Step 1: The experiment. Rutherford directed a beam of fast \(\alpha\)-particles at a very thin gold foil and recorded the angles at which they scattered. Most particles passed almost straight through, a few were deflected through large angles, and a very small number (about 1 in 8000) bounced back through more than \(90^\circ\).
Step 2: Interpretation. Since most \(\alpha\)-particles were undeviated, most of the atom is empty space. The rare large-angle deflections require a strong, concentrated repulsive force, which is possible only if all the positive charge and nearly all the mass of the atom are packed into a very small central region.
Step 3: Result. The experiment established the existence of a tiny, dense, positively charged core, the nucleus. Its size is of the order of \(10^{-15}\text{ m}\), about \(10^{4}\) times smaller than the atom (\(\sim10^{-10}\text{ m}\)), and it carries essentially the entire mass and all the positive charge of the atom, with electrons revolving around it.
\[\boxed{\text{Atom has a small, dense, positively charged nucleus at its centre.}}\]