Experiments · High school and university

The gold foil experiment

Fire alpha particles at gold foil; swing the detector, count the ones that bounce back and trace the nucleus.

In the learning section below the figure, predict, try, complete the tasks and check yourself with short questions.

Fig. 1The gold foil experiment

Fire; drag the detector arm

θ = 45° · 0 counts

The window shows shots that pass within 170 fm of the nucleus.

Atom model

Foil metal

Number of shots

Alpha energy

Nuclear charge Z

Gold

Detector angle

Counts by angle

counts ÷ solid angle (log)

Fired0 / 1,000
Bounced back (θ > 90°)0 · 0.00%theory: 0.76%
Detector (45° ± 5°)0expected ≈ 0.0
Distance of closest approach d29.5 fmnuclear radius ≈ 7.0 fm
Bounced back in a real 0.4 µm foil≈ 1 / 62,000

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1Predict
2Try
3Explain

If Thomson’s model were right, how many of 1000 alphas fired at a gold foil would turn through more than 90°?

Purple track: path of an alpha particleGold: the foilFlash: an alpha hitting the screenThe numbers come from one model: Coulomb repulsion between an alpha (charge 2e) and a nucleus of charge Z, with k·e² = 1.44 MeV·fm and the recoil of the nucleus neglected. Each shot is drawn, with a fixed-seed random number generator, from the true distribution of alphas passing within 170 fm of one nucleus in the foil, so the same settings always give the same result. In a real foil almost every alpha passes much farther from any nucleus and goes straight through; the real-foil fraction is worked out separately. The detector counts the alphas scattered into a ±5° band at the screen’s angle. In Thomson’s model the deflection is the random sum of tiny pushes from the atoms in the foil.

The gold foil experiment

Counts by angle

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