Sponara: Hertha Sponer and the Birge–Sponer Method
Quantum Foundations arc, page 28 of 193. Back to The Pixelated Physics Universe
Who they are
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.
Sponara is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
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.
$$ \begin{gathered} G(v) = \omega_e\left(v + \tfrac{1}{2}\right) - \omega_e x_e\left(v + \tfrac{1}{2}\right)^{2} \\ \Delta G\!\left(v + \tfrac{1}{2}\right) = G(v+1) - G(v) = \omega_e - 2\,\omega_e x_e\,(v + 1) \\ D_0 = \sum_{v=0}^{v_{\max}} \Delta G\!\left(v + \tfrac{1}{2}\right) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $v$ | vibrational quantum number, 0, 1, 2, … | 1 |
| $G(v)$ | vibrational term value of level v | m⁻¹ (cm⁻¹ customary) |
| $\omega_e$ | harmonic vibrational wavenumber | m⁻¹ |
| $\omega_e x_e$ | anharmonicity constant | m⁻¹ |
| $\Delta G(v+\tfrac{1}{2})$ | gap between adjacent levels, G(v+1) − G(v) | m⁻¹ |
| $v_{\max}$ | last bound level | 1 |
| $D_0$ | dissociation energy from v = 0 (× hc for J per molecule) | m⁻¹ |
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 characterCount 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.
Sources
- Birge & Sponer (1926) The Heat of Dissociation of Non-Polar Molecules, Phys. Rev. 28, 259
- Duke Physics — Hertha Sponer
- MIT OCW 5.73 Lecture 8
Crossovers
Sponara meets Decouplarch (Born Oppenheimer Approximation). Decouplarch lets molecules have vibrational levels at all, with nuclei moving on a potential the electrons provide. Sponara counts those levels: the gaps shrink toward the dissociation limit, and extrapolating them estimates the bond energy.
Sponara meets Recoilwyn (Radioactive Recoil). Sponara and Recoilwyn are both portraits of real physicists. Hertha Sponer read molecular energy levels from spectra; Harriet Brooks followed radioactive recoil. Different experiments, same rule: momentum and energy are conserved in every event they recorded.
Wear the lore
- Sponara – Hertha Sponer and the Birge–Sponer Method Pixel Hoodie
- Related infographic poster: The Balmer Ladder – Plate 041 Physics Poster
Concept keywords: Hertha Sponer and the Birge–Sponer Method, Sponara, Quantum Foundations, physics lore, Pixelated Physics