Theme E · Nuclear and Quantum Physics · SL 6h + HL 3h

E.1 Structure of the Atom

How did experiment overturn the plum-pudding model and reveal the nuclear atom?

In 1909, Geiger and Marsden fired alpha particles at a thin gold foil and found that some bounced almost straight back. Thomson's plum-pudding model (a diffuse positive sphere with electrons embedded in it) could not account for this — the positive charge would need to be concentrated in a tiny, dense nucleus. Rutherford worked backwards from the experimental data to propose the nuclear model of the atom: a tiny, massive, positively charged nucleus surrounded by orbiting electrons in mostly empty space.

Atomic emission spectra delivered the next blow to classical physics. Each element emits light at fixed, discrete wavelengths — not a continuous spectrum. Bohr explained this by quantising electron orbits: electrons can only exist at specific energy levels, and when an electron transitions between levels, it emits or absorbs a photon of exactly the right energy: E = hf.

The Bohr model gives energy levels E_n = −13.6/n² eV for hydrogen. Calculate the wavelength of photon emitted when an electron falls from n = 3 to n = 2. In which part of the spectrum does this line lie?

Key equations

Nuclear notation: ᴬ_ZX (A = nucleon number, Z = proton number)

Photon energy: E = hf (h = 6.63 × 10⁻³⁴ J s)

Nuclear radius: R = R₀A^(1/3) where R₀ ≈ 1.2 × 10⁻¹⁵ m

HL Bohr energy levels: E_n = −13.6/n² eV

HL Quantised angular momentum: mvr = nh/(2π)

What students must understand

Geiger-Marsden-Rutherford experiment: evidence for a small, dense, positively charged nucleus
Nuclear notation ᴬ_ZX; nucleon number A, proton number Z
Emission and absorption spectra as evidence for discrete atomic energy levels
Photons emitted and absorbed during transitions; E = hf relates frequency to energy gap
Emission and absorption spectra as chemical fingerprints
Nuclear radius: R = R₀A^(1/3) — implies roughly constant nuclear density
HL Distance of closest approach in head-on scattering
HL Bohr model: discrete energy levels E_n = −13.6/n² eV; quantised angular momentum
HL Deviations from Rutherford scattering at high energies (nuclear force becomes significant)

Linking questions

How can electron orbits be modelled on planetary motion, and where does this model fail? → D.1 (NOS)
How do emission spectra determine astronomical distances and stellar composition? → E.5, C.5 Doppler