Is the atom's positive charge smeared through it (Thomson's plum-pudding) or concentrated in a tiny core — and how do you tell from how alpha particles bounce off?
▶ Launch the interactive simulationFire 7.7-MeV alpha particles (Z=2) at gold (Z=79) and treat each as a pure repulsive-Coulomb (1/r²) two-body problem. One length sets the whole pattern — the head-on closest approach D = k_e·Z₁Z₂e²/E — and the closed-form deflection of an alpha with impact parameter b is θ = 2·arctan(D/2b) (cross-checked by verlet-integrating the Coulomb hyperbola). Monte-Carlo a million alphas with impact parameters spread uniformly over the beam disk, histogram the deflection into solid-angle bins, and least-squares fit log(dN/dΩ) against log(sin(θ/2)).
the Rutherford exponent −4 — recovered as the SLOPE of a single straight line on log–log axes, giving the differential cross section dσ/dΩ = (D/4)² / sin⁴(θ/2). A 1/sin⁴(θ/2) tail is the unique fingerprint of scattering from a point Coulomb charge; Thomson's diffuse plum-pudding sphere has no such large-angle tail at all — it can never turn a fast, massive alpha straight back ("as if a 15-inch shell bounced off tissue paper"). From the same D the lab bounds the nuclear size: a head-on alpha gets no closer than D ≈ 3×10⁻¹⁴ m, so the gold nucleus is smaller than that — thousands of times smaller than the atom (~10⁻¹⁰ m), which is therefore almost entirely empty space. Geiger & Marsden's 1909 result and Rutherford's 1911 analysis — the discovery of the nucleus, the foundation under Bohr's hydrogen and Franck–Hertz