Nuclear Model Simulator

One alpha particle, one nucleus. Set the energy, pick the target, choose how far off centre you aim, then read off how far in it got. Aim dead centre and the alpha comes straight back out at 180°. Why that matters is the third readout: a ball of charge the size of a whole atom could never manage a hundredth of a degree.

Scattering angle  theta = 2 arctan(alpha / b)
97.36°
aimed 20.00 fm off centre at gold, at 5.0 MeV
Closest approach  r_min
53.04 fm
it never gets closer than this
A plum-pudding atom manages
0.00711°
the most a sphere of charge can ever give is 0.0181°
Count rate vs 90°
0.79
how often this angle happens, against 90°
head-on, this energy would reach 45.50 fm
a pudding's absolute maximum 0.0181°
orbit eccentricity 1.3314
alpha speed 5.18% of c
Alpha energy E5.0 MeV
Target nucleusgold (Z = 79)
Aim off centre b20.00 fm
Along the flight0.000 of the flight
theta = 2 arctan(alpha / b), with alpha = k z Z e² / 2E — half the head-on distance d, never d itself — and r_min = alpha (1 + 1/sin(theta/2)), which at b = 0 collapses to exactly d. d bounds the nuclear radius from above, and only at the energy it belongs to. It is not the radius: gold's is about 7.3 fm against a 45.50 fm bound at 5 MeV, 6.2x looser.
The marker steps in equal slices of time through t = (alpha/v)(eps sinh(xi) + xi), so it bunches at the turn: the outermost tenth of the flight covers 1.85x the path of the tenth straddling it, and there the alpha is down to 37.70% of its incoming speed — to zero dead centre. The slowing is in the speed and the arc length, not in xi, which sweeps fastest nearest the nucleus. A point nucleus gives 180°; a sphere of the same charge gives 0.0181° at best, a factor of 9942. The rate band stops at 1e+8, so at tiny angles its marker rides the top edge as a hollow triangle and the panel carries the true figure.
Model: point nucleus, fixed target, pure Coulomb repulsion, one scattering event, no electrons, no nuclear force, non-relativistic alpha (5.2% of c at 5 MeV). The plum-pudding comparison uses a uniformly charged sphere of radius 1.44e-10 m, the gold atomic radius, for every target. These are the lab's assumptions, not measurements.