Sponara

Sponara is a respectful pixel portrait of Hertha Sponer, after a 1913 public-domain photograph, beside a glowing ladder whose rungs close up toward a bright limit line.

The Physics

Hertha Sponer (1895–1968) took her doctorate at Göttingen in 1920 under Peter Debye and worked with James Franck on molecular spectroscopy. On a fellowship at Berkeley she and Raymond T. Birge showed in 1926 how to estimate a molecule’s dissociation energy from its band spectrum. The vibrational levels of a real bond crowd together as they climb. Adding up the gaps until they shrink to zero gives the energy at which the molecule falls apart. Dismissed from Göttingen under Nazi law in 1934, she went to Oslo and in 1936 joined Duke University, the first woman on its physics faculty.

G(v) = ω_e(v + ½) − ω_ex_e(v + ½)²

D₀ ≈ Σ_v ΔG_v+½ (for this two-term form, D_e ≈ ω_e² / 4ω_ex_e)

• G(v): vibrational term value of level v (cm⁻¹)
• v: vibrational quantum number, 0, 1, 2, …
• ω_e: harmonic vibrational constant (cm⁻¹)
• ω_ex_e: anharmonicity constant (cm⁻¹)
• ΔG_v+½: spacing G(v+1) − G(v) between neighbouring levels (cm⁻¹)
• D₀: dissociation energy from the lowest level v = 0 (cm⁻¹ or eV)
• D_e: dissociation energy measured from the bottom of the potential well

Plot ΔG against v + ½ and extrapolate to ΔG = 0; the area under the line is D₀. Source: R. T. Birge & H. Sponer, “The heat of dissociation of non-polar molecules”, Phys. Rev. 28, 259 (1926), doi:10.1103/PhysRev.28.259; Duke Physics, “Hertha Sponer”.

Honest caveat: Birge–Sponer is an extrapolation and only an estimate: real level spacings near the dissociation limit bend away from a straight line, so the method can overestimate or underestimate D₀.

In character

Count the steps, watch them shrink, and follow them to where there are no more. That is where the bond lets go, and that is the number.

On the hoodie

Front: a tiny ladder with shrinking gaps under a pixel crown. Back: a pixel portrait of Hertha Sponer with “CROWNED IN HER OWN LIGHT” and “HERTHA SPONER - 1926”. Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.

Part of the Unsung Hands set with Recoilwyn, Ayrtha. Browse all physics hoodies, more quantum designs, or the Deep Cuts.