- 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.