Rutherford's nuclear model

By 1900 it was known that atoms contain light, negative electrons and are neutral overall. But where is the positive charge?

Thomson's model ('plum pudding'): positive charge spread evenly through the whole atom, with electrons dotted inside like seeds in a watermelon.

The test: Geiger and Marsden, guided by Rutherford, fired fast α-particles (helium nuclei, charge +2e) at a very thin gold foil and counted where they went:

• Most went straight through, hardly deflected.
• A few were turned through large angles.
• About 1 in 8000 bounced almost straight back.

Thomson's spread-out charge could never push an α-particle back. Rutherford said it was 'as if you fired a shell at tissue paper and it came back and hit you'.

Rutherford's nuclear model: almost all the mass and all the positive charge are packed into a tiny nucleus at the centre, about 10⁻¹⁵ m across, while the atom is about 10⁻¹⁰ m: 100 000 times bigger. The atom is mostly empty space, which is why most α-particles pass straight through.

The impact parameter b is how far off-centre the α-particle is aimed. Small b (nearly head-on) means a big deflection; large b means a small one.

Distance of closest approach d: a head-on α-particle slows down as it climbs the Coulomb 'hill', stops, and turns back. At that point all its kinetic energy has become potential energy: K = 2Ze² / (4πε₀d).

Example: a 5 MeV α-particle on gold (Z = 79): d = 2 × 9 × 10⁹ × 79 × 1.6 × 10⁻¹⁹ / (5 × 10⁶) ≈ 4.5 × 10⁻¹⁴ m. The nucleus must be smaller than this.

The problem: an electron going round a nucleus is accelerating, and classical physics says it should radiate energy and spiral into the nucleus in a tiny fraction of a second. Real atoms are stable, so something was missing. Bohr supplied it.