{"title":"Unsung Hands","description":"Women whose work in physics was under-credited.","products":[{"product_id":"sponara-pixel-hoodie","title":"Sponara – Hertha Sponer and the Birge–Sponer Method Pixel Hoodie","description":"\u003cp\u003eSponara 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.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eHertha 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.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eG(v) = ω\u003csub\u003ee\u003c\/sub\u003e(v + ½) − ω\u003csub\u003ee\u003c\/sub\u003ex\u003csub\u003ee\u003c\/sub\u003e(v + ½)²\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eD₀ ≈ Σ\u003csub\u003ev\u003c\/sub\u003e ΔG\u003csub\u003ev+½\u003c\/sub\u003e   (for this two-term form, D\u003csub\u003ee\u003c\/sub\u003e ≈ ω\u003csub\u003ee\u003c\/sub\u003e² \/ 4ω\u003csub\u003ee\u003c\/sub\u003ex\u003csub\u003ee\u003c\/sub\u003e)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eG(v): vibrational term value of level v (cm⁻¹)\u003c\/li\u003e\n\u003cli\u003ev: vibrational quantum number, 0, 1, 2, …\u003c\/li\u003e\n\u003cli\u003eω\u003csub\u003ee\u003c\/sub\u003e: harmonic vibrational constant (cm⁻¹)\u003c\/li\u003e\n\u003cli\u003eω\u003csub\u003ee\u003c\/sub\u003ex\u003csub\u003ee\u003c\/sub\u003e: anharmonicity constant (cm⁻¹)\u003c\/li\u003e\n\u003cli\u003eΔG\u003csub\u003ev+½\u003c\/sub\u003e: spacing G(v+1) − G(v) between neighbouring levels (cm⁻¹)\u003c\/li\u003e\n\u003cli\u003eD₀: dissociation energy from the lowest level v = 0 (cm⁻¹ or eV)\u003c\/li\u003e\n\u003cli\u003eD\u003csub\u003ee\u003c\/sub\u003e: dissociation energy measured from the bottom of the potential well\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003ePlot ΔG against v + ½ and extrapolate to ΔG = 0; the area under the line is D₀. Source: R. T. Birge \u0026amp; H. Sponer, “The heat of dissociation of non-polar molecules”, \u003cem\u003ePhys. Rev.\u003c\/em\u003e 28, 259 (1926), doi:10.1103\/PhysRev.28.259; Duke Physics, “Hertha Sponer”.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e 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.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eCount 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.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: 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.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eUnsung Hands\u003c\/strong\u003e set with \u003ca href=\"\/hi\/products\/recoilwyn-pixel-hoodie\"\u003eRecoilwyn\u003c\/a\u003e, \u003ca href=\"\/hi\/products\/ayrtha-pixel-hoodie\"\u003eAyrtha\u003c\/a\u003e. Browse all \u003ca href=\"\/hi\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/hi\/collections\/quantum-physics-t-shirts\"\u003equantum designs\u003c\/a\u003e, or the \u003ca href=\"\/hi\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Pixelated Physics","offers":[{"title":"Black \/ S","offer_id":50964469383271,"sku":"21994265210478376952","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964469416039,"sku":"32205395793648449551","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964469448807,"sku":"59886375318620799164","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964469481575,"sku":"32306011724677858891","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964469514343,"sku":"19658560549868276941","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964469547111,"sku":"24150544771332124072","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964469579879,"sku":"22576485165543150713","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964469612647,"sku":"26212679212273883683","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H05_72846dbf-4aef-4ee6-b837-e32ca67a9537.png?v=1793678478"},{"product_id":"recoilwyn-pixel-hoodie","title":"Harriet Brooks: First Glimpse of Radioactive Recoil (1904)","description":"\u003cp\u003eRecoilwyn is a respectful pixel portrait of Harriet Brooks, after William Notman \u0026amp; Son’s 1898 photograph, with two motes of light flying apart before her: a light fast one and a heavy slow one.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eHarriet Brooks (1876–1933) was Ernest Rutherford’s first graduate student at McGill. She helped show that radium’s “emanation” was a new radioactive gas (radon), early evidence that one element can turn into another. Her 1904 \u003cem\u003eNature\u003c\/em\u003e letter, “A Volatile Product from Radium”, reported active deposit turning up on the walls of the vessel, an early observation of what was later explained as alpha recoil: when a nucleus emits an alpha particle, the daughter nucleus is kicked the other way.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ep\u003csub\u003eα\u003c\/sub\u003e = −p\u003csub\u003eR\u003c\/sub\u003e   ⇒   E\u003csub\u003eR\u003c\/sub\u003e = (m\u003csub\u003eα\u003c\/sub\u003e \/ m\u003csub\u003eR\u003c\/sub\u003e) E\u003csub\u003eα\u003c\/sub\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003ep\u003csub\u003eα\u003c\/sub\u003e, p\u003csub\u003eR\u003c\/sub\u003e: momenta of the alpha particle and the recoiling daughter nucleus (kg m s⁻¹)\u003c\/li\u003e\n\u003cli\u003eE\u003csub\u003eα\u003c\/sub\u003e, E\u003csub\u003eR\u003c\/sub\u003e: their kinetic energies (non-relativistic) (J or MeV)\u003c\/li\u003e\n\u003cli\u003em\u003csub\u003eα\u003c\/sub\u003e, m\u003csub\u003eR\u003c\/sub\u003e: their masses (kg or u)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eFor radium-226 (E\u003csub\u003eα\u003c\/sub\u003e ≈ 4.78 MeV) the radon-222 daughter recoils with about 4.78 × 4.0\/222 ≈ 86 keV, enough to fly free of a surface and lodge in the walls. Sources: H. Brooks, \u003cem\u003eNature\u003c\/em\u003e 70, 270 (1904), doi:10.1038\/070270b0; Dictionary of Canadian Biography, “Brooks, Harriet”; Russ \u0026amp; Makower, \u003cem\u003eProc. R. Soc. A\u003c\/em\u003e 82, 205 (1909), doi:10.1098\/rspa.1909.0028.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Brooks observed the effect; the recoil explanation came later (Hahn, and Russ \u0026amp; Makower, 1909). The discovery of radon is shared with Rutherford, Owens and Dorn.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eSomething leapt from the radium and landed where it should not have been. I wrote down exactly what I saw. The explanation could catch up later.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: two arrows from one dot, a long thin one and a short thick one. Front label: “HARRIET BROOKS · FIRST OBSERVED 1904”. Back: a pixel portrait of Harriet Brooks with “CROWNED IN HER OWN LIGHT” and “HARRIET BROOKS - 1904”. Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eUnsung Hands\u003c\/strong\u003e set with \u003ca href=\"\/hi\/products\/sponara-pixel-hoodie\"\u003eSponara\u003c\/a\u003e, \u003ca href=\"\/hi\/products\/ayrtha-pixel-hoodie\"\u003eAyrtha\u003c\/a\u003e. Browse all \u003ca href=\"\/hi\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/hi\/collections\/particle-physics\"\u003eparticle \u0026amp; nuclear physics designs\u003c\/a\u003e, or the \u003ca href=\"\/hi\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Pixelated Physics","offers":[{"title":"Black \/ S","offer_id":50964469678183,"sku":"19100564941867237194","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964469710951,"sku":"11023687066335426289","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964469743719,"sku":"18878982911652344048","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964469776487,"sku":"20926109071667663055","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964469809255,"sku":"66217581007825812341","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964469842023,"sku":"99630455220650024172","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964469874791,"sku":"13135308702553509835","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964469907559,"sku":"22030571145965897991","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H14_9bbbba37-6e77-4f00-8ebe-63e945d3389c.png?v=1793678488"},{"product_id":"ayrtha-pixel-hoodie","title":"Ayrtha – Hertha Ayrton, the Electric Arc and Sand Ripples Pixel Hoodie","description":"\u003cp\u003eAyrtha is a respectful pixel portrait of Hertha Ayrton, after a Bain News Service photograph of about 1900, holding a white-violet carbon arc above a basin of sand ripples.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eHertha Ayrton (1854–1923) showed that the hissing and instability of carbon arc lamps came from oxygen reaching the hot crater of the positive carbon, and summed up her arc work in \u003cem\u003eThe Electric Arc\u003c\/em\u003e (1902). There she gave an empirical law for the voltage across an arc, now called the Ayrton equation. Her ripple paper on how vortices build sand ripple marks, “The origin and growth of ripple-mark”, was read before the Royal Society on 16 June 1904. In 1906 she became the first woman to receive the Society’s Hughes Medal.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eV = a + b l + (c + d l) \/ I\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eV: voltage across the arc (V)\u003c\/li\u003e\n\u003cli\u003eI: arc current (A)\u003c\/li\u003e\n\u003cli\u003el: arc length, the gap between the carbons (m)\u003c\/li\u003e\n\u003cli\u003ea, b, c, d: empirical constants fitted for given electrodes (units V, V m⁻¹, W, W m⁻¹)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eThe (c + d l)\/I term makes V fall as I rises, a negative differential resistance, which is why an arc needs a series resistor to stay stable. Sources: H. Ayrton, \u003cem\u003eThe Electric Arc\u003c\/em\u003e (1902); \u003cem\u003eProc. R. Soc. Lond.\u003c\/em\u003e 74, 565 (1904), doi:10.1098\/rspl.1904.0159, and full paper \u003cem\u003eProc. R. Soc. A\u003c\/em\u003e 84, 285 (1910), doi:10.1098\/rspa.1910.0076; MacTutor, “Hertha Marks Ayrton”; English Heritage blue plaque.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The Ayrton equation is empirical, fitted to carbon arcs; it is not derived from plasma physics and does not hold for every arc. How sand ripples grow and choose their spacing is still studied.\u003c\/p\u003e\u003ch3\u003eIn character\u003c\/h3\u003e\u003cp\u003e\u003cem\u003eThey said the arc hissed because it was fickle. It hissed because it was breathing oxygen. I listened until it told me why.\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eOn the hoodie\u003c\/h3\u003e\u003cp\u003eFront: a tiny arc between two rods over three ripples. Back: a pixel portrait of Hertha Ayrton with “CROWNED IN HER OWN LIGHT” and “HERTHA AYRTON - 1906”. Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.\u003c\/p\u003e\u003cp\u003ePart of the \u003cstrong\u003eUnsung Hands\u003c\/strong\u003e set with \u003ca href=\"\/hi\/products\/sponara-pixel-hoodie\"\u003eSponara\u003c\/a\u003e, \u003ca href=\"\/hi\/products\/recoilwyn-pixel-hoodie\"\u003eRecoilwyn\u003c\/a\u003e. Browse all \u003ca href=\"\/hi\/collections\/hoodies\"\u003ephysics hoodies\u003c\/a\u003e, more \u003ca href=\"\/hi\/collections\/electromagnetism\"\u003eelectromagnetism designs\u003c\/a\u003e, or the \u003ca href=\"\/hi\/collections\/deep-cuts\"\u003eDeep Cuts\u003c\/a\u003e.\u003c\/p\u003e","brand":"Pixelated Physics","offers":[{"title":"Black \/ S","offer_id":50964470005863,"sku":"10012611444486418513","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ M","offer_id":50964470038631,"sku":"17536997199752288188","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ L","offer_id":50964470071399,"sku":"35361978633547981427","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ XL","offer_id":50964470104167,"sku":"30667800467075846342","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 2XL","offer_id":50964470136935,"sku":"15658650901028805190","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 3XL","offer_id":50964470169703,"sku":"20426556088540888526","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 4XL","offer_id":50964470202471,"sku":"19461674590263711571","price":64.99,"currency_code":"USD","in_stock":true},{"title":"Black \/ 5XL","offer_id":50964470235239,"sku":"10402213787029082724","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/03_H15_4f43f7cb-cfac-4d6e-af1a-f76a730e0d82.png?v=1793678497"}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/collections\/unsung-hands.png?v=1793678030","url":"https:\/\/pixelatedphysics.com\/hi\/collections\/unsung-hands.oembed","provider":"Pixelated Physics","version":"1.0","type":"link"}