Rutherford discovered that:
atoms are mostly empty space with a positively charged core
atoms have negative charges scattered within a sphere of positive charge
atoms are mostly empty space with a neutrally charged core
atoms are mostly empty space with negatively charged core

Atoms are mostly empty space with a positively charged core

Explanation:

Ernest Rutherford conducted a series of experiments together with Hans Geiger and Ernest Marsden; in order to corroborate Thomson's raisin pudding atomic model (positive and negative charges evenly distributed, the atom, which is electrically neutral).

However the results of the experiment were surprising an led Rutherford to find out there is a concentration of charge in the atom's core (which was later called nucleus) surrounded by electrons.

This lead to a new atomic model, in which the atom has a positive charged nucleus surrounded by negative charged particles, hence the atom is not electrically neutral.