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2-4: Thomson's Atomic Model

[J. J. Thomson's raisin bread model (plum pudding model)]
J. J. Thomson considered that the structure of an atom is something like a raisin bread, so that his atomic model is sometimes called the raisin bread model. He assumed that the basic body of an atom is a spherical object containing N electrons confined in homogeneous jellylike but relatively massive positive charge distribution whose total charge cancels that of the N electrons. The schematic drawing of this model is shown in the following figure. Thomson's model is sometimes dubbed a plum pudding model.

[Thomson's Model and Alpha Particle Scattering]
As stated on the preceding page, Geiger and Marsden carried out an experiment in which the alpha rays were collided against a thin metal foil. Their results showed that almost all incident alpha particles penetrate the foil and go straight in forward direction but a few are scattered in very large angles.
Is it possible to explain this result by using Thomson's model? This question will be studied below, but before explaining it, let us present the answer in advance: The results of the alpha particle scattering cannot be explained by Thomson's atomic model. Thomson's raisin bread model (plum pudding model) therefore cannot be valid as an atomic model.
The reason will be explained below. Since we need somewhat detailed mathematical expressions, it will be given on the other page,
2-4-A: Alpha Particle Scattering by Thomson's model
As seen on the other page (2-4-A), we can consider that the scattering angle of the alpha particle by Thomson's model is at most 0.01 degrees.
The thickness of the metal foil in the scattering experiment of the alpha rays is about 10-6 m. When assuming that the atoms are tightly packed in the metal, there are about 10000 atoms lining up in the direction of thickness, because the size of an atom is approximately 10-10m. (See the following figure.)

When the alpha particle collides with these atoms in the metal foil 10000 times successively, the scattering angle of each individual collision in such a multiple scattering is less than 0.01 degrees as discussed above. The resultant scattering angle is obtained by an accumulation of these individual scatterings of 10000 times. One may expect that, even if the scattering angle of each individual scattering is very small like 0.01 degrees, we can have as large resultant angle as

This is however unrealistic, because the direction of each individual scattering must be random, and an accumulation of random values would give nearly zero only. So that we never obtain such a large resultant scattering angle after the multiple scattering.
Accordingly, such a large scattering angle as those obtained in Geiger and Marsden's experiment cannot be reproduced by such a multiple scattering as stated above. Thus we can conclude that Thomson's atomic model is not held.
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