Rutherford Model
Alpha scattering — toggle Thomson (pudding) vs Rutherford (point nucleus). Coulomb deflection.
Key Notes
Rutherford's alpha-particle scattering experiment (Geiger-Marsden, 1909): bombarded thin gold foil with α-particles, observed scattering pattern.
Most α's passed through nearly undeflected ⇒ atom is mostly EMPTY space.
A small fraction scattered at LARGE angles (some > 90°) ⇒ atom has a tiny, dense, positively charged core (nucleus).
Result: nuclear (planetary) model. Positive charge and almost all mass concentrated in nucleus (~10⁻¹⁵ m); electrons orbit at ~10⁻¹⁰ m.
Distance of closest approach for head-on collision: r_min = (1/4πε₀) · (2Ze²/K_α). For 5 MeV α on gold: r_min ~ 3×10⁻¹⁴ m.
Impact parameter b vs scattering angle: cot(θ/2) = (4πε₀·2K·b)/(2Ze²).
Limitations of Rutherford's model: orbiting electrons would radiate, spiral in, atoms would collapse — needs quantum fix (Bohr).
Formulas
Distance of closest approach (head-on)
Equates initial KE to electrostatic PE.
Scattering angle vs impact parameter
Small b ⇒ large θ; head-on (b = 0) ⇒ θ = 180°.
Number scattered through angle θ (Rutherford formula)
Confirmed experimentally — quartic falloff with θ/2.
Important Points
Rutherford's experiment killed J.J. Thomson's 'plum-pudding' model — uniformly distributed positive charge could never deflect α's at large angles.
Most space inside an atom is EMPTY: nucleus is ~10⁻⁵ × the atomic radius (nucleus < grape, atom = football stadium).
Distance of closest approach gives an upper bound on nuclear size, NOT exact.
Rutherford couldn't explain: (i) why electrons don't radiate and spiral in, (ii) why atomic spectra are discrete.
Bohr (1913) fixed both limitations by introducing quantization.
The 1/sin⁴(θ/2) law from inverse-square Coulomb scattering — historically important confirmation of Coulomb's law down to 10⁻¹³ m.
Rutherford Model notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.