A SMALL NUCLEUS. A BIG DEFLECTION.

Rutherford scattering

Fire alpha particles at gold. Change their energy and discover when a purely electrical explanation stops being enough.

Through a gold foil

Schematic view

Most of an atom is empty space. Most alpha particles pass through; the few that approach a nucleus can scatter strongly. Nuclei and close encounters are enlarged here; atomic spacing and event frequency are not to scale.

One close encounter

Coulomb repulsion

● Gold nucleus (+79e)● Alpha particle (+2e)Dashed path: Coulomb-only prediction

Trajectories are shown relative to the gold nucleus, at the nuclear scale. Motion is slowed enormously. The nuclear surface region is shaded; a flash marks removal from the elastic beam, not a calculated path inside the nucleus.

Coulomb-predicted deflection

Coulomb closest approach

Gold nuclear radius (approx.)

When does Rutherford’s prediction change?

Elastic scattering

Elastic scattering leaves both nuclei unexcited. Nuclear interactions can remove particles from this channel. Compare the relative number of alpha particles detected at each angle or energy. A higher curve means more particles reach the detector.

Rutherford predictionNuclear-interaction model

Detected alpha particles vs angle

Detected alpha particles vs energy

Relative count · Rutherford

Relative count · nuclear model

Model / Rutherford

Both graphs use the same reference: Rutherford’s predicted count at 5 MeV and 90° is set to 1. The number of incoming particles, foil thickness and detector opening are held fixed. These relative counts are separate from the close-up launch counter.

These are model curves, not measured data. The nuclear curve illustrates loss from elastic scattering; it does not reproduce the full quantum interference pattern, nuclear attraction, resonances or reaction products.

What to look for

Lower energy: electrical repulsion

The positive alpha particle is repelled by the positive gold nucleus. A smaller impact parameter gives a larger deflection. At fixed b, a higher energy gives a smaller Coulomb deflection.

Higher energy: probe the nuclear surface

A more energetic alpha particle can get closer. Once the two nuclei approach within nuclear-interaction range, Coulomb repulsion alone is insufficient. At a fixed angle, Rutherford predicts that the number detected is proportional to the inverse square of energy. Here N is the relative number of alpha particles detected.

This is a limit of the Coulomb-only scattering model, rather than the separate problem of explaining atomic stability. The strong nuclear interaction can be attractive at the surface, while excitation and reactions alter the elastic scattering. Deviations need not always be a decrease: real patterns depend on energy, angle and the target.

Physics, approximations and research

The incident energy is measured in the laboratory. For alpha particles on gold-197, E_cm = (197/201)E_lab. Rutherford’s relative orbit and the graphs use this centre-of-mass energy; angles are centre-of-mass angles. The gold-frame close-up shows relative separation, not the separate recoil of both bodies. No electron screening, foil energy loss or multiple scattering is calculated.

The gold charge is +79e; the alpha charge is +2e. The gold radius is estimated as 1.2 A^1/3 fm. The illustrative interaction distance is D = 1.5 A^1/3 + 1.4 fm, inspired by a historical heavy-target strong-absorption description. It is not an experimentally fitted gold boundary or a universal threshold. A smooth elastic-survival factor 1 / [1 + exp((D − r_min)/0.65 fm)] multiplies Rutherford’s differential cross section. For the close-up beam, the same factor sets a random elastic survival probability; a removed event ends on entering the illustrative surface region (D + 1.3 fm), or near closest approach for a grazing encounter. This is an effective absorption picture, not a simulation of the nuclear force itself. There is no sharp physical switch at D. Trajectory lines are Coulomb orbits up to removal.

1 fm = 10⁻¹⁵ m; 1 barn = 10⁻²⁸ m². The foil overview is a schematic of independent encounters, not a densely packed lattice of nuclear-scale gold atoms. Close-up paths are intentionally selected with small impact parameters.

Gove (1955): measured angular departures for 27.5 MeV alpha particles on gold. Farwell & Wegner (1954): energy dependence and a strong-absorption interpretation for heavy targets. The latter studied other heavy elements, not gold; its approximate scale is used only to illustrate the mechanism here.

Explore alpha-particle scattering

Investigate Rutherford scattering by varying alpha-particle energy and impact parameter around gold nuclei. Follow close-up Coulomb trajectories and compare relative detector counts against scattering angle and incident energy. The schematic foil overview illustrates why most alpha particles pass through, while close encounters can produce large deflections.

At higher energies, explore an illustrative nuclear-interaction model that removes events from the elastic scattering channel. Graphs compare this model with the Coulomb-only prediction; they are not measured experimental data. This free interactive resource supports IB, A Level and AP Physics lessons on atomic and nuclear structure.