Rutherford scattering
Alpha particles fired at a gold nucleus are deflected by Coulomb repulsion. The scattering angle depends on the impact parameter — how close the particle would pass if the nucleus weren’t there. Most sail past. A few bounce nearly straight back. That’s how Rutherford discovered the nucleus in 1911.
In 1909, Hans Geiger and Ernest Marsden fired alpha particles at thin gold foil under Ernest Rutherford’s direction. Most passed through with minimal deflection, but a small fraction bounced back at large angles. Rutherford reportedly said it was “as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”
The explanation required a tiny, dense, positively charged nucleus at the center of the atom. The Coulomb force between the alpha particle (charge Z₁ = 2) and the nucleus (charge Z₂) produces hyperbolic trajectories. The scattering angle θ is related to the impact parameter b by:
b = (a/2) cot(θ/2), where a = Z₁Z₂e² / (4πε₀ · 2E)
The distance of closest approach d = a for a head-on collision (b = 0) defines the “forbidden zone” — the region the particle cannot enter at a given energy. This simulation integrates the equations of motion in the Coulomb potential to show the actual hyperbolic trajectories.