When Geiger and Marsden shot alpha particles at their metal foils, they noticed only a tiny fraction of the alpha particles were deflected by more than 90°. Most just flew straight through the foil. This suggested that those tiny spheres of intense positive charge were separated by vast gulfs of empty space. Most particles passed through the empty space and experienced negligible deviation, while a handful struck the nuclei of the atoms and bounced right back.
Rutherford thus rejected Thomson's (plum) model of the atom,and instead proposed a model where the atom consisted of mostly empty space. (Geiger-Marsden experiment).
As an analogy I want to use an thought experiment with a "modified" peach containing a tiny kernel, where the kernel would have a much greater density than the peaches fruit.
If one shoot (with a not very precise gun and from a long distance) another such kernels towards the peach mostly the kernels are going through the fruit and doesn't get deflected. Only if the shoot was by randomness directed to the tiny peaches kernel mostly a noticeable deflection takes place.
If one would be able to shoot small marbles from the peaches fruit of the diameter of the peaches kernel towards the peach there will be a different result. Since the density of this marbles according to our thought experimental setup is of low density the marbles will be deflected from the boundary of the peach.
Rutherford thus rejected Thomson's model of the atom, and instead proposed a model where the atom consisted of mostly empty space, with all its positive charge concentrated in its center in a very tiny volume, surrounded by a cloud of electrons (Geiger-Marsden experiment).
If Rutherford had repeated the gold foil experiment with electrons he would have get a result, in which the electrons will get reflected at low kinetic energies and only on higher energies get through the foil. Performing at least a time measurement to compare the time of flight of electrons through the foil and without the foil one will see that the foil electrons are slower the electrons not passing the foil. The high energy electrons passing the foil somehow get influenced from the foil atoms and by this are not going through empty space.
From this can be concluded that the empty space is a miss-interpretation. What says the theory and what are empirical facts (phenomena) which shows that the proposed "peach" model is not holdable?
