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Unformatted text preview: PHY6938 Proficiency Exam Spring 2003 March 28, 2003 Modern Physics and Quantum Mechanics 1. Light of wavelength 300 nm strikes a metal plate, producing photoelec- trons that move with speed of . 002 c . In the photoelectric effect the incoming photons remove electrons from the target. There is a minimum energy required to remove an electron from the interior of a solid to a position just outside. This minimum energy is called the work function . The relation between the energy of photon E , the energy of electron E e , and the work function is given by E = E e + . (1) Note that energy of electron E e is equal to the kinetic energy of electron, since when electron is outside the solid it is not affected by any potential. In other words electron will be considered as a free particle. (a) What is the work function of the metal ? Use Eq.1, since the speed of the electron is much less than speed of the light we do not need to use the special relativity formula for the kinetic energy. E e = 1 2 mv 2 (2) = 1 2 (511 keV c 2 ) (0 . 002 c ) 2 = 1 . 022 eV (3) E = h (4) = hc = 1420 eV nm 300 nm = 4 . 13 eV (5) = E - E e (6) = 3 . 111 eV. (7) (b) What is the critical wavelength for this metal, so that photoelectrons are produced ? The critical wavelength is defined as the wavelength for photons which remove remove electrons from interior of a solid to a position outside the solid. In this case the kinetic energy of electrons outside the solid is equal zero E e = 0. Using the Eq.1 and the results from part (a) we obtain E = (8) hc critical = critical = hc (9) critical = 1420 eV 3 . 111 eV critical = 398 . 6 eV. (10) (c) What is the significance of the critical wavelength ? Photons with a lower wavelength than the critical wavelength cannot produce photo- electrons. This led Einstein to the postulation of quantized energy for the electro- magnetic fields....
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