Rutherford Scattering visualizes the hyperbolic trajectories of a charged particle, like an alpha particle, deflected by the repulsive Coulomb force from a massive, fixed atomic nucleus. This simulation is a direct application of classical mechanics to a central force problem, governed by an inverse-square law repulsion. The core physics is derived from the conservation of energy and angular momentum. The total energy E = (1/2)μv₀² determines the orbit's shape, while the angular momentum L = μv₀b, set by the initial speed v₀ and impact parameter b, dictates the particle's orbital plane and the distance of closest approach. The resulting trajectory is a hyperbola, with the scattering angle θ given by the Rutherford formula: cot(θ/2) = (2E b) / (k), where k = (q₁q₂)/(4πε₀). By adjusting b and E, users see how these parameters control the deflection, from a gentle bend to a dramatic back-scatter. The model simplifies the real scattering event by treating the nucleus as an immobile point charge, neglecting relativistic effects, nuclear forces, and radiation losses. It also assumes a perfect vacuum. Interacting with this simulator reinforces understanding of conservation laws in central force motion, the geometry of conic sections in physics, and the historic experiment that revealed the atomic nucleus.
Who it's for: Undergraduate physics students studying classical mechanics, central forces, and the historical development of atomic models. It is also valuable for educators demonstrating the link between conservation laws and scattering phenomena.
Key terms
Coulomb scattering
Impact parameter
Scattering angle
Central force
Hyperbolic orbit
Conservation of angular momentum
Rutherford model
Distance of closest approach
How it works
The nuclear discovery story: large-angle backscatter implied a compact charged core — not a smeared pudding of positive charge.
Frequently asked questions
Why is the trajectory always a hyperbola and not an ellipse like a planet's orbit?
The orbit's shape is determined by the total energy. For an attractive 1/r² force like gravity, bound orbits (negative total energy) are ellipses. In Rutherford scattering, the Coulomb force is repulsive, giving the particle positive total energy, which corresponds to unbound hyperbolic trajectories. The particle approaches from infinity and escapes to infinity after deflection.
What does the impact parameter represent physically?
The impact parameter (b) is the perpendicular distance between the initial velocity vector of the incoming particle and a parallel line through the center of the target nucleus. It quantifies how 'off-center' the collision is. A large b results in a weak deflection, while b=0 represents a head-on collision leading to direct back-scattering.
Does this simulator show what Rutherford actually saw in his experiment?
It visualizes the trajectory of a single alpha particle. The actual experiment observed the statistical distribution of many particles. The famous result was that a tiny fraction scattered at very large angles, which this model explains: only particles with a very small impact parameter (aimed nearly directly at the nucleus) undergo large-angle scattering, proving the nucleus is small and massive.
Why is the nucleus fixed and not moving? Is that realistic?
This is a key simplification of the model. Because the nucleus is thousands of times more massive than an alpha particle, its recoil is negligible. For precise calculations, we use the reduced mass (μ), but fixing the nucleus is an excellent approximation that makes the visualization clearer and aligns with the analysis in Rutherford's original paper.