Editing History of atomic theory (section)

==Statistical mechanics==
In 1738, Swiss physicist and mathematician [[Daniel Bernoulli]] postulated that the pressure of gases and heat were both caused by the underlying motion of particles. Using his model he could predict the  [[ideal gas law]] at constant temperature and suggested that the temperature was proportional to the velocity of the particles. These results were largely ignored for a century.<ref name="Uffink-2006">{{Cite book |last=Uffink |first=Jos |url=https://linkinghub.elsevier.com/retrieve/pii/B9780444515605500129 |title=Philosophy of Physics |date=2007-01-01 |publisher=North-Holland |editor-last=Butterfield |editor-first=Jeremy |series=Handbook of the Philosophy of Science |location=Amsterdam |pages=923–1074 |chapter=Compendium of the foundations of classical statistical physics|doi=10.1016/b978-044451560-5/50012-9 |isbn=978-0-444-51560-5 |editor-last2=Earman |editor-first2=John |chapter-url=https://philsci-archive.pitt.edu/2691/}}</ref>{{rp|25}}

[[James Clerk Maxwell]], a vocal proponent of atomism, revived the kinetic theory in 1860 and 1867. His key insight was that the velocity of particles in a gas would vary around an average value, introducing the concept of a distribution function.<ref name="Uffink-2006"/>{{rp|26}}<ref>See:
* Maxwell, J.C. (1860) [https://books.google.com/books?id=-YU7AQAAMAAJ&pg=PA19 "Illustrations of the dynamical theory of gases. Part I. On the motions and collisions of perfectly elastic spheres,"] ''Philosophical Magazine'', 4th series, '''19''' : 19–32.
* Maxwell, J.C. (1860) [https://books.google.com/books?id=DIc7AQAAMAAJ&pg=PA21 "Illustrations of the dynamical theory of gases. Part II. On the process of diffusion of two or more kinds of moving particles among one another,"] ''Philosophical Magazine'', 4th series, '''20''' : 21–37.</ref> [[Ludwig Boltzmann]] and [[Rudolf Clausius]] expanded his work on gases and the laws of [[thermodynamics]] especially the second law relating to entropy. In the 1870s, [[Josiah Willard Gibbs]] extended the laws of entropy and thermodynamics and coined the term "statistical mechanics."{{Citation needed|date=October 2024}}

Boltzmann defended the atomistic hypothesis against major detractors from the time like [[Ernst Mach]] or [[Energeticism|energeticists]] like [[Wilhelm Ostwald]], who considered that energy was the elementary quantity of reality.<ref>{{Cite journal |last=Deltete |first=Robert |date=1999-04-01 |title=Helm and Boltzmann: Energetics at the Lübeck Naturforscherversammlung |url=https://link.springer.com/article/10.1023/A:1005287003138 |journal=Synthese |language=en |volume=119 |issue=1 |pages=45–68 |doi=10.1023/A:1005287003138 |issn=1573-0964|url-access=subscription }}</ref>

At the beginning of the 20th century, [[Albert Einstein]] independently reinvented Gibbs' laws, because they had only been printed in an obscure American journal.<ref>Navarro, Luis. "Gibbs, Einstein and the Foundations of Statistical Mechanics." Archive for History of Exact Sciences, vol. 53, no. 2, Springer, 1998, pp. 147–80, http://www.jstor.org/stable/41134058.</ref> Einstein later commented that had he known of Gibbs' work, he would "not have published those papers at all, but confined myself to the treatment of some few points [that were distinct]."<ref>Stone, A. Douglas,  Einstein and the quantum : the quest of the valiant Swabian, Princeton University Press, (2013). {{ISBN|978-0-691-13968-5}} quoted from Folsing, Albert Einstein, 110.</ref> All of statistical mechanics and the laws of heat, gas, and entropy took the existence of atoms as a necessary postulate.{{citation needed|date=October 2024}}

===Brownian motion===
In 1827, the British botanist [[Robert Brown (botanist, born 1773)|Robert Brown]] observed that dust particles inside pollen grains floating in water constantly jiggled about for no apparent reason. In 1905, Einstein theorized that this [[Brownian motion]] was caused by the water molecules continuously knocking the grains about, and developed a mathematical model to describe it. This model was validated experimentally in 1908 by French physicist [[Jean Perrin]], who used Einstein's equations to measure the size of atoms.<ref>{{Cite web |title=The Nobel Prize in Physics 1926 |url=https://www.nobelprize.org/prizes/physics/1926/perrin/lecture/ |access-date=2023-02-08 |website=NobelPrize.org |language=en-US}}</ref>

{| class="wikitable"
|+ Kinetic diameters of various simple molecules
|-
! Molecule !! Perrin's measurements<ref name="Perrin 1909 p. 50">[[#refPerrin1909|Perrin (1909). ''Brownian Movement and Molecular Reality'', p. 50]]</ref> !! Modern measurements
|-
| Helium || 1.7 × 10<sup>−10</sup> m || 2.6 × 10<sup>−10</sup> m
|-
| Argon || 2.7 × 10<sup>−10</sup> m || 3.4 × 10<sup>−10</sup> m
|-
| Mercury || 2.8 × 10<sup>−10</sup> m || 3 × 10<sup>−10</sup> m
|-
| Hydrogen || 2 × 10<sup>−10</sup> m || 2.89 × 10<sup>−10</sup> m
|-
| Oxygen || 2.6 × 10<sup>−10</sup> m || 3.46 × 10<sup>−10</sup> m
|-
| Nitrogen || 2.7 × 10<sup>−10</sup> m || 3.64 × 10<sup>−10</sup> m
|-
| Chlorine || 4 × 10<sup>−10</sup> m || 3.20 × 10<sup>−10</sup> m
|}

{| class="wikitable"
|+ Atomic masses in kilograms
|-
! Molecule !! Perrin's measurements<ref name="Perrin 1909 p. 50"/> !! Modern measurements
|-
| Hydrogen || 1.43 × 10<sup>−27</sup> kg || 1.66 × 10<sup>−27</sup> kg
|-
| Oxygen || 22.7 × 10<sup>−27</sup> kg || 22.8 × 10<sup>−27</sup> kg
|}