anderson1 - convenient to draw an auxiliary triangle with...

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convenient to draw an auxiliary triangle with its sides labeled in accordance with the quantities in Equation 3.18. 4. BOHR'S THEORY OF ATOMIC SPECTRA r + COs Be Differentiating Equation 3.18, 2 0 . d8 _ 1 + r cos Oe dO sec L L - -;-----:--7-:: (r + cos ()d2 The nuclear atom proposed by Rutherford settled the problem associate, with the scattering of alpha particles, but did not explain the stability of th atom. Since it is impossible to have a stable configuration ofcharges subject tl electrostatic forces only, a dynamical system was proposed, analogous to ; planetary system. Such a system could account for the fact that the nucleu is only of the order of l'x 10- 12 em while the atom as a whole has an effectiv diameter of the order of I X 10- 8 em. However, a serious problem arose il connection with electromagnetic theory, namely, that a charge undergoin, continuous centripetal acceleration should radiate continuously. If this wer the case, the energy of the dynamical system would decrease continuousl and the planetary charge would spiral into the nucleus after a nominal lifetim of about 10- 8 second. That this does not occur is borne out by the infinit lifetimes ofmost elementary atoms and by the nature oftheir radiation spectra Atoms do not radiate unless excited, and when radiation does occur its spectrun consists of discrete frequencies rather than the continuum of frequencie required by the classical theory of radiation. In 1913, Bohr-! proposed a theory which was successful in explaining th radiation spectra of one-electron atoms, although it is in direct disagreemen with the classical theory of radiation. Bohr's postulates may be summarize as follows: (3.19) sin (Jc . Using the fact that the total cross section is the same in each frame, we write, II (:~t sin 8L d()L d(PL =11 (:~tsin ()e d()e dePe, 21T I (:~t sin 8 L dOL = 21T I (:~tsin ()e dOc· Then, PROBLEM 3-4 An isotropic scattering cross section in the C-frarne will thus be peaked in the forward direction in the laboratory by the factor (I + r). or From the triangle above, (1) The Coulomb force on a planetary electron provides the centripeta acceleration required for a dynamically stable circular orbit. (2) The only permissible orbits are those in the discrete set for which th angular momentum of the electron equals an integer times li; wher Ii = h/21T. (3) An electron moving in one of these stable orbits does not radiate. (4) Emission or absorption of radiation occurs only when an electro makes a transition from one orbit to another. From the second postulate note that we now have angular momentum (a well as charge and energy) quantized in atomic systems. The third postulat rejects the troublesome claim that an accelerated charge must radiate i atomic systems, in spite of its validity in the macroscopic world. The fourt postulate provides the link with Planck's theory ofradiation, since the frequenc ofthe photon emitted or absorbed is given by the energy difference ofthe tw states divided by h.
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This note was uploaded on 08/06/2008 for the course PHYS 25 taught by Professor Nelson during the Spring '08 term at UCSB.

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anderson1 - convenient to draw an auxiliary triangle with...

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