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A few months after Thomson's paper appeared, [[George Francis FitzGerald|George FitzGerald]] suggested that the corpuscle identified by Thomson from cathode rays and proposed as parts of an atom was a "free electron", as described by physicist [[Joseph Larmor]] and [[Hendrik Lorentz]]. While Thomson did not adopt the terminology, the connection convinced other scientists that cathode rays were particles, an important step in their eventual acceptance of an atomic model based on sub-atomic particles.<ref>{{Cite journal |last=Falconer |first=Isobel |date=July 1987 |title=Corpuscles, Electrons and Cathode Rays: J.J. Thomson and the 'Discovery of the Electron' |url=https://www.cambridge.org/core/product/identifier/S0007087400023955/type/journal_article |journal=The British Journal for the History of Science |language=en |volume=20 |issue=3 |pages=241–276 |doi=10.1017/S0007087400023955 |issn=0007-0874}}</ref>
In 1899 Thomson reiterated his atomic model in a paper that showed that negative electricity created by ultraviolet light landing on a metal (known now as the [[photoelectric effect]]) has the same mass-to-charge ratio as cathode rays; then he applied his previous method for determining the charge on ions to the negative electric particles created by ultraviolet light.<ref name="PaisInwardBound">{{Cite book |last=Pais |first=Abraham |title=Inward bound: of matter and forces in the physical world |date=2002 |publisher=Clarendon Press [u.a.] |isbn=978-0-19-851997-3 |edition=Reprint |___location=Oxford}}</ref>{{rp|86}} He estimated that the electron's mass was 0.0014 times that of the hydrogen ion (as a fraction: {{sfrac|1|714}}).<ref name=Thomson1899>{{Cite journal |last=J. J. Thomson |year=1899 |title=On the Masses of the Ions in Gases at Low Pressures. |url=https://www.chemteam.info/Chem-History/Thomson-1899.html |journal=Philosophical Magazine |series=5 |volume=48 |pages=547–567 |number=295}}<br />"...the magnitude of this negative charge is about 6 × 10<sup>
{{blockquote|I regard the atom as containing a large number of smaller bodies which I shall call corpuscles; these corpuscles are equal to each other; the mass of a corpuscle is the mass of the negative ion in a gas at low pressure, i.e. about 3 × 10<sup>
===1904 Mechanical model of the atom ===
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where ''k'' is the [[Coulomb constant]], ''q''<sub>e</sub> is the charge of the beta particle, ''q''<sub>g</sub> is the charge of the positive sphere, ''m'' is the mass of the beta particle, and ''R'' is the radius of the sphere. Because the atom is many thousands of times heavier than the beta particle, no correction for recoil is needed.
Thomson did not explain how this equation was developed, but the historian [[John L. Heilbron]] provided an educated guess he called a "straight-line" approximation.<ref>Heilbron (1968). p. 278</ref> Consider a beta particle passing through the positive sphere with its initial trajectory at a lateral distance ''b'' from the centre. The path is assumed to have a very small deflection and therefore is treated here as a straight line.
[[File:Thomson model beta scattering positive sphere.svg|center|thumb|upright=2|Diagram is not to scale. The beta particle's deviation is in fact so small, the path is practically a straight line.]]
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===Deflection by the electrons===
Thomson modelled the collisions between a beta particle and the electrons of an atom by calculating the deflection of one collision then multiplying by a factor for the number of collisions as the particle crosses the atom.
[[File:Thomson model beta scattering electrons.svg|center|thumb|upright=2]]
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