Chapter4_1 - and the nucleus 2 But instead of the infinity...

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PHY3063 R. D. Field Department of Physics Chapter4_1.doc University of Florida The Size and Lifetime of Atoms All hydrogen atoms are the same size ( 10 -10 m). Circular Motion (Classically): Assume that the proton is at rest and the electron travels in a circular orbit around the proton ( i.e. assume M p >> m e ). The force on the electron is r v m a m r Ke F e e 2 2 2 = = = and 2 2 v m Ke r e = . The radius is a continuous function. Given any speed v, get an allowed radius. So why do all hydrogen atoms have the same radius? Hydrogen atoms are stable. The electron is being accelerated with acceleration a = v 2 /r = ω 2 r and classically it will thus radiate electromagnetic radiation and loose energy. The electron will spiral in toward the proton and the atom will collapse in a very short time. So why are atoms stable? . Bohr’s Theory (1913): Based on the following postulates. 1. An electron in an atom moves in a circular orbit about the nucleus under the influence of the Coulomb attraction between the electron
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Unformatted text preview: and the nucleus. 2. But, instead of the infinity of orbits which would be possible in classical mechanics, it is only possible for an electron to move in an orbit for which its orbital angular momentum, L , is an integral multiple of Planck’s constant, h , divided by 2 π . 3. Despite the fact that it is constantly accelerating, an electron moving in such an allowed orbit does not radiate electromagnetic energy. Thus, its total energy E remains constant. 4. Electromagnetic radiation is emitted if an electron, initially moving in an orbit of total energy, E i , discontinuously changes its motion so that it moves in an orbit of total energy, E f . The frequency of the emitted radiation f is equal to the change in energy (E i –E f ) divided by Planck’s constant h . r v electron charge = -e proton charge = +e F r Elecromagnetic Radiation proton charge = +e...
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