Talk:Plum pudding model: Difference between revisions

Revision as of 16:02, 7 October 2024

Latest revision as of 04:42, 17 March 2025

(14 intermediate revisions by 2 users not shown)

Line 15:

{{Archives|banner=yes|age=90}}

== Reorient to beta particle scattering ==

==My diagram==

{{ping|Ajrocke|Johnjbarton}} I drew this diagram of the plum pudding model based on a 1905 diagram by JJ Thomson. The electrons are arranged in a pentagonal dipyramid, equidistant from the center. Is this a good diagram or misleading? [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 19:15, 28 April 2024 (UTC)

{{ping|Johnjbarton}} Now that Headbomb has agreed that the maths stuff for the Thomson model should be in the '''Rutherford scattering experiments''', I think we should rework the stuff in this article to beta particle scattering. That should do better historical justice to Thomson's work, which is something you want. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 20:39, 26 September 2024 (UTC)

:As a re-drawing of a historical diagram I think it is fine. I will tweak the caption. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 15:24, 29 April 2024 (UTC)

::Should all the electrons be the same distance from the center of the sphere? I wonder if the peaks of the pyramids should be a different distance. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 08:48, 12 July 2024 (UTC)

:::The diagram looks like the ones in Thomson's paper. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 00:37, 13 July 2024 (UTC)

::::Have you seen one that shows multi-shell electrons? I have heard of the "Thomson problem" in mathematics but all the diagrams I find constrain the electrons to the surface of the sphere. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 06:52, 13 July 2024 (UTC)

:::::I have not see such a diagram. Thomson's analysis of the multi-ring case was very limited. Above 6 electrons he finds that stability requires adding electrons in the center of the atom. Above 9 electrons the number of electrons in the center increase until at 15 he needs 15 in the center. (Recall that as more electrons are added the positive sphere also increases in strength). The electrons in the center then repel, leading to an inner ring. By this analysis he gets multi-rings. But he cannot do stability calculations on multiple rings, he's just guessing at this point.

:::::Bohr later said the equivalent of "he's making stuff up". Pais notes that Thomson generally considered physical models to be stories useful for generating ideas rather than the basis of quantitative analysis. (I can something about this to the article if you think it useful). And note that the great success of Bohr's later shell model follows the idea of rings of special stability. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 16:25, 13 July 2024 (UTC)

::::::Nobody has tried a computer simulation? [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 18:20, 13 July 2024 (UTC)

:::::::Perhaps if we expand the section on the Thomson problem one will come up. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 02:25, 14 July 2024 (UTC)

:It looks fine to me.[[User:Ajrocke|Ajrocke]] ([[User talk:Ajrocke|talk]]) 17:56, 30 April 2024 (UTC)

{{ping|Johnjbarton}} On that note, could you direct me to some papers by Thomson which contain his beta scattering studies? You mentioned several times that the plum pudding model lined up with Thomson's data on beta scattering, I want to look at that. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 10:43, 27 September 2024 (UTC)

[[File:Thomson atom seven electrons.svg|right|thumb]]

== Lead sentenceImage is inappropriate.upside down ==

In the section "Deflection by the positive sphere", the image Thomson_model_alpha_particle_scattering_3.svg show a deflection away from the center correct for + on + scattering. However the Thomson's model was for beta particles, - on + and thus the deflection should be towards the center. This difference does not alter the model's predictions because every path on one side of the atom has a matching one on the other and they are added to compare to experiment. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 17:38, 27 September 2024 (UTC)

The lead sentence is currently

* The plum pudding model is an obsolete scientific model of the atom.

This incorrectly makes "obsolete" the most significant characteristic of the Thomson model. That does not, for example, distinguish it among other articles on atomic models:

* {{annotated link|Bohr atom}}

* {{annotated link|Cubical atom}}

* {{annotated link| Rutherford model }}

or models without their own page, including [[Joseph Larmor]]'s Solar System model (1897), [[Jean Perrin]]'s model (1901), [[Hantaro Nagaoka]]'s Saturnian model (1904), [[Arthur Haas]]'s quantum model (1910), and [[John William Nicholson]]'s nuclear quantum model (1912).

The distinguishing feature of the Thomson model was the first use of internal structure. In addition the concept of "obsolete" is not a major point of discussion in the article as an aspect of the model, making "obsolete" a secondary point.

:Right, I will get on that. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 17:49, 27 September 2024 (UTC)

I changed the first sentence to one that matches the subject, but @[[User:Kurzon|Kurzon]] [https://en.wikipedia.org/w/index.php?title=Plum_pudding_model&diff=prev&oldid=1231306309 changed it back]. I disagree and want a sentence that describes this model more clearly. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 17:00, 28 June 2024 (UTC)

==Positive units==

:The point you want to make is just a few sentences further. It's ok. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 17:01, 28 June 2024 (UTC)

{{ping|Johnjbarton"|Tjlafave}} In his 1910 paper, Thomson presented an equation that modeled beta scattering in the scenario where the positive charge exists in discrete units.

::I disagree. If a later sentence is adequate for the most important characteristic of the model (being the first with internal structure), then it certainly is adequate for the least important characteristic (being obsolete). [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 17:53, 28 June 2024 (UTC)

:::I like it because it signals to students "You don't have to know any of this for the exam. You can take a nap instead of reading this if you want.". [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 21:14, 28 June 2024 (UTC)

::::That's not a Wikipedia goal. Plus any student who can't figure this out is probably napping already. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 00:52, 29 June 2024 (UTC)

:::::@[[User:Johnjbarton|Johnjbarton]] and @[[User:Kurzon|Kurzon]]

:::::Thanks for all the remarkable changes to this page. They were very much needed and are solidly geared to the educational and informative purposes of Wikipedia.

:::::I'm surprised it took 7 years (2023) for someone to remove my egregious "self-promotion" (from 2016) citations that I added in the hopes that the subject matter would be taken up with much more seriousness than this page originally had. A student alerted me to this over the weekend when she couldn't find the citations and images she heard about from former students! I wish I had the time over the last several years to do what you've done in the last year or so with this page.

:::::On that note, I'm happy to see the 1904 model cited as the first atomic model with internal components. It was quite a dramatic theological and empirical break from the "atomic" nature of the Greek "atomos".

:::::I guess I wasn't crass enough at the time nor as deeply invested in pushing historical science fact in response to flippant "classroom" views on Wikipedia. I'm seeing a similar trend on reddit which has an almost purely mindless and pedantic academic tone today on physics-related threads rather than genuine knowledge- and skill-building thinking. Got to keep up those exam scores up, I guess, rather than actually learn, invent, or create anything meaningful.

:::::I often wonder if the internet we built will ever fulfill its leveled playing field goal before it's dumbed-down to the point of informational extinction.

:::::Carry on. This is great work! [[User:Tjlafave|TJ LaFave]] ([[User talk:Tjlafave|talk]]) 19:32, 1 October 2024 (UTC)

::::::Well this is the first time in the 20 years I've been on Wikipedia that somebody notices my work.

::::::Why do teachers push such a simplistic narrative about the plum pudding model anyway? When I started going through the original papers by Thomson and Rutherford, I found that the truth deviated considerably from the narrative. The stuff you teach in schools gets the physics right but not the history. And that bugs me because I'm a history guy (Johnjbarton is the actual physicist). [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 19:42, 1 October 2024 (UTC)

:::::::"The stuff you teach in schools gets the physics right but not the history."

:::::::As a physicist, a scientific discovery I made in the closing months of my PhD program (in Electrical Engineering!) has a specific historical link to developments in atomic theory. I believe I can best put a pin in about 1922/23 when Bohr finally had something constructive to say with regard to chemists' static models. (I'm actually trying to hunt down a paper of Bohr's from this time that I recall reading in about 2013 ...I believe it's an unpublished response paper of some 6 or 7 pages mentioned in the Bohr archives. Still no luck finding that paper!) My work picks up, it appears, where the chemists left off. Their work was cast out of the limelight because of the blinding flurry of quantum mechanical developments in the 1920s and 30s. I think my work makes important connections between the static and dynamic models that are difficult to impress upon today's science students as worthwhile. After all, a common misconception that persists is that we know all we need to know -- well, unless it's cosmology or string theory.

:::::::Thus, I'm quite interested in the historical developments as well -- and my first boss as an undergraduate student was a History professor.

:::::::I think the underlying response to your remark above is that "hindsight is 20/20". That's to say that as we look back at the historical science record, we already know the outcome -- the facts, the scientific laws, the failings of others, and such. So, we shed from our lesson plans those things that don't give a direct line of sight to the "solution" of any given science problem. Perhaps we've cut too much philosophy from science education today.

:::::::I vividly recall a theoretical electrical engineering professor I did research with back in Dallas who was excited as a bright-eyed kid in a candy store to come up to me after my seminar on my doctoral research to tell me that he was reminded so much of all the exciting physical chemistry lectures he attended in the 60s and 70s. He said my work was too important to ignore but no one today will care about it because students just want nicely wrapped answers. [[User:Tjlafave|TJ LaFave]] ([[User talk:Tjlafave|talk]]) 20:01, 1 October 2024 (UTC)

::::::::What do your students think of this article and [[Rutherford scattering experiments]]? [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 16:02, 7 October 2024 (UTC)

::::::Also I remember what the Internet was like in the 1990s, Wikipedia f*cking amazing compared to what I had back then. I don't think the Internet is dumbing us down and making us less empathetic, I think it does the opposite. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 19:59, 1 October 2024 (UTC)

:::::::I'm pointing to the internet being dumbed down too much. Social media is king today.

:::::::For those willing to reflect on what's discussed and posted online, it definitely improves our empathy, awareness, and knowledge.

:::::::As for 1990s internet, I'm glad I managed to ween so many people off left-hand justified pages of text on grey Netscape backgrounds. That was an information design technology change that transformed the world.

:::::::We also used to FTP into the U. Hawaii library to search for books and journal articles in our own library. Why spend hours at a card catalog when you can just stay in your dorm room and perform simple queries on the network before even stepping into the library? [[User:Tjlafave|TJ LaFave]] ([[User talk:Tjlafave|talk]]) 20:07, 1 October 2024 (UTC)

::::::We have also improved the [[Rutherford scattering experiments]] article. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 23:38, 1 October 2024 (UTC)

:Alternatives include:

:* The plum pudding model was the first modern scientific model of the atom.

:Per

:* Kragh, Helge. "Before Bohr: Theories of atomic structure 1850-1913." RePoSS: Research Publications on Science Studies 10 (2010). https://css.au.dk/fileadmin/reposs/reposs-010.pdf

:** "The atomic model developed by the famous Cavendish physicist Joseph John Thomson in the early years of the twentieth century can with some justification be called the first modern model of the atom".

:or

:* The plum pudding model was the first scientific model of the internal structure of the atom.

:Per

:* "J. J. Thomson's plum-pudding atomic model: The making of a scientific myth" Giora Hon, Bernard R. Goldstein 06 September 2013 https://doi.org/10.1002/andp.201300732

:** "What distinguishes Thomson's theory is his assignment of a specific inner structure to the atom as well as a set of dynamical assumptions."

:[[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 18:27, 28 June 2024 (UTC)

::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)

<math display="block">\bar{\theta}_2 = \frac{16}{5} \cdot \frac{k q_e q_e}{m v^2} \cdot \frac{1}{R} \cdot \sqrt{\frac{3N}{2}} \sqrt{1 - \left (1 - \frac{\pi}{8} \right ) \sqrt{\sigma}}</math>

== J. Arnold Crowther ==

Heilbron doesn't offer a guess as to how Thomson came up with this equation. Thomson doesn't call these units particles and I assume they're just as permeable as the positive sphere. If the positive charge units were particles then a direct collision would affect an alpha particle much differently. Is it correct of me to say that Thomson came close to deducing the existence of the proton? Rutherford deduced the existence of protons based on charge numbers of atoms. Interactions between particles is not just a question of electric fields because neutrons can split nucleui.

One of the main protagonists in the atomic theory of 1905-1910 is [[James Arnold Crowther]]. Given so many dubiously notable biographies on Wikipedia I was surprised to discover nothing about him here. In addition to his publications on beta scattering, consider published books:

* Crowther, James Arnold. Ions, electrons, and ionizing radiations. Longmans, Green, 1924.

** "Many have owed their first acquainance with modern physics to this excellent intermediate text, which reached its eigth and final edition in 1949, the year before Crowther's death." Heilbron, 1968, footnote on page 296.

* Crowther, James Arnold. A manual of Physics. H. Frowde, 1919.

* Crowther, James Arnold. Molecular Physics. J. & A. Churchill, 1923.

* Crowther, James Arnold. The life and discoveries of Michael Faraday. Society for promoting Christian knowledge, 1920.

His obitutary:

* Whiddington, R. [https://www.nature.com/articles/165750b0.pdf "Prof. JA Crowther."] Nature 165.4202 (1950): 750-751.

[[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 18:02, 6 July 2024 (UTC)

It's strange that Thomson did not propose the existence of the proton in his atomic model. Wasn't there enough information at the time to suggest the existence of protons if not prove them? Physicists at the time speculated on the existence of "positive electrons" that carried the elementary unit of positive charge just as negative electrons carry the elementary negative charge. Hydrogen ions and alpha particles were positively-charged particles. Thomson did not know exactly how many electrons were in an atom so perhaps a hydrogen ion could contain some remaining electrons. I suppose the missing piece of the puzzle was the nucleus, where the positive charge existed separate from the negative charge and therefore could be probed separately. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 20:41, 12 October 2024 (UTC)

:I created a page for [[James Arnold Crowther]]. {{done}} [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 16:06, 12 July 2024 (UTC)

==Kepler?==

== Thomson problem ==

{{ping|Johnjbarton}}

<math>\theta = 2\arctan\frac{k q_1 q_2}{m v^2 b}</math>

Has anyone ever done a computer simulation of a Thomson atom with 100 or so atoms, arranged in shells like Thomson imagined? The Thomson problem solutions I found online constrain the electrons to the surface of the sphere. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 16:45, 11 July 2024 (UTC)

Did Kepler come up with this equation? In the Rutherford scattering article, you mentioned Kepler in the part where we explain how Rutherford calculated the scattering angle.[[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 20:41, 16 March 2025 (UTC)

:Thomson's 1906 paper discusses analytic stability of his shells in detail. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 16:59, 11 July 2024 (UTC)

::I am looking for a diagram. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 08:44, 12 July 2024 (UTC)

==Dalton's was the first==

{{ping|Johnjbarton}} I don't want to be pedantic, but Dalton's model of the atom was the first. It had atomic weights, which is not much but ''something''. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 21:44, 13 July 2024 (UTC)

:I have previously discussed this issue under [[Talk:Plum_pudding_model#Lead_sentence_is_inappropriate |Lead_sentence_is_inappropriate.]] [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 03:48, 14 July 2024 (UTC)

::You're good at physics, not so much prose. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 13:49, 22 July 2024 (UTC)

:::How about this as the first sentence:

:::* The plum pudding model was the first scientific model of the atom with internal structure.

:::This simple declarative sentence notes the historical significance of the topic. Dalton's model did not have internal structure. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 18:01, 22 July 2024 (UTC)

==How is this image incorrectly labelled?==

[[File:Alpha particle electron collision.svg|400px]]

Explain. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 18:50, 25 July 2024 (UTC)

:The image that was added to the page did not have the electron labeled. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 20:42, 25 July 2024 (UTC)

::Well once again there is no edit summary but this time the image is complete. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 21:05, 25 July 2024 (UTC)

== Why the Thomson model was(n't) wrong ==

We now have a section entitled "Why the Thomson model was wrong". This kind title gives an inaccurate sense of how scientific models work. I think you will almost never see "wrong" in print for a science model. Every single scientific model is "wrong" in some way: what's the point? Model are "useful" or "not useful" according to successful predictions in specific circumstances. Until the Geiger-Marsden experiment and Rutherford's explanation, Thomson model was useful. Then new circumstances: it could not predict the large angle scattering.

I think Thomson's scattering model should be presented straight-up, then contrasted with the new results of Rutherford. As it is I don't understand what part of the section is representing Thomson scattering and what part is tearing it down. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 23:52, 11 August 2024 (UTC)

:I think you're splitting hairs here. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 07:51, 12 August 2024 (UTC)

::No, it's an aspect of the philosophy of science. You might like to read about how "[[All models are wrong |all models are wrong]]":

::* [[George Box|Box, George EP]]. "Science and statistics." Journal of the American Statistical Association 71.356 (1976): 791-799. https://www.tandfonline.com/doi/pdf/10.1080/01621459.1976.10480949?casa_token=lTCK50__6ckAAAAA:2VcLVFFpsex1vPJy6_Cd94z96xKpRUAGrVbIG8rtqhy3cEK1sr4t9S7TNgG-fVszjiv9MXSD5GBYDQ

::[[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 15:43, 13 August 2024 (UTC)

:::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. &#32;<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)

== Scattering section incorrect. ==

* Rutherford did not use Thomson's scattering model.

* The formulas partly consider multiple scattering when the claim is single.

* Thomson did not consider Geiger/Marsden results, obviously.

* Thomson never considered large angle scattering in his model.

* the section is based on Thomson's 1910 paper, long after he determined the more correct number of electrons

[[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 01:18, 17 August 2024 (UTC)

:I think this section is attempting to do too much. It mixes Thomson/Rutherford theory/experiment and jumbles up the timeline. A better presentation would just focus on Thomson's scattering model as promised and mention Crowther's experimental confirmation. Then, in the next subsection, we can summarize Rutherford scattering experiment and the consequences, already well covered in that article. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 03:16, 17 August 2024 (UTC)

:[https://en.wikipedia.org/w/index.php?title=Plum_pudding_model&oldid=1240710478#How_scattering_should_work_according_to_the_Thomson_model This revision] of the article corrects all of the above issues. However @[[User:Kurzon|Kurzon]] reverted it with the edit summary "this is better". [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 15:15, 19 August 2024 (UTC)

::Yeah maybe yours is better. I've decided to adapt Heilbron's explanation of how Thomson produced the equation for positive sphere scattering, tell me what you think. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 15:56, 19 August 2024 (UTC)

== Adding Crowther's experimental results. ==

The section on the 1910 paper would be better if Crowther's results were summarized. That would help clarify that Thomson's model seemed to work until the Geiger-Marsden experiment results became known. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 00:00, 25 August 2024 (UTC)

:I added one paragraph about one set of Crowther experiments. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 00:33, 25 August 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 ==

{{ping|Johnjbarton}} Now that Headbomb has agreed that the maths stuff for the Thomson model should be in the '''Rutherford scattering experiments''', I think we should rework the stuff in this article to beta particle scattering. That should do better historical justice to Thomson's work, which is something you want. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 20:39, 26 September 2024 (UTC)

{{ping|Johnjbarton}} On that note, could you direct me to some papers by Thomson which contain his beta scattering studies? You mentioned several times that the plum pudding model lined up with Thomson's data on beta scattering, I want to look at that. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 10:43, 27 September 2024 (UTC)

== Image is upside down ==

In the section "Deflection by the positive sphere", the image Thomson_model_alpha_particle_scattering_3.svg show a deflection away from the center correct for + on + scattering. However the Thomson's model was for beta particles, - on + and thus the deflection should be towards the center. This difference does not alter the model's predictions because every path on one side of the atom has a matching one on the other and they are added to compare to experiment. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 17:38, 27 September 2024 (UTC)

:Right, I will get on that. [[User:Kurzon|Kurzon]] ([[User talk:Kurzon|talk]]) 17:49, 27 September 2024 (UTC)