Chapter4_all - PHY3063 R D Field The Size and Lifetime of...

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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 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
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This note was uploaded on 04/17/2008 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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Chapter4_all - PHY3063 R D Field The Size and Lifetime of...

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