Rutherford's Gold Foil Experiment — How the Nucleus Was Discovered

In 1909, Ernest Rutherford directed Hans Geiger and Ernest Marsden to fire alpha particles at a thin gold foil and observe what happened. The expectation, based on the Thomson "plum pudding" model, was that alpha particles would pass through with only slight deflections. Most did. But about 1 in 8,000 bounced back at large angles. Some came nearly straight back.

Rutherford later said it was as if you fired an artillery shell at tissue paper and it bounced back. The only explanation was that the atom is mostly empty space, with virtually all its mass and positive charge in a tiny, dense core — the nucleus. The nucleus is about 10⁻¹⁵ metres across, while the atom is about 10⁻¹⁰ metres — making the atom roughly 99.9999999999996% empty space.

The scattering formula

Rutherford derived a formula predicting the angular distribution of scattered particles: the fraction scattered at angle θ goes as 1/sin⁴(θ/2). Most scatter forward, very few backward. Our Rutherford scattering calculator computes this differential cross-section for any projectile energy and target.

The formula works because at Rutherford's energies, alpha particles never got close enough for the strong force to matter — it's pure Coulomb scattering. The distance of closest approach in a head-on collision gave the first measurement of nuclear size: femtometres across.

Why it still matters

Rutherford scattering remains a standard technique. Modern experiments look for deviations from the Coulomb prediction to probe nuclear structure. In materials science, Rutherford Backscattering Spectrometry (RBS) analyzes thin film composition. The physics behind our nuclear radius calculator traces directly back to this experiment.