7th_IPhO_1974 - Problems of the 7th International Physics...

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Problems of the 7th International Physics Olympiad 1 (Warsaw, 1974) Waldemar Gorzkowski Institute of Physics, Polish Academy of Sciences, Warsaw, Poland 2 Abstract The article contains the competition problems given at the 7th International Physics Olympiad (Warsaw, 1974) and their solutions. Introduction The 7 th International Physics Olympiad (Warsaw, 1974) was the second one organized in Poland. It took place after a one-year organizational gap, as no country was able to organize the competition in 1973. The original English version of the problems of the 7 th IPhO has not been preserved. We would like to remind that the permanent Secretariat of the IPhOs was established only in 1983; previously the Olympic materials had been collected by individual people in their private archives and, in general, are not complete. English texts of the problems and simplified solutions are available in the book by R. Kunfalvi [1]. Unfortunately, they are somewhat deformed as compared to the originals. Fortunately, we have very precise Polish texts. Also the full solutions in Polish are available. This article is based on the books [2, 3] and article [4]. The competition problems were prepared especially for the 7 th IPhO by Andrzej Szymacha (theoretical problems) and Jerzy Langer (experimental problem). THEORETICAL PROBLEMS Problem 1 A hydrogen atom in the ground state, moving with velocity v , collides with another hydrogen atom in the ground state at rest. Using the Bohr model find the smallest velocity 0 v of the atom below which the collision must be elastic. At velocity 0 v the collision may be inelastic and the colliding atoms may emit electromagnetic radiation. Estimate the difference of frequencies of the radiation emitted in the direction of the initial velocity of the hydrogen atom and in the opposite direction as a fraction (expressed in percents) of their arithmetic mean value. Data: J 18 2.18 eV 6 . 13 2 18 - 2 4 = = = me E i ; (ionization energy of hydrogen atom) kg 10 67 . 1 27 = H m ; (mass of hydrogen atom) 1 This article has been sent for publication in Physics Competitions in September 2003 2 e-mail: gorzk@ifpan.edu.pl
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( m - mass of electron; e - electric charge of electron; - Planck constant; numerical values of these quantities are not necessary.) Solution According to the Bohr model the energy levels of the hydrogen atom are given by the formula: 2 n E E i n = , where n = 1, 2, 3, … The ground state corresponds to 1 = n , while the lowest excited state corresponds to 2 = n . Thus, the smallest energy necessary for excitation of the hydrogen atom is: i i E E E E E 4 3 4 1 1 2 ) 1 ( = = = . During an inelastic collision a part of kinetic energy of the colliding particles is converted into their internal energy. The internal energy of the system of two hydrogen atoms considered in the problem cannot be changed by less than E . It means that if the kinetic energy of the colliding atoms with respect to their center of mass is less than E , then the collision must be an elastic one. The value of 0 v can be found by considering the critical case, when the kinetic energy of the colliding atoms is equal to the smallest energy of excitation.
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This note was uploaded on 11/08/2011 for the course PHYS 0000 taught by Professor Na during the Spring '11 term at Rensselaer Polytechnic Institute.

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7th_IPhO_1974 - Problems of the 7th International Physics...

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