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::I have incorporated these references and an additional secondary history ref in a new section called "Significance". [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 03:50, 14 July 2024 (UTC)
:::@[[User:Kurzon|Kurzon]] Please stop changing the lead sentence without discussion. It is inappropriate per sources and personally rude in my opinion. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 16:13, 21 July 2024 (UTC)
==Deflection by the electrons==
{{ping|Johnjbarton}} Where did Thomson get that <math>\sqrt{L} = \tfrac{4}{5} \sqrt{2R}</math>? [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 18:26, 29 August 2024 (UTC)
:I don't know. I assume it was "simple" geometry, averaging the sqrt of the chord length crossing the sphere over the circular face of the atom. Here is a ref for the average of the chord length: https://inis.iaea.org/collection/NCLCollectionStore/_Public/34/035/34035593.pdf [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 21:21, 2 September 2024 (UTC)
::I thought he meant the average length an alpha particle travels through a sphere, which would be <math>\frac{4}{3} \pi r^3 \div \pi r^2 = \frac{4}{3} r</math> [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 07:51, 3 September 2024 (UTC)
:::Thomson says explicitly that the formula is for the "mean value of <math>\sqrt{l}</math>". [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 13:29, 3 September 2024 (UTC)
{{ping|Headbomb|Mohammadidea|Mike Peel|Michael C Price|Materialscientist}} Perhaps one of you guys can help us? Please refer to the section '''Deflection by the electrons''' of this article and [https://archive.org/details/proceedingsofcam15190810camb/page/464/mode/2up Thomson's 1910 paper on the plum pudding model]. J. J. Thomson sad that the average of <math>\sqrt{L}</math> is equal to <math>\tfrac{4}{5}\sqrt{2R}</math>. He never explained how he arrived at this equation. How might he have come to this? [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 05:04, 21 September 2024 (UTC)
It probably involves integrating the fourth root of something, as in <math>\int \sqrt[4]{x} = \tfrac{4}{5} x^{\frac{5}{4}} + C</math> [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 12:24, 22 September 2024 (UTC)
{{ping|Johnjbarton}} I think I got it.
[[File:Thomson_model_alpha_particle_scattering_3.svg|thumb|left]]
<math>L = \sqrt{R^2 - b^2}</math>
<math>L = 2 \sqrt{R^2 - b^2}</math>
<math>\sqrt{L} = \sqrt{2} \sqrt[4]{R^2 - b^2}</math>
<math>\frac{1}{\pi R^2} \int_0^R \sqrt{2} \sqrt[4]{R^2 - b^2} \cdot 2\pi b \cdot db</math>
<math>mean of \sqrt{L} = \frac{4}{5} \sqrt{2R}</math>
[[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 17:38, 22 September 2024 (UTC)
:Yes, nice work. That looks good as far as your explanation here goes. The integral of the chord length is unexplained but I guess the chord length for impact ''b'' gets weighted by the diameter of the corresponding circle facing the incoming particle. That would be <math>\pi b</math> and to get the average divide by the area facing the particle. Not sure where the 2 comes in. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 22:11, 23 September 2024 (UTC)
::I altered the notation to suit my diagrams. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 05:29, 24 September 2024 (UTC)
::Now I need to figure this out:
::<math>\theta_1 = \frac{4k q_a q_e}{mv^2 g} \cdot \sqrt{N_0 \pi g^2 L}</math>
::<math>\overline{\sqrt{L}} = \frac{4}{5}\sqrt{2R}</math>
::<math>\Rightarrow \bar{\theta}_1 = \frac{32}{5} \cdot \frac{k q_a q_e}{mv^2} \cdot \sqrt{N_0 \pi R}</math>
::<math>= \frac{16}{5} \cdot \frac{k q_a q_e}{m v^2 R} \cdot \sqrt{\frac{3N}{2}}</math>
::I don't know where that 32 comes from. If you multiply <math>\tfrac{4}{5}</math> by 4 you get <math>\tfrac{16}{5}</math>, not <math>\tfrac{32}{5}</math> [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 05:41, 24 September 2024 (UTC)
::The more I fiddle with Thomson's equations, the more I think the <math>\tfrac{32}{5}</math> was a misprint. It should have been <math>\tfrac{16}{5}</math>. See for yourself on pg 466 of his paper: https://archive.org/details/proceedingsofcam15190810camb/page/466/mode/2up [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 07:23, 24 September 2024 (UTC)
:::IMO it is important to express the reasoning but the factors of two here don't matter: use your best judgement. After all these formula involve the number of electrons, a value that was changing by orders of magnitude in this time frame. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 02:27, 25 September 2024 (UTC)
::::That's irrelevant. What matters is how Thomson rearranged his equations. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 02:32, 25 September 2024 (UTC)
:::::Huh? If that is what you believe then you have to present what he presented. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 02:58, 25 September 2024 (UTC)
::::::No, I think there was a misprint. I wonder if Thomson published a correction in a later article. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 03:01, 25 September 2024 (UTC)
== Reorient to beta particle scattering ==
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