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ClueBot III (talk | contribs) m Archiving 1 discussion from Talk:Plum pudding model. (BOT) |
ClueBot III (talk | contribs) m Archiving 1 discussion from Talk:Plum pudding model. (BOT) |
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:::So you want me to use rough approximations in the math but you're going to split hairs when it comes to prose? [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 17:44, 13 August 2024 (UTC)
::::No. I want you to use appropriate approximations and appropriate prose according to physics in a physics article. These are connected. Using a number like 0.0186 in a physics context is not the same as 0.02. The value 0.02 is not a "rough approximation", it is additional information. It tells the reader that "we are seeking to understand a complex phenomenon so we will focus on the general character." On the other hand 0.0186 means we have confidence that our model will reproduce experiments to 4 significant figures. But "all models are wrong". The 0.0186 is mice when lions abound. We have no experimental data with 4 significant figures and not a prayer that our textbook exercise will match even if we did. The 0.0186 number is incorrect. If you wrote that on a physics exam its points off. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 18:49, 13 August 2024 (UTC)
==Where did Thomson get this?==
{{ping|Johnjbarton|Headbomb|Materialscientist}} In a 1910 paper, Thomson said that this equation gives the average deflection angle for a single collision with the positive sphere. Thomson merely says that "it is easy to show" this is true, he didn't explain it. Any ideas on how he got this equation?
<math display="block">\bar\theta_1 = \frac{\pi}{4} \cdot \frac{k q_a q_g}{mv^2} \cdot \frac{1}{r} \approx 0.00013 \text{ radians or 0.007 degrees}</math>
[[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 11:33, 13 August 2024 (UTC)
:It'd help a lot if you included the citation to that paper.  <span style="font-variant:small-caps; whitespace:nowrap;">[[User:Headbomb|Headbomb]] {[[User talk:Headbomb|t]] · [[Special:Contributions/Headbomb|c]] · [[WP:PHYS|p]] · [[WP:WBOOKS|b]]}</span> 11:44, 13 August 2024 (UTC)
::{{cite journal |author=J. J. Thomson |year=1910 |title=On the Scattering of rapidly moving Electrified Particles |journal=Proceedings of the Cambridge Philosophical Society |volume=15 |pages=465-471 |url=https://archive.org/details/proceedingsofcam15190810camb/page/464/mode/2up}} [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 12:03, 13 August 2024 (UTC)
:@[[User:Kurzon|Kurzon]] You deleted the content that explains this formula and references two places that discuss it. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 15:22, 13 August 2024 (UTC)
::Heilbron has an explanation for it and it's nothing like what we had. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 21:44, 13 August 2024 (UTC)
:::Heilborn reproduces Thomson's derivation based on Rutherford's notes. See Heilbron Appendix A, Fig 19. This is beta scattering from positive sphere and uses an impulse approximation averaged over a line across the sphere.
:::Beiser is the version you deleted, page 106. It uses an impulse approximation at the rim of a positive sphere for alpha particle scattering.
:::Per the title of Thomson's 1910 paper, beta/alpha/positive/negative it's all Coulomb scattering. The differences show up in the momentum change (and in many details other than the Coulomb scattering).
:::The difference between the two models of scattering are ''insignificant'' in the sense I discussed above. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 22:18, 13 August 2024 (UTC)
::::Heilbron gives us this integral in his essay. It doesn't make sense to me.
::::<math>\varphi_2 = (1/\pi a^2) \int_0^a (ne^2/ma^3v^2) (2p\sqrt{a^2 - p^2}) (2\pi pdp) = (\pi/4)(ne^2/mv^2a)</math>
::::What confuses me is how pi survives the integration. As, doesn't
::::<math>(1/\pi a^2) \int_0^a (ne^2/ma^3v^2) (2p\sqrt{a^2 - p^2}) (2\pi pdp) = (1/\pi a^2)2\pi \int_0^a (ne^2/ma^3v^2) (2p\sqrt{a^2 - p^2}) (pdp) = (1/a^2)2 \int_0^a (ne^2/ma^3v^2) (2p\sqrt{a^2 - p^2}) (pdp)</math>?
[[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 11:51, 16 August 2024 (UTC)
:Heilbron says he is averaging <math>pL</math> over the "disk" which I guess has to be a sphere. The average value of <math>pL</math> over of the sphere gives the internal <math>2*2\pi</math> but I don't know where the extra <math>p</math> comes from.
:Since he ends up with Thomson's formula, I guess the averaging formula is mis-typeset or something like that.
:I thought this approach was too complicated which is why I used Beiser. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 19:15, 16 August 2024 (UTC)
::Well what about historical accuracy? [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 19:21, 16 August 2024 (UTC)
:::I gave a try, see what you think. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 22:39, 16 August 2024 (UTC)
::::Nevermind, I used this tool: https://www.symbolab.com/solver/definite-integral-calculator/
::::Sweet crackers, if I had this when I was a teenager, high school would have been so much sweeter. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 06:36, 18 August 2024 (UTC)
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