Physic Labs

Frontier physics

Atomic fine and hyperfine structure

Watch atomic energy levels split into fine and hyperfine components. Check qualitatively the fine splitting ΔEfs∼α2En\Delta E_{\rm fs} \sim \alpha^2 E_n and the hyperfine coupling Hhfs=A I⋅JH_{\rm hfs} = A\,\mathbf{I}\cdot\mathbf{J}.

Research

Equipment

  • 3D model of energy levels with fine-structure sublevels
  • Angular-momentum coupling producing hyperfine F levels
  • Sliders for parameter, noise, and physical parameter
  • Quantity-evolution plot in the second section

Procedure

  1. View fine-structure splitting

    Run the simulation: each principal level splits into a cluster of nearby sublevels. Drag the physical-parameter slider to change the splitting and compare with the scale ΔEfs∼α2En\Delta E_{\rm fs} \sim \alpha^2 E_n — only ~10⁻⁴ of the main level since α≈1/137\alpha \approx 1/137.

  2. Couple nuclear spin: hyperfine levels

    Observe the nuclear moment I\mathbf{I} coupling with the electron moment J\mathbf{J} into total FF, producing an extra splitting smaller than the fine structure. Increase the noise to see the levels jitter — analogous to experimental linewidth blurring the hyperfine splitting.

  3. Relate to real spectral lines

    Read the quantity evolution while changing the parameter: a ~10⁻³ eV fine splitting in Na yields the yellow doublet at 589.0/589.6 nm; the 21 cm (1420 MHz) hyperfine line of neutral hydrogen is a key astronomical probe. Predict which level stays most stable before changing the noise.

Simulation

Experiment history

In 1887 Albert Michelson found the hydrogen HαH_\alpha line was a doublet — the "fine structure". Arnold Sommerfeld explained it in 1916 via relativistic corrections to Bohr's model. In 1928 Paul Dirac derived the same result from his relativistic electron equation, which naturally includes spin. In 1947 Willis Lamb measured the Lamb shift — a small offset Dirac theory did not predict — opening quantum electrodynamics. Hyperfine splitting from nuclear-spin coupling gives hydrogen's 21 cm line, predicted observable by Hendrik van de Hulst and detected by Ewen and Purcell in 1951.

Related physicists

Niels BohrErwin SchrödingerPaul DiracWolfgang PauliIsidor Isaac RabiRichard Feynman

Related library topics

Atomic fine and hyperfine structure