How did rutherford's gold leaf experiment prove the existence of the nucleus?

Firstly the gold foil was flattened so that it was one atom thick. The researchers knew that alpha particles were positively charged, and so would be repelled by other positive charges. At the atomic scale there is no such thing as "solid matter" the only thing that matters is electric fields.The plumb pudding model suggested that an atom was a sphere of positive charge, with electrons within it. If this were the case the gold leaf atoms would form a wall of positive charge, so no alpha particles could get through. [see diagram]The fact that the vast majority of alpha particles went through without being deflected meant that the vast majority went nowhere near a source of positive charge, therefore positive charge occupies a very small space within the atom, which we called the nucleus. [see diagram]. It's size is determined by the % of alpha particles that travelled through without being blocked.