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Ernest RutherfordSome Came BackSticker

Ernest Rutherford Sticker – Some Came Back | Physics Sticker

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How did we learn that atoms have a nucleus? Ernest Rutherford’s lab fired alpha particles at thin gold foil. Almost all passed through, but a few bounced straight back. In 1911 Rutherford explained this: an atom’s positive charge and nearly all its mass sit in a tiny nucleus. This is a 3" pixel-art physicist sticker from Pixelated Physics.

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Size3″ × 3″

3″ × 3″ kiss-cut sticker.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

In 1909 Hans Geiger and Ernest Marsden, working in Ernest Rutherford’s lab, fired alpha particles at a thin gold foil. Almost all went straight through. A very few came back.

In 1911 Rutherford explained why. Nearly all the atom’s mass and positive charge sit in a tiny nucleus. An alpha particle aimed far from it barely bends; one aimed almost dead-on is turned right round. The angle follows tan(θ/2) = d/2b.

Every path in the art is integrated from the Coulomb force and matches that formula to within 0.05°. The nucleus is drawn hugely magnified.

Rutherford played rugby for his school, Nelson College in New Zealand, so here he takes the catch himself.

Some came back.

Equations

\[\frac{d\sigma}{d\Omega} = \left(\frac{zZe^2}{16\pi\varepsilon_0 E}\right)^2\frac{1}{\sin^4(\theta/2)}\]
\[\tan\frac{\theta}{2} = \frac{d}{2b},\qquad d = \frac{zZe^2}{4\pi\varepsilon_0 E}\]
SymbolMeaningUnit
\(d\sigma/d\Omega\) differential cross section per solid angle \(\mathrm{m^2/sr}\)
\(z\) charge number of the alpha particle (2) \(\mathrm{1}\)
\(Z\) charge number of the target nucleus (gold: 79) \(\mathrm{1}\)
\(e\) elementary charge \(\mathrm{C}\)
\(\varepsilon_0\) vacuum permittivity \(\mathrm{F/m}\)
\(E\) kinetic energy of the alpha particle \(\mathrm{J}\)
\(\theta\) scattering angle \(\mathrm{rad}\)
\(b\) impact parameter: how far off-centre the alpha is aimed \(\mathrm{m}\)
\(d\) distance of closest approach in a head-on collision \(\mathrm{m}\)

Sources

  1. Rutherford (1911) The scattering of α and β particles by matter and the structure of the atom, Phil. Mag. 21, 669
  2. Geiger & Marsden (1909) On a diffuse reflection of the α-particles, Proc. R. Soc. A 82, 495
  3. Te Ara, Dictionary of New Zealand Biography: Rutherford, Ernest
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