The atom was supposed to be soft
J. J. Thomson pictured electrons embedded in diffuse positive matter. A heavy, fast alpha particle passing through thin gold foil should then suffer only many tiny deflections.
In Manchester, Hans Geiger and Ernest Marsden counted faint flashes on a screen. Most particles passed straight through. A few turned sharply. A very small number came almost back.
Diagram description
Static physics diagram: rutherford_gold_foil.
Like a shell bouncing from tissue paper
Rutherford compared the result to firing artillery at tissue paper and having it rebound. A single strong deflection required positive charge and most atomic mass to be concentrated in a region far smaller than the atom.
Diagram description
Static physics diagram: rutherford_nuclear_atom.
The foil did not photograph a nucleus. Positions of thousands of flashes were interpreted through a model of an invisible structure. Modern particle physics still follows that logic: launch a known probe, measure how it scatters, and infer what it struck.