By D. Ter Haar
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Extra resources for The Old Quantum Theory
Example text
In the Thomson atom, the scattering is due to the corpuscles (electrons), while in the Rutherford atom, it is partly due to the electrons and partly due to the nucleus. In the case of ß-mys, we would not expect qualitative differences in the scattering characteristics of the Thomson and Rutherford atoms, as the )S-rays are electrons. However, in the case of α-particle scattering, we could not expect scattering over large angles to take place, if the a t o m had the structure postulated by Thomson and if the observed scattering angle were due to a single scattering process.
Let us consider the scattering of a particle of mass m and charge Z i e by a fixed charge (Fig. l). Let V be the velocity of m at infinity, and let ρ be the impact parameter, that is, the distance at which m would pass the fixed charge, if there were n o forces acting between the two charges. Let π—20 be the scattering angle, that is, the angle over which m is deflected. If we are not interested in the details of the orbit (for such details see, for instance, ter Haar, 1961, chap. I), we can easily find how θ depends on p.
42)) that a single electron is responsible for the spectrum, we must consider the motion of one electron in the combined field of the nucleus and the 10 other electrons. A theoretical justification is afforded by the shell model of the atom which we shall brieñy ATOMIC SPECTRA I N THE O L D Q U A N T U M THEORY 53 discuss later in this chapter. As there is no preferred direction, we may assume that the field acting upon the electron is spherically symmetric. The potential energy, U(r), will far from the nucleus be simply -e^/r, as the 10 electrons will screen out all but YY of the nuclear charge.