Geiger–Nuttall

Plate 48 speaks for itself: “One line.”

The Physics

Alpha-decay half-lives span over twenty orders of magnitude, yet their logarithm falls on near-straight lines against Z/√Q. Gamow explained it in 1928 as quantum tunnelling through the Coulomb barrier.

log₁₀ t½ ≈ a Z / √Q + b

• t½: half-life, s
• Z: charge number of the daughter nucleus, dimensionless
• Q: alpha-decay energy, J (quoted in MeV)
• a, b: empirical constants

²³⁸U: 4.468×10⁹ yr. ²¹²Po: 294 ns. Ratio ≈ 10^23.7.

Sources

• H. Geiger, J. M. Nuttall, Phil. Mag. 22, 613 (1911).
• G. Gamow, Z. Phys. 51, 204 (1928).

On the poster

Plate 048, “Geiger–Nuttall”: the pixel-art plate with its slogan “One line.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.