What it does
In 1909 Geiger and Marsden, working with Ernest Rutherford, fired fast alpha particles (helium nuclei, charge +2e) at a very thin gold foil. The accepted picture of the atom then was Thomson’s plum pudding: positive charge spread through the whole atom with electrons dotted in it. That predicts every alpha particle should go almost straight through. Most did, but about 1 in 8,000 bounced back, which Rutherford compared to a shell bouncing off tissue paper. The only explanation was a tiny, heavy, positive nucleus. This page lets you fire a beam at either model and count where the particles go, and, on the Class 12 level, aim a single particle and see its scattering angle and closest approach.
It follows the school topics on atomic structure: Class 9 Science, Structure of the Atom (Thomson’s model, Rutherford’s alpha-particle scattering experiment, Rutherford’s model), and Class 12 Physics, Atoms (alpha-particle scattering and Rutherford’s nuclear model, alpha-particle trajectory, impact parameter, distance of closest approach). Before this, states of matter shows that matter is made of particles; afterwards, hydrogen spectrum shows how Bohr added energy levels, and hydrogen orbital viewer shows the modern picture.
How to use it
- Choose the model: Nucleus (Rutherford) or Plum pudding (Thomson).
- With A beam, particles fly in at random heights. The counters show how many went almost straight (under 10°), were turned 10° to 90°, or bounced back (over 90°). Reset counts starts again.
- Change the foil and the alpha particle energy. Faster particles and lighter nuclei mean less bending.
- Switch the Level to Class 12 for the formulas, then choose One particle and slide its aim b (the impact parameter, the distance by which it would miss the nucleus if it were not pushed). The graph shows the angle against the aim.
Worked example
With the page as it opens (gold, Z = 79, alpha particles of 5 MeV), a particle aimed straight at the nucleus stops where all its energy has become electric energy: d = 1.44 MeV fm × 2 × 79 / 5 MeV = 45.5 fm (1 fm = 10⁻¹⁵ m). That is much smaller than the atom (about 140,000 fm across) but larger than the gold nucleus itself (about 7 fm), so the particle never touches it.
On One particle with aim b = 1.00 d = 45.5 fm, tan(θ/2) = d / 2b = 0.5, so the particle is turned through θ = 53.13°, and it comes no closer than (d/2)(1 + √5) = 73.6 fm. With b = 0.5 d it turns through exactly 90°.
Check yourself
Five questions, fresh each time: the head-on closest approach, the angle for a given aim, what the experiment showed about empty space and about the nucleus, and how the closest approach changes with energy. Nothing is saved.
Tips
- The picture is zoomed in thousands of times on one nucleus. In a real foil the nuclei are so far apart that almost every particle passes far from all of them, which is why only about 1 in 8,000 bounced back.
- The paths are hyperbolas: the push of the nucleus gets weaker as 1/r², exactly like gravity but repelling.
- Rutherford’s formula breaks down for very fast alpha particles on light nuclei, when they get close enough to touch: the first hint of the strong nuclear force.
FAQ
Why do the electrons not stop the alpha particles? An electron is about 7,000 times lighter than an alpha particle, so it is like a fly hitting a bus.
Why does the plum pudding model fail? Its positive charge is spread over the whole atom, so the push on a passing alpha particle is never strong: it can only turn it by a tiny fraction of a degree.
Is this from NCERT? No. It is an independent study aid that follows the same school topics, with its own pictures and numbers.
Where the numbers come from
- Rutherford scattering of alpha particles by a point nucleus: head-on closest approach d = k(2e)(Ze)/K, tan(θ/2) = d/(2b), closest approach (d/2)(1 + √(1 + (2b/d)²)); Thomson's plum pudding model: standard physics.
- e²/(4πε₀) = 1.43996448 MeV fm (CODATA 2018).
- Checked against an independent Python calculation and a step-by-step integration of the Coulomb path (angles within 0.1°, closest approach within 1%).
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.