Atomic models

Alpha-particle scattering

Geiger and Marsden, working with Rutherford, fired alpha particles at a thin gold foil. Most passed straight through, a few were deflected through small angles, and very few (about 1 in 8000) were turned back by more than 90°. Thomson's "plum pudding" model could not explain large-angle scattering.

Rutherford's nuclear model

Rutherford concluded that the atom is mostly empty space, with all its positive charge and almost all its mass in a tiny central nucleus (size about 10⁻¹⁵ m, compared with atomic size about 10⁻¹⁰ m). Electrons revolve around it. However, an orbiting electron is accelerating, and classical theory says it should radiate energy and spiral into the nucleus; the model also predicts a continuous spectrum, not the observed lines.

Bohr's model of hydrogen

Bohr's postulates:

• Electrons move only in certain stationary orbits without radiating.
• In these orbits, angular momentum is quantised: mvr = nh/2π.
• Radiation is emitted or absorbed only when an electron jumps between orbits: hν = Eᵢ – E_f.

Results for hydrogen:

• Radius: rₙ = n²a₀, with a₀ ≈ 0.529 Å (Bohr radius). So r₂ = 4a₀ ≈ 2.12 Å.
• Energy: Eₙ = –13.6/n² eV. E₁ = –13.6 eV (ionisation energy 13.6 eV), E₂ = –3.4 eV, E₃ = –1.51 eV.

De Broglie's idea explains the quantisation: an orbit fits a whole number of electron wavelengths, 2πr = nλ.

Hydrogen spectrum

Wavelengths are given by 1/λ = R(1/n_f² – 1/nᵢ²), with R ≈ 1.097 × 10⁷ m⁻¹.

• Lyman (n_f = 1): ultraviolet; series limit about 91.2 nm.
• Balmer (n_f = 2): visible; the 3 → 2 line (energy 1.89 eV) has λ ≈ 656 nm (red).
• Paschen (3), Brackett (4), Pfund (5): infrared.

Key points

• Most alpha particles undeflected → atom mostly empty.
• Large deflections → small, heavy, positive nucleus.
• mvr = nh/2π; rₙ ∝ n²; Eₙ = –13.6/n² eV.
• Lyman UV, Balmer visible, others infrared.

Exam tips

• Photon energy for a jump = difference of 13.6/n² values; then λ (nm) ≈ 1240/E (eV).