= Rutherford model
{c}
{tag=Atomic nucleus}
{wiki}
= Nuclear model of the atom
{synonym}
The Rutherford model places a concentrated central <electric charge> inside a much larger <chemical atom>. In 1911, <Ernest Rutherford> argued that rare large deflections were predominantly single close encounters, rather than accumulated small deviations in a diffuse-charge atom. He treated the central <electric charge> as positive for calculation while noting that the scattering deductions did not establish its sign. He explicitly deferred atomic stability.<The Scattering of Alpha and Beta Particles by Matter and the Structure of the Atom by Ernest Rutherford>[The Scattering of α and β Particles by Matter and the Structure of the Atom, §§1–3, printed pp. 669–675]{ref}
The physical inference is a compact region generating a strong <electric field>, not a miniature hard wall. Most <impact parameters> miss that region, while a small subset give large deflections. The model supplies a way to infer interior structure from outgoing <angles>, a central use of scattering throughout <atomic physics> and <nuclear physics>. This inference does not by itself specify <Electron> <quantum states> or explain <spectral lines>.
The repulsive model also sets a probing scale. At closest approach, <conservation of energy> with zero radial <velocity> gives
$$
E=\frac{L^2}{2mr_{\min}^2}+\frac{\kappa}{r_{\min}},\qquad
r_{\min}=a+\sqrt{a^2+b^2}.
$$
For the numerical model above, even a head-on projectile turns at $r_{\min}=2a=45.504\,\mathrm{fm}$. This is a calculated closest-approach distance, not a measured <atomic nucleus> <radius>. A point-charge fit can constrain how compact the scattering centre must be, but cannot directly resolve structure at distances the projectiles never reach.
The <Rutherford differential cross-section> must not be extrapolated to zero <angle>: the unscreened point model has a forward divergence, while real neutral <chemical atoms> exhibit the <screening effect>, finite beam acceptance, and accumulated small deflections. At very short separation, finite nuclear size and the <nuclear force> can change the interaction. <Nuclear recoil> changes the relation between laboratory and centre-of-mass <angles> for lighter targets; appreciable <energy> loss or repeated large deflections invalidates the simple <thin-foil scattering counts>. These limits delimit the calculation rather than supplying evidence for a nuclear contact collision in the early experiment.
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