Rutherford Scattering

What is Rutherford Scattering?

In 1909, Rutherford's students Geiger and Marsden did one of the most surprising experiments in physics. They fired alpha particles — fast, heavy, positively charged helium nuclei — at a thin sheet of gold foil, expecting them to plow straight through like bullets through paper. Most did. But every now and then one bounced almost straight back. Rutherford said it was 'as if you fired a 15-inch shell at tissue paper and it came back and hit you.' That backscattering killed the 'plum pudding' model and gave birth to the nuclear atom: nearly all the mass and all the positive charge crammed into a tiny core, with electrons spread far around it. This simulation lets you reproduce that experiment, aim alpha particles at any nucleus from hydrogen to fermium, and watch Coulomb repulsion sling them off at angles set by how close they pass to the nucleus.

Parameters explained

Nuclear Charge Z(e)

The number of protons in the target nucleus, set by the element's atomic number Z. The original gold-foil experiment used gold (Z=79). Doubling Z roughly doubles the Coulomb force at any given distance, which means more particles deflect at large angles. Drop Z to 1 (hydrogen) and the alpha barely notices the target — there's almost nothing there to push back on it.

Alpha Energy(MeV)

The kinetic energy of the incoming alpha particle in MeV. Rutherford used 5 MeV alphas from a radium source. Higher energy alphas can punch closer to the nucleus before electrostatic repulsion stops them, so cranking the energy up reveals smaller-scale structure. At very high energies (50+ MeV) the alpha can actually touch the nucleus and the simple Coulomb-scattering formula starts to fail — you'd see deviations that signal the strong nuclear force kicking in.

Impact Parameter(fm)

The perpendicular miss distance the alpha would have if there were no force at all, measured in femtometers (10⁻¹⁵ m). A small impact parameter (aim almost dead-on) gives a large scattering angle. A large impact parameter means the alpha sails past at a comfortable distance and barely deflects. Setting impact_param to zero models a head-on collision, where the alpha stops at the distance of closest approach and reverses direction.

Common misconceptions

• MisconceptionAtoms are mostly empty space, so light and matter should pass right through them all the time.

  CorrectAtoms are mostly empty space *for very high-energy particles like alphas* — the nucleus occupies about 1/100,000 the diameter of the atom. But for light and ordinary matter, the electron cloud fills the entire atomic volume and absolutely interacts with anything passing through. 'Mostly empty' refers to a specific scale and probe; it doesn't mean atoms are hollow.

• MisconceptionRutherford's experiment proved electrons orbit the nucleus in fixed paths.

  CorrectIt did no such thing. Scattering only revealed the *positive charge distribution* — that the positive charge is concentrated, not spread out. Where the electrons live and how they move was completely outside the experiment's reach. Bohr's quantized orbits came four years later (1913) by combining Rutherford's nuclear atom with quantum theory of light. Today we know electrons aren't on fixed paths at all.

• MisconceptionMost alphas got deflected by the nucleus, which is how Rutherford detected it.

  CorrectThe opposite is true. Most alphas passed straight through with almost no deflection because they sailed far from any nucleus. Only about 1 in 8,000 deflected by more than 90°. The fact that *any* of them backscattered — combined with how often it happened — is what set the upper bound on nuclear size. Rutherford's stroke of genius was realizing that rare large-angle scattering is just as informative as the common small angles.

• MisconceptionThe alpha particle bounces off the nucleus the way a ball bounces off a wall.

  CorrectThere's no contact. The alpha is repelled by the long-range Coulomb force from the protons in the nucleus — same physics as two like-charged balloons pushing each other apart, just with much more force at much smaller distance. The closer the alpha gets, the harder the push. For 5 MeV alphas on gold, the alpha never actually touches the nucleus; it stops about 50 femtometers away and reverses.

How teachers use this lab

1. Plum-pudding death match: have students predict what they'd see if Thomson's plum-pudding model were correct (nearly all small-angle deflections, no backscattering). Run the simulation and compare. The mismatch is what killed the model.
2. Distance of closest approach lab: students compute d = kq_α q_Au / KE for a head-on 5 MeV alpha on gold and verify against the simulation. This is a perfect Coulomb's-law-meets-conservation-of-energy problem and is exactly the AP Physics 2 SAP-style calculation.
3. Z scan: students vary nuclear charge from 1 to 100 in steps and record the fraction backscattering. Plot fraction vs. Z² (since cross section scales as Z²). The straight line is a great moment of 'wait, the math actually predicts this.'
4. Impact parameter geometry: at fixed energy, vary impact parameter and record scattering angle. Plot cot(θ/2) vs. b. Students should get a straight line whose slope encodes the nuclear charge — exactly how Geiger and Marsden estimated Z for gold.
5. Historical context: pair the simulation with the original 1909 Geiger–Marsden paper or Rutherford's 1911 paper. Students see what raw data looked like and how Rutherford reasoned from a histogram of scintillation flashes to a model of the atom.