2D companion to the 3D gold-foil lab, driven by the same Rutherford scattering relation:
- tan(θ/2) = D / b — θ is the scattering angle, b is the impact parameter (perpendicular distance from the particle's path to the nearest gold nucleus), and D folds in charge, energy and Coulomb's constant into one "distance of closest approach" style number.
- Nuclear model concentrates all the positive charge into a tiny nucleus, so a close pass (small b) gives a large D/b ratio and a sharp, sometimes reversing, deflection.
- Plum-pudding model smears that same charge across the whole atom, so D is far weaker and capped at a few degrees — it can never explain a real backscatter, which is exactly why the 1909 result overturned it.
- Denser atom spacing shrinks the average impact parameter, raising the deflection rate — a thicker or denser foil scatters more particles.