Final answer:
Rutherford concluded from his gold foil experiment that atoms have a small, dense, positively-charged nucleus, around which electrons orbit, and that the atom is mostly empty space.
Step-by-step explanation:
When Rutherford found that some of the alpha particles fired at the gold foil were widely deflected, he concluded that atoms must consist of a small, dense, positively-charged nucleus. This conclusion was drawn from observing that while most alpha particles passed through the gold foil undeflected, suggesting that the atom is mostly empty space, a small fraction were deflected at large angles. Rutherford's gold foil experiment overturned the plum pudding model of the atom and led to the establishment of the nuclear model of the atom, where electrons orbit around this dense nucleus.
Rutherford drew two conclusions from his experiment: first, since the alpha particles are positively charged and only a few were deflected, it indicated that the positive charge in the atom is not spread out but concentrated in a small volume. Second, the fact that some alpha particles were deflected at very sharp angles, and a few even recoiled back, demonstrated that the center of positive charge, the nucleus, must be extremely dense and tiny compared to the overall size of the atom.