E.1 Structure of the atomIB Physics HL: Revision notes

In the Geiger–Marsden–Rutherford experiment, alpha particles were fired at thin gold foil in a vacuum. Most passed straight through (the atom is mostly empty space); a very few were deflected through large angles or rebounded, showing that the positive charge and nearly all the mass sit in a tiny, dense nucleus.

A nuclide is written $^{A}_{Z}\mathrm{X}$: A = nucleon number, Z = proton number, X = chemical symbol. Neutrons N = A − Z; a neutral atom has Z electrons. Example: $^{208}_{82}\mathrm{Pb}$ has 82 protons and 126 neutrons.

Electrons occupy discrete energy levels. A downward transition emits one photon with hf = ΔE; absorption needs a photon with exactly the right energy. Line emission spectra (bright lines) and absorption spectra (dark lines on a continuous background, at the same wavelengths) are the evidence. Each element's line pattern is a fingerprint, so spectra reveal chemical composition, for example of a star's outer layers.

Nuclear radius follows R = R₀A^(1/3) with R₀ ≈ 1.20 × 10⁻¹⁵ m. So volume ∝ A, and since mass ∝ A the nuclear density is the same for all nuclei: ρ = u / ((4/3)πR₀³) ≈ 2.3 × 10¹⁷ kg m⁻³, about 10¹⁴ times the density of water. Nucleons are packed like incompressible spheres.

In a head-on collision the alpha particle stops momentarily when all its kinetic energy has become electric potential energy: Ek = k(2e)(Ze)/d, giving the distance of closest approach d. This is an upper limit on the nuclear radius.

Rutherford's formula assumes only the electrostatic force. At high energies the alpha particle gets close enough to feel the strong nuclear force, and scattering at large angles falls below the prediction. The energy at which deviations begin gives an estimate of nuclear size (d = R_nucleus + R_alpha).

Bohr postulated that the electron's angular momentum is quantised: mvr = nh/2π. With electrostatic attraction as the centripetal force, this allows only certain orbits, with energies E = −13.6/n² eV. An electron in an allowed orbit does not radiate; photons are emitted when it jumps down (hf = ΔE).

The model predicts hydrogen's lines very accurately but fails for atoms with more than one electron, and does not explain line intensities.