The Nuclear Atom

Rutherford's scattering experiment — alpha particles were fired at a very thin gold foil and their deflections recorded.

What was observed

Most alpha particles passed straight through with little or no deflection.

A small fraction were deflected through large angles.

A very few — roughly one in eight thousand — bounced back through more than 90°.

What each observation implies

Most passing through undeflected means the atom is mostly empty space.

Large deflections mean the positive charge is concentrated, not spread out.

Backscattering means that concentration is also massive, since a light target could not reverse an alpha particle.

Example: the reasoning matters more than the result. The prevailing model had positive charge spread thinly through the whole atom, which would have deflected alphas by fractions of a degree at most. A single particle coming straight back was, as Rutherford put it, as surprising as a shell rebounding from tissue paper — and one clear anomaly was enough to destroy the model.

Estimating nuclear size — the closest approach of an alpha particle occurs when all its kinetic energy has been converted to electric potential energy:

½ m v² = Q₁ Q₂ / (4 π ε₀ r)

Solving for r gives an upper bound on the nuclear radius.

Nuclear radius and nucleon number — experiments give

R = r₀ A^(1/3)

with r₀ about 1.2 × 10⁻¹⁵ m. The cube root appears because volume is proportional to R³, so R³ ∝ A means each nucleon takes up the same volume however large the nucleus.

Nuclear density is enormous and constant — roughly 10¹⁷ kg m⁻³, the same for every nucleus, because the nucleons are packed at a fixed spacing. A teaspoon of nuclear matter would have a mass of hundreds of millions of tonnes, and a neutron star is essentially one vast nucleus.

Scale — a nucleus is about 10⁻¹⁵ m across and an atom about 10⁻¹⁰ m: a factor of 100 000. If the nucleus were a marble at the centre of a sports field, the nearest electrons would be at the boundary, and everything between would be empty.