An alpha particle aimed directly at a gold nucleus (Z=79). What is the closest approach distance?

D = k×q_α×q_Au/KE; use KE=5MeV=8×10⁻¹³J; q_α=3.2×10⁻¹⁹C; q_Au=79e.

Why did most alpha particles pass through the foil almost undeflected?

The nucleus is tiny compared to atomic size; most alphas pass far from any nucleus.

How did Rutherford estimate the nucleus size from the maximum scattering angle?

Closest approach for direct hits gives upper bound on nuclear radius.

Pro 🔒~20 min

Rutherford Scattering

Discover the nuclear model of the atom through alpha particle scattering

How it works

Rutherford Scattering demonstrates a key principle: In 1909, Geiger and Marsden fired alpha particles at gold foil. In 1909, Geiger and Marsden fired alpha particles at gold foil. Most passed through, but a few scattered at large angles — even backward. This contradicted the Thomson 'plum pudding' model and led Rutherford to propose the nuclear model: nearly all atomic mass is concentrated in a tiny, positively-charged nucleus. The scattering angle depends on how close the alpha particle passes to the nucleus, governed by Coulomb repulsion.

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Step-by-step

Fire alpha particles using the gun.
Most will deflect only slightly.
Decrease the impact parameter (aim closer to the center) to see large deflections.
Watch the occasional alpha particle bounce back.
The scattering angle histogram reveals the nuclear structure.

Key formulas

$\cot(\theta/2) = \frac{2bE_k}{k q_\alpha q_{Au}}$ Rutherford scattering formula
$d_{closest} = \frac{kq_\alpha q_{Au}}{E_k}$ Distance of closest approach

Frequently asked questions

An alpha particle aimed directly at a gold nucleus (Z=79). What is the closest approach distance?: D = k×q_α×q_Au/KE; use KE=5MeV=8×10⁻¹³J; q_α=3.2×10⁻¹⁹C; q_Au=79e.
Why did most alpha particles pass through the foil almost undeflected?: The nucleus is tiny compared to atomic size; most alphas pass far from any nucleus.
How did Rutherford estimate the nucleus size from the maximum scattering angle?: Closest approach for direct hits gives upper bound on nuclear radius.