S ) and Intensity Stopping potential is independent on the intensity

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Einstein Theory The energy of light wave is not continuously distributed over the wave front, but instead is concentrated in localized bundles (photons). The energy of each photon is given by

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Einstein Theory (continued) Since photons travel with the electromagnetic waves at the speed of light, they must obey the relativistic relation Therefore, Like other particles, photons carry linear momentum as well as energy.

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Einstein Theory (continued) Despite the rest mass of photon, according to the theory of relativity, is zero and photon vanishes at speed lower than that of light, its energy is still given by

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If the photon energy is greater than the work function of the metal surface, photoelectron is released, or photoelectric effect doesn’t occur. In this equation the intensity I of the light source doesn’t appear. if the photon energy is hardly equal to the work function, the photon frequency in this case is called cutoff frequency and is given by

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Work function and Planck’s constant

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Example 3.3 What are the energy and momentum of a red light photon of wavelength 650 nm? What is the wavelength of a photon of energy 2.4 eV?

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Example 3.4 The work function for tungsten metal is 4.52 eV. What is the cutoff frequency and wavelength? What is the maximum kinetic energy of the electrons when radiation of wavelength 198 nm is used? What is the stopping potential in this case?

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Black Body Radiation

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I is the total intensity of electromagnetic radiation emitted at all wavelengths The intensity dI in the wavelength interval between and is given by dI = R( d R( ) is the radiancy : which is the intensity per unit wavelength interval.

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Stefan’s Radiation Law The total intensity I is given by the area under the radiancy curve.

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Wein’s Displacement Law It is noticed from the spectrum figure that the wavelength max at which the radiancy reaches it maximum value is inversely proportional to the temperature T. max 1/T max T = X m.K

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Example 3.5 (a) At what wavelength does a room-temperature (T=20 O C) object emit the maximum thermal radiation? (b) To what temperature must we heat it until its peak thermal radiation is in the red region of the spectrum? (c) How many times as much thermal radiation does it emit at the higher temperature?

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Rayleigh-Jeans Formula

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Comparison between the experimental data and Rayleigh-Jeans formula: AT long wavelengths R( ) approaches the experimental data, but at short wavelengths, the classical theory fails. This failure is called ultraviolet catastrophe.

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Planck’s Theory and Radiation Law

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The relation between Stefan-Boltzmann constant and Planck’s constant

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The Compton Effect Radiation scatter from nearly loosely bound electrons. The incident radiation gives part of its energy to the electron; which is released from the atom, and the remainder of this energy is reradiated as electromagnetic radiation.

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Compton scattering formula

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Example 3.6 X-rays of wavelength nm are Compton-scattered, and the scattered beam is observed at an angle of 60 o relative to the incident beam. Find: (a) the wavelength of the scattered X-rays. (b) the energy of the scattered X-rays (c) the kinetic energy of the scattered electrons (d) the direction of travel of the scattered electrons.

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Bremsstrahlung and X-Ray Production

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Electron=electron(with less energy) +photon

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Pair Production

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Electron-Positron Annihilation

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