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Unformatted text preview: k = p k = 1 p k x = 1 p x > 2 x p > 2 = h 2 2 = h x p > h The Bohr model In 1897, J.J. Thompson discovered the electron. It was then clear that matter, whch is macroscopically neutral, is made of charged parts, the electron being a negatively charged particle. There must be therefore a positively charged part, and Thompson suggested the plum pudding model, in which here is a continuum of positive charge distribution, in which negatively charged electrons are embedded. In 1909, Geiger and Marsden found that alpha particles (that are positively charged) are sometimes (about 1 in 10,000) reflected by very large angles when are fired at a thin gold leaf. It is very hard to reconcile this experimental result with the plum pudding model. Rutherford described this expriment as follows: It was almost as if you fired a fifteeninch shell at a piece of tissue paper and it bounced back and hit you. Rutherford was motivated by the GeigerMarsden results to propose the solar system model, in which most of the atoms mass is in a small nucleus , and the electrons orbit the nucleus. There is an obvious problem with this model: an electron orbiting the nucleus must radiate, becasue it is constantly accelerated. Losing energy to radiation, the orbit must decay. We next estimate the lifetime of the hydrogen atom based on the Rutherford model. The radiated power is given by Larmors formula, P = 2 3 ke 2 a 2 c 3 where k = 1 / (4 ), e is the electron charge, and a is the acceleration. Take now a = v 2 /r , and find P = 2 3 ke 2 v 4 r 2 c 3 = 2 3 ke 2 ( v/c ) 4 c r 2 ....
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