Talk:Rutherford scattering experiments

Historical measurements of the variables

This section of the article is not properly referenced. It makes claims about a potential source of Rutherford data, Jean Perrin, with no attribution. This is original research. The rest of the paragraph is similarly improper. History needs references to historians.

@Kurzon Johnjbarton (talk) 23:03, 31 May 2024 (UTC)

Non-scientific use of significant figures.

The section on the impulse model uses an inappropriate number of significant figures creating the impression that 1) the model is somehow amazing accurate and 2) that the mass of the atom is significant. Neither of these are true. Rutherford's own paper only uses 2 figures.

The current text directly contradicts physics: it attempts to show that the mass effect of gold is significant, but it was not historically and the impulse model assumes infinite mass for the target.

To account for finite mass, the reduced mass can be used (with a reference) and if Aluminum is used for the example a significant effect will be shown, as was noted by Rutherford on page 385. Johnjbarton (talk) 14:28, 1 June 2024 (UTC)

I am not even sure what calculations Rutherford used. I think it's enough that it be consistent with the history, not a perfect reflection. Kurzon (talk) 14:50, 1 June 2024 (UTC)

Rutherford's calculation are in his paper, and in particular he considers the effect of finite mass on page 384 in the section "Alteration of velocity in an atomic encounter". The content is not consistent with history, that is exactly my point. Johnjbarton (talk) 15:02, 1 June 2024 (UTC)

My changes to the article to correct this error have been reverted by @Kurzon. I want to know why.

A scientific model typically start with conceptual ideas that approximate a physical scenario. The ideas generate a mathematical model which leads to calculations. The results of the calculation, being numerical can be exact as far as mathematicians are concerned. But this article is about physics and the model is an approximation to an immensely complex physic system. It is inappropriate and incorrect to write three significant figures for a result that is this crude. The model prediction is about 0.02 degrees, not 0.0186 degrees. Johnjbarton (talk) 18:09, 18 June 2024 (UTC)

@Kurzon Once again I had to fix the article for this error. Please stop. Johnjbarton (talk) 22:17, 5 August 2024 (UTC)

@Johnjbarton: I looked through some history books and it seems that while Perrin and Rutherford knew each other they didn't collaborate much. Still, I'd like to know how Rutherford knew that atomic radii were on the order of 10^-10. It's a pity that you had to delete that information because I think it's interesting for readers to know where scientists got these measurements and how, though perhaps you are correct that they belong in another article, perhaps History of atomic theory. Kurzon (talk) 12:25, 2 June 2024 (UTC)

@Kurzon Just want to point out that this reply belongs on the topic "Historical measurements of the variables".

You have reverted may change to the significant figures without discussion. I continue to disagree with the content. Johnjbarton (talk) 14:01, 2 June 2024 (UTC)

Considering I'm working with an incomplete picture of what happened, I think it's OK for me to fill in a few gaps in the mathematics with educated guesses, so long as I get the maths and the physics right. Kurzon (talk) 16:19, 2 June 2024 (UTC)

I disagree, it is not OK. Your "fill in" is incorrect. Using an approximate model, adjusting it for an insignificant factor, and then using lots of significant figures to make it look significant is not correct.

And it so unnecessary! The recoil effect was discussed by Rutherford using Aluminum. Just put my text back and change your formula to use Al mass in the second case.

If your picture is incomplete, then omit it. Don't add stuff that is wrong. Johnjbarton (talk) 00:26, 3 June 2024 (UTC)

Ok Kurzon (talk) 00:28, 3 June 2024 (UTC)

Are the electrons in the plum pudding model held in place?

Thomson compared the electrons in the positive sphere to magnetized pins floating in water, with an electromagnet pulling them towards the center. They could move about, the positive electrification wasn't solid. So that makes me think that if an alpha particle grazes the edge of the plum pudding atom, it's just like another electromagnet grazing the edge of the basin. The pins should move slightly towards the electromagnet, shouldn't they? Kurzon (talk) 21:19, 2 June 2024 (UTC)

Sure, why not. But why does such a hypothetical motion of a hypothetical system matter? The alpha particle is traversing hundreds of atoms, most of the time with no effect. Occasionally there is an interaction. In the Thomson model the interaction was alpha-electron; Rutherford showed it had to be alpha-nucleus. But these are close range interactions. No medium or long range interaction is significant.

And for the purpose of the article we would need a reference for such a motion, which I don't expect to see. Johnjbarton (talk) 01:51, 3 June 2024 (UTC)

Well if the electrons are like pins in water, then the simplistic model I used, wherein I ignore the electrons because they are so light, should be OK.

By contrast, look at what I recently put in the article concerning a direct collision in a Rutherford atom. I treat the electron cloud as a large sphere of negative charge that has infinite mass. As if that sphere negative charge is welded to the nucleus. It feels inconsistent but I was trying to arrive at that equation Rutherford put in his 1911 paper. I feel like I am making progress yet also messy. Kurzon (talk) 23:31, 3 June 2024 (UTC)

• "I was trying to arrive at that equation Rutherford put in his 1911 paper."

? Which equation? Johnjbarton (talk) 03:09, 4 June 2024 (UTC)

I remember reading somewhere that around the start of the 19th century, physicists were still uncertain how electric charges worked. Thomson didn't like the positive sphere in his model of the atom and wanted to attribute the neutrality of the atom to a property of the electrons. Kurzon (talk) 01:15, 4 June 2024 (UTC)

Perhaps you mean "start of the 20th century".

I remain mystified at your focus on Thomson in an article about Rutherford scattering. Johnjbarton (talk) 03:11, 4 June 2024 (UTC)

This article has always been about both. There is a separate article dedicated to Rutherford scattering itself. Kurzon (talk) 10:23, 4 June 2024 (UTC)

Conservation laws

A couple of times I delete an editorial comment like the phrase following "and" here:

• ...treat it as having infinite mass and ignore the law of conservation of momentum.

Rutherford's scattering model explicitly uses conservation of momentum. When he models scattering from Au, he has one particle, the alpha particle. The Au has "infinite mass" is just another way of saying it is not part of the dynamics. Rutherford equates the angular momentum of the one particle at two points in the trajectory; similarly energy. (The only other fact he uses is the hyperbolic trajectory due to the Coulomb force.) Conservation of momentum is just an accounting fact, like "your savings account balance equals deposits minus withdrawals".

When Rutherford treats recoil for the Al atom, he adjusts his model: two particles exchange energy. But again it's just accounting: the total momentum of the two particles and total energy of two particles.

His first model does explicitly ignore the transfer of energy and momentum between the alpha particle and nucleus, but that is different from ignoring the "law". Defining the system boundaries in a model -- one vs two particles -- is often the most important step in physics. (Quantum mechanics amounts to the discovery that the classical boundaries don't apply in subatomic systems). Johnjbarton (talk) 03:13, 3 June 2024 (UTC)

Thanks, I will take another look at that. Kurzon (talk) 11:18, 3 June 2024 (UTC)

Direct collision

The content in Rutherford_scattering_experiments#Direct_collision is historically incorrect, is more complicated than it needs to be, and is not referenced. Rutherford's paper gives a much simpler derivation based on potential energy and using his approach can be reference to his 1911 paper. The connection between work integration and potential energy is outlined in Work_(physics)#Path_independence. A description of Rutherford's approach is in Rutherford_scattering#Maximum_nuclear_size_estimate. Johnjbarton (talk) 02:55, 6 June 2024 (UTC)

Are you referring to this equation?

${\frac {1}{2}}mu^{2}=NeE\left({\frac {1}{b}}-{\frac {3}{2R}}+{\frac {b^{2}}{2R^{3}}}\right)$ Kurzon (talk) 15:50, 6 June 2024 (UTC)

Yes, but the last two terms have no consequence because b << R, so 1/b >> 1/R. Johnjbarton (talk) 17:13, 6 June 2024 (UTC)

Perrin

@Johnjbarton: I put back in a mention of Perrin's measurement of hydrogen's mass even though Rutherford does not reference it, for the sake of reader curiosity, and because I use modern measurements anyway in all the mathematical demonstrations. I do not insist on it, however. I would appreciate it if you could explain to me how Rutherford accounted for the alpha particle's momentum if he did not use its weight in kg. As a historian, I appreciate your desire to tell the story from Rutherford's perspective as faithfully as possible. If I can better understand his perspective, I will do the same. Kurzon (talk) 16:18, 6 June 2024 (UTC)

Please re-read my comments in 'Historical measurements of the variables' topic above. Rutherford did not cite Perrin, but that is only part of the issue. We have very detailed historical analysis of Rutherford's and they don't mention Perrin. They do mention many other aspects: to include Perrin and not these others is WP:UNDUE. Failing to find a source for some kind of information does not mean we should make it up.

I'm unsure what part of which paper of Rutherford you are concerned about for alpha particle momentum. Rutherford worked on alpha particle properties from the time Rutherford named them "alpha particles" (around 1895), including:

• Rutherford, E. (1906). XLI. The mass and velocity of the α particles expelled from radium and actinium. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 12(70), 348–371. https://doi.org/10.1080/14786440609463549

His 1911 paper does not need momentum. Johnjbarton (talk) 17:11, 6 June 2024 (UTC)

As a historian, I like to remind readers of the fuzziness of history in the name of fairness. Unlike the laws of physics, it's often hard to prove what event in history caused this other event. I'd like to write that Millikan and Perrin came up with these measurements in 1909 and while it's possible Rutherford took note of them, it's unlikely because of the timing. Kurzon (talk) 07:53, 9 June 2024 (UTC)

I encourage you use your role as a historian to write articles or books about fairness, fuzziness, Millikan, or Perrin. However, the rules and criteria on Wikipedia are not the same as historical or scientific publications. As an editor on Wikipedia the policy is clear that we rely on existing reliable publications. In such publications that exist, which in the case of Rutherford are exceptionally detailed, Perrin's role is never even mentioned in passing.

Even more important for this article on historical experiments, Rutherford had no need for the mass of hydrogen atom in kilograms. Such a number plays no role in his theory or its comparison to experimental measurements. Rutherford would not need to take note of Perrin's result because he did not need the information. The relationship between hydrogen and alpha particles or between hydrogen and gold was not known in 1911. Rutherford's own work established the mass of alpha particles and the ratio to gold was known. Johnjbarton (talk) 15:13, 9 June 2024 (UTC)

Rutherford's first scattering experiment

@Kurzon moved the section on the first scattering experiment from a full section to 'background' with an edit comment:

• Moving this to Background as this was not a deliberate attempt to measure alpha particle scattering

According to the references, the edit comment is incorrect. The 1906 experiment was the first clear evidence that alpha particles scattered. All of the subsequent experiments discussed in the article followed the pattern set by this one: a radioactive source in an evacuated tube with a target and then a detector at the other end. Rutherford was exactly setting out to measure alpha particle scattering, what else could the experiment be about? Johnjbarton (talk) 18:14, 6 June 2024 (UTC)

Ok Kurzon (talk) 18:36, 6 June 2024 (UTC)

Your writeup

@Johnjbarton: I saw your write up on Rutherford scattering. A line says "Rutherford used the geometry of hyperbolas to arrive at this equation". Well Rutherford didn't write his working because he wasn't teaching a maths class. I want that maths class. I didn't copy Rutherford's equations faithfully because I couldn't understand them like I understood the Hyperphysics site. Kurzon (talk) 22:46, 7 June 2024 (UTC)

Earlier the page said:

• Rutherford observed that the alpha particle will take a hyperbolic trajectory in the repulsive force near the center of the atom as shown in Fig. 1.

If it is not clear then I propose we work on hyperbolic trajectory. Maybe a reminder later will help?

Understanding always depends upon the the background of the reader. We have to make choices. I honestly do not think most readers will follow integration of work for example. Johnjbarton (talk) 02:15, 8 June 2024 (UTC)

I added some text, does that help? Johnjbarton (talk) 02:29, 8 June 2024 (UTC)

For the sake of other readers, this comment regards Rutherford_scattering#Single_scattering_from_heavy_nuclei and should be on that Talk page. Johnjbarton (talk) 02:16, 8 June 2024 (UTC)

Headbomb

@Headbomb: I am looking for a second opinion on this. In the section A simplistic mathematical look at the Thomson model, I removed the electrons from the plum pudding model to look at just the effect of the sphere on the alpha particle. This is how the site Hyperphysics did it, it was my reference. Thomson likened the positive part of the plum pudding model to a liquid, the electrons could move around in it. Since the electrons have so little mass, their influence on the alpha particle should be negligible. Johnjbarton doesn't like it because it doesn't come out of Rutherford's paper, but in this specific section I am not concerned with Rutherford yet. The Rutherford stuff comes in the following section.

For what it's worth I did study Rutherford's paper but it's really hard for me to make sense of it, whereas the Hyperphysics site lays it all out better. Kurzon (talk) 19:16, 15 June 2024 (UTC)

I'm not sure exactly what the question is. Rutherford's model evolved over time, the plum pudding model being a later term that applies better to both the early (unspecified/uniform electron distribution, 1899)/late versions (more or less free electrons within a sphere, that would self-organize 1907) than the middle steps, like versions involving a ring of electrons inside a uniformly charged sphere (1904), or some other specific arrangement of electrons (1905).

Hyperphysics, which is a bog-standard mainstream site and fantastic source, gives the math of the early version of the model, I believe. The exact distribution of electrons doesn't really matter, because Thomson model (in any variety) just can't deflect alphas by more than a few degree. It's rather irrelevant that the prediction for Thomson scattering doesn't come from a Thomson/Rutherford paper. [1] also has a great explanation. Headbomb {t · c · p · b} 19:37, 15 June 2024 (UTC)

Yeah OK so what I wrote isn't wrong. Certainly not when it comes to the physics. The historicity is shaky but then again that specific section doesn't have to be perfect to history so long as it doesn't conflict. Kurzon (talk) 19:50, 15 June 2024 (UTC)

@Headbomb I have many complaints about the presentation of scattering in this article that I have raised numerous times. Most of the content is maybe correct but unnecessarily complex original research that cannot be verified by any means other than repeating the derivation one's self. But let's start with "A simplistic mathematical look at the Thomson model".

The reference here is the typically excellent hyperphysics site. It presents a small-angle impulse force approximation, rather than the classic Rutherford solution found in most textbooks. A suitable section could be based on that presentation, but the presentation in this article is not correct.

First note that this article is called "Rutherford scattering experiments". I think readers deserve a historically correct description of such experiments and their theory. The Thomson model was based on electrons: he discovered the electron! All of Thomson's analysis was based on multiple scattering from electrons. There is no historical evidence presented here or in any reference I have seen to support a model of scattering from the positive jelly as even remotely relevant. The closest presentation is Rutherford_scattering#Maximum_nuclear_size_estimate Rutherford's own discussion where he quickly concludes the core is much smaller than the atom.

Is there a modern way to analyze Thomson's model using the impulse approximation? Yes, you could apply the impulse model to the electrons or you would apply the impulse model to Rutherford's nucleus and show that it's radius has to be small. But it makes no physical sense to apply the impulse model to a neutral atom. Claiming this is ok because we want to ignore the electrons is physically and historically unjustified. Moreover, showing that an atomic sized positive sphere only gives small angle scattering is a negative result: the physical cause of large angle scattering not revealed by that exercise. The only real value of the presentation is that @Kurzon likes it.

We can ignore my rant and simply focus on references. On one side we have a page from a web site, on the other we have three widely used textbooks in classical mechanics (I'm sure I can find more), several treatments by science historians, and Rutherford's own words.

Rutherford's scattering theory paper is a classic, it is not hard to follow, and it uses principles studied in physics undergrad courses just the way Rutherford presented it. That is how we should present it. Johnjbarton (talk) 01:50, 16 June 2024 (UTC)

Is there a modern way to analyze Thomson's model using the impulse approximation? Yes, you could apply the impulse model to the electrons or you would apply the impulse model to Rutherford's nucleus and show that it's radius has to be small. But it makes no physical sense to apply the impulse model to a neutral atom. Claiming this is ok because we want to ignore the electrons is physically and historically unjustified. Moreover, showing that an atomic sized positive sphere only gives small angle scattering is a negative result: the physical cause of large angle scattering not revealed by that exercise. The only real value of the presentation is that @Kurzon likes it.

It makes sense when you want to show the limit of of what Thomson scattering can account for and contextualize the discovery. At best, the Thomson atom can deflect alphas by a few degrees. There is nothing controversial about this. The failure of the Thomson model doesn't need to explain why charge is localized, because the only thing this is doing is ruling out Thomson, which was the prevailing model of the atom at the time. This is based on references, you can find the same treatment Hyperphysics does in dozens of textbooks, and this explains why it was Rutherford was as surprised at alphas scattering be as if you shot 15 inch shells at tissue paper, and they came back at you. Headbomb {t · c · p · b} 03:56, 16 June 2024 (UTC)

When I read Thomson's paper's on the plum pudding model, he uses the analogy of magnetized pins floating in a pool of water. The pins repel each other but they're also pulled to the center by an electromagnet suspended above the center of the pool. So I figure that a passing alpha particle would be like a second electromagnet passing over the pool. The pins wouldn't stay in place like Johnjbarton seems to be saying, they would be pulled towards the second electromagnet while the first electromagnet would repel it, and the main electromagnet would have a stronger effect because it is heavier. Kurzon (talk) 12:19, 16 June 2024 (UTC)

Let's suppose the electrons do move towards the alpha particle. Now you have a neutral alpha particle scattering from a +2 charge. That's not the model you presented. Johnjbarton (talk) 14:46, 16 June 2024 (UTC)

@Headbomb says:

• "This is based on references, you can find the same treatment Hyperphysics does in dozens of textbooks, and this explains why it was Rutherford was as surprised at alphas scattering be as if you shot 15 inch shells at tissue paper, and they came back at you."

Your claim that "this explains why it was Rutherford was surprised" is not correct. Yes you can find the impulse model in at least one textbook, but it was not used by Rutherford at any time for any reason. We know this because historians like John L. Heilbron:

• Heilbron, John L. (1968). "The Scattering of α and β Particles and Rutherford's Atom". Archive for History of Exact Sciences. 4 (4): 247–307. doi:10.1007/BF00411591. ISSN 0003-9519. JSTOR 41133273.

and Trenn:

• Trenn, Thaddeus J., et al. "The geiger-marsden scattering results and rutherford's atom, july 1912 to july 1913: the shifting significance of scientific evidence." Isis 65.1 (1974): 74-82.

Hielbron analyzes Rutherford's work in great detail, investigating his notebooks and correspondence. Rutherford's paper was a paradigm of scientific reasoning. It's a shame for us to present a mythological and physically implausible alternative. We should present Rutherford scattering not Beiser (or whomever invented it) scattering. Johnjbarton (talk) 15:06, 16 June 2024 (UTC)

Why then, did Rutherford only expect, at most, a few degrees of deflection, just like the Thomson model, which was the prevailing model of the time, predicted? The answer is because that's what the Thomson model predicted. This is not an implausible alternative, this is what happened. Headbomb {t · c · p · b} 15:10, 16 June 2024 (UTC)

Yes, the Thomson model was the prevailing model and yes it predicted only a few degrees of scattering. Thomson and Crowther's model of scattering is analyzed in great detail by Heilbron, please see page 277. They did not assume scattering from a positive sphere. (No one did). Their model was based on multiple scattering from electrons. That is another reason the current article representation is so annoying: it removes exact those elements Thomson used in his scattering model!

Rutherford analyzes the Thomson/Crowther model at the end of his paper. There he says:

• It is thus clear that the main relations on the theory of compound scattering of Sir J. J. Thomson, which were verified experimentally by Crowther, hold equally well on the theory of single scattering.

The man's own words on Thomson's model. Heilbron also discusses this section in detail. At no point is impulse scattering from a positive sphere discussed.

The existing model did not predict backscattering but the existing model was not an atomic sized positive sphere as implied by the article. Johnjbarton (talk) 15:38, 16 June 2024 (UTC)

Sections of original research

1. The section Direct collision cites no sources, is overly complex, and not how such physics should be presented. Rutherford's 1911 paper uses conservation of energy, see Rutherford_scattering#Maximum_nuclear_size_estimate.
2. The section Maximum deflection cites no sources and is overly complex. Rutherford's 1911 paper uses conservation of angular momentum and energy together with simple orbits, see Rutherford_scattering#Single_scattering_from_heavy_nuclei.
3. The section Stopping distance on direct collision presents Rutherford's argument then an overly complex one based on original research with no references.
4. The section Historical measurements of the variables mentions Jean Perrin's work without a reference. There is no historical evidence that Rutherford used Perrin's value.

Johnjbarton (talk) 15:22, 16 June 2024 (UTC)

"There is no historical evidence that Rutherford used Perrin's value."

This is called context. That Rutherford didn't use this value is compltely irrelevant. Headbomb {t · c · p · b} 15:38, 16 June 2024 (UTC)

This is context:

• Rutherford, E. (1906). XLI. The mass and velocity of the α particles expelled from radium and actinium. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 12(70), 348–371. https://doi.org/10.1080/14786440609463549

Johnjbarton (talk) 15:41, 16 June 2024 (UTC)

That is not context, that is a reference. And Rutherford does not exist in a vacuum. Also nothing in this section is original research. It could use refs though, but it's bog standard physics encountered in any undergrad program. Headbomb {t · c · p · b} 15:48, 16 June 2024 (UTC)

Johnjbarton put up his preferred version on the Rutherford scattering article. Perhaps you could take a look at it. I can't fully understand it because it doesn't lay out all the steps like the Hyperphysics site does. Notably, it assumes the reader is well versed with the geometry of hyperbolas. If someone could expand it more, I may end up copying it to this article. Kurzon (talk) 22:46, 16 June 2024 (UTC)

Please make your comments on the Rutherford scattering article in Talk:Rutherford scattering not here. Johnjbarton (talk) 23:04, 16 June 2024 (UTC)

Beiser

@Johnjbarton and Headbomb: You might be interested in checking out this book, particularly pages 103-116: https://archive.org/details/perspectivesofmo0000arth/page/102/mode/2up Kurzon (talk) 16:52, 18 June 2024 (UTC)

Yes, this is the ref that Hyperphysics uses. I wrote to the email on the hyperphysics site to see if I could learn more about why that choice, but I think the author is no longer active. I guess this is an example of the refs that @Headbomb discussed but it is the only example I have seen. Johnjbarton (talk) 17:01, 18 June 2024 (UTC)

That book was published in 1969, he dead. Kurzon (talk) 17:12, 18 June 2024 (UTC)

As of 2024 Dr. Ron Nave remains active on the internet even though he retired from teaching at Georgia State. Johnjbarton (talk) 17:27, 18 June 2024 (UTC)

I think the Beiser treatment broadly corroborates my claims against the current treatment in this article.

• Beiser considers both electron and positive scattering for Thomson model, then discusses multiple scattering (pg 106)
• Beiser does not exaggerate the number of significant figures in his estimates. (pg 107, 109)
• Beiser cites the low probability of high angle scattering as evidence against Thomson, not the low scattering angle for one impact parameter. (pg 109)

Johnjbarton (talk) 17:55, 18 June 2024 (UTC)

I look through Beiser's book and don't see anything the contradicts my understanding. Perhaps we're misunderstanding each other. Kurzon (talk) 21:09, 18 June 2024 (UTC)

• Page 106 "We shall first discuss the influence of the atomic electrons on the alpha particle motion."
  • Current article: " in this calculation we shall isolate the effect of the positive sphere by removing the electrons from the model"
• Page 109: "Even though the deflection of an incident alpha particle by either an atomic electron or a positive charge cloud the size of an atom is minute, might not the succession of such deflections produce an appreciable total scattering angle?"
  • Current article: silent on multiple scattering, despite this being Thomsom's main claim.
• Page 109: "This is the really crucial result of the experiment...the likelihood on the basis of the Thomson model that an alpha particle be scattering through 90 degrees is therefore...10^-3500.
  • Current article: silent on subject.
• Page 109: The positive scattering effect using impulse model is < 0.02 degrees.
  • Current article: 0.0186 degrees.

Johnjbarton (talk) 22:10, 18 June 2024 (UTC)

It looks to me that the part where Beiser models the effect of electrons it is in terms of physical collisions whereas with the positive sphere it's Coulomb force. Aren't these different things? If the alpha particle just grazes the edge of the positive sphere without actually making contact, then it won't hit any electrons either. Kurzon (talk) 23:28, 18 June 2024 (UTC)

Every model here is Coulomb force. There is no "positive sphere", just a region of positive potential. Nothing is "touching" in any of these models. In fact the very meaning of "touching" in everyday life is just electron-electron repulsion. Johnjbarton (talk) 01:40, 19 June 2024 (UTC)

Ok I've got one of your requested modifications done. Kurzon (talk) 21:53, 19 June 2024 (UTC)

which delta?

@Headbomb and Johnjbarton: I wrote this:

$${\bar {F}}\cdot \mathrm {d} x=\int _{r}^{\infty }{\frac {kq_{a}q_{g}}{x^{2}}}\cdot \mathrm {d} x$$

Would it be better if I wrote:

$${\bar {F}}\cdot \Delta x=\int _{r}^{\infty }{\frac {kq_{a}q_{g}}{x^{2}}}\cdot \mathrm {d} x$$ Kurzon (talk) 14:28, 20 June 2024 (UTC)

No need to ask us, just look it up in your source. Johnjbarton (talk) 15:07, 20 June 2024 (UTC)

Come on, give me your opinion. The source is a bit unclear. Kurzon (talk) 08:38, 21 June 2024 (UTC)

I think you should read the first sentence of Electric_potential and the section Electric_potential_due_to_a_point_charge. As I have discussed before, calculation of the work done by forces is not how such problems are approached. So both equations are irrelevant. Johnjbarton (talk) 17:41, 20 June 2024 (UTC)

Why was this removed?

This legitimate, referenced content was removed by @Kurzon. Why?

• The experiments did not go smoothly. The angular spread of the particle on the screen varied greatly with the shape of the apparatus and its internal pressure. Rutherford suggested that Marsden should look for diffusely reflected or back-scattered alpha particles, even though these were not expected. Marsden's first crude reflector got results, so Geiger helped him create a more sophisticated apparatus. They were able to demonstrate that 1 in 8000 alpha particle collisions were diffuse reflections. Although this fraction was small, it was much larger than what the Thomson model of the atom could explain. This critical experiment was published in 1909.

References

Johnjbarton (talk) 14:40, 25 June 2024 (UTC)

Another unexplained removal

The following reference sentence was removed by @Kurzon without explanation. Why?

• Rutherford worked for almost 2 years before publishing his landmark 1911 paper with a new model for the atom.

References

Johnjbarton (talk) 14:42, 25 June 2024 (UTC)

Because this information is already in The experiments section. I would like the Summary section to be concise. Kurzon (talk) 14:44, 25 June 2024 (UTC)

I see nothing like that in the current article. Johnjbarton (talk) 15:07, 25 June 2024 (UTC)

Maximum deflection in collision with an electron

@Johnjbarton and Headbomb: What do you think of this stuff?

In his treatment of beta particle scattering, Thomson provided the following equation for how a beta particle might be scattered by a single atomic electron:

$\tan {\frac {\theta }{2}}={\frac {kq_{\beta }q_{\beta }}{bm_{\beta }v^{2}}}$

where m_β and q_β are the mass and charge of an electron or beta particle. We will replace m_β and q_β with m_a and q_a and, in not assuming the atomic electron has infinite mass due to atomic binding, we account for conservation of momentum:

$\theta =2\arctan \left({\frac {kq_{a}q_{e}}{bm_{a}v^{2}}}\cdot {\frac {m_{e}}{m_{a}+m_{e}}}\right)$

Kurzon (talk) 18:58, 1 July 2024 (UTC)

In his 1911 paper Rutherford writes:

$$\cot {\frac {\phi }{2}}={\frac {2p}{b}}.$$

Inverting this formula and replacing Rutherford's variable for the impact parameter ($p$) with yours, $b$, while substituting for Rutherford's b:

$$b=-{\frac {NeE}{{\tfrac {1}{2}}m_{\alpha }v_{0}^{2}}}.$$

gives

$$\tan {\frac {\phi }{2}}={\frac {NeE}{bm_{\alpha }v^{2}}}.$$

This looks like your first formula, but there may be a factor of 2 for the reduced mass in electron-beta collisions:

$$\mu ={\frac {m_{\beta }m_{e}}{m_{\beta }+m_{e}}}=2m_{e}$$

For collisions between alpha and electron, $m_{\alpha }$ is replaced by:

$$\mu ={\frac {m_{\alpha }m_{e}}{m_{\alpha }+m_{e}}}\approx m_{e}$$

so your second equation seems incorrect to me. Johnjbarton (talk) 19:28, 1 July 2024 (UTC)

@Johnjbarton: So it really should be

$\theta =2\arctan \left({\frac {kq_{a}q_{e}}{bm'v^{2}}}\right)$

where $m'={\frac {m_{a}m_{e}}{m_{a}+m_{e}}}$

That's what I think it says in Heilbron's paper on page 270, but I get weird results when I punch that formula and values into Desmos. I get a scattering angle of 179° (when b = 7×10⁻¹⁵ m).

Kurzon (talk) 19:45, 1 July 2024 (UTC)

Rutherford writes his equation as a ratio of impact parameter (his $p$) to the minimum approach distance (his $b$):

$$\cot {\frac {\phi }{2}}={\frac {2p}{b}}.$$

That choice was not an accident. The ratio amounts to measuring the impact parameter in units of the minimum approach distance, so much easier to think about.

For electron + alpha, from the formula

$$r_{\text{min}}={\frac {1}{4\pi \epsilon _{0}}}\cdot {\frac {2q_{1}q_{2}}{mv^{2}}}$$

the minimum approach will be 7200 times larger for the ratio of alpha and electron mass but 79 times smaller for the charge ratio.

His minimum approach was 3.4 x 10^-14, so the new minimum is about 300 x 10^-14. If your impact parameter is 0.7 x 10^-14, the ratio is very small, and thus you get 179 degrees (see the Rutherford's table). You basically hit the bullseye and got direct backscatter.

The kinetic energy of an electron at the same velocity as an alpha particle is 7200 times less, and the potential energy due to charge difference is only 79 times less. So the electron can't get as close to the alpha particle as the alpha particle can get to the nucleus. Another way to say this is that the cross section for the electron is large. The difference in mass means that the electron recoil is huge, the alpha particle basically plows through and the electron gets blasted off. Johnjbarton (talk) 21:51, 1 July 2024 (UTC)

That kinda sounds like what I put in the article that you criticized. The electrons are so light compared to the alpha particle that they get blasted out of the way and therefore have negligible impact.

OK, so what should I go with? Kurzon (talk) 00:34, 2 July 2024 (UTC)

I suggest putting the Thomson scattering discussion in the plum pudding model article.

Use Thomson/Heilbron for beta-electron scattering. Use Beiser/hyperphysics for alpha scattering from positive sphere since Thomson evidently is silent on this subject. That directly eliminates many of my complaints on this article. Johnjbarton (talk) 01:55, 2 July 2024 (UTC)

But what about alpha scattering by the atomic electrons? Kurzon (talk) 02:09, 2 July 2024 (UTC)

Rutherford explicitly ignores this effect on the alpha particle scattering, citing Thomson's work that any single encounter results in small angle scattering. Thomson's results were for beta particles with even less momentum than alpha particles. Rutherford's assumption is ultimately justified by his success in explaining the small but not insignificant large angle scattering. This is the key to Rutherford's paper -- large angle scattering is not insignificant as assumed by Thomson -- and that is why the Geiger-Mardsen experiment is so much the focus of modern explanations.

That is core to my complaint with the use of the Thomson model in an article on Rutherford scattering. The fact that the Thomson model gives only small angle scattering is only in support of ignoring the electrons: a big deal is made of that part of the model that Rutherford completely ignores.

I did add a section to Rutherford scattering based on your question here. Johnjbarton (talk) 15:37, 2 July 2024 (UTC)

So for this article I should say "Here is a scattering of a beta particle by a single encounter with an electron. It is trivially small. Since alpha particles have thousands times more momentum, alpha particle scattering by electron collisions will be even smaller, and there is no need to go into the math for that". Kurzon (talk) 16:50, 2 July 2024 (UTC)

I suppose I should go with the conservation of momentum approach in the Beiser textbook. Kurzon (talk) 00:53, 2 July 2024 (UTC)

"integral above has three unknown variables"

In the integral above the subject phrase, dt is not an unknown. using capital R for a variable is not standard notation. the integral would be much clearer if you write the radius and angle as functions of time. the steps which follow convert to a polar coordinate form, which is where standard treatments start. Johnjbarton (talk) 18:57, 2 July 2024 (UTC)

I have made several attempts to fix the math content in the scattering sections to match the textbook reference that this derivation seems to be based on:

• Beiser (1969). Perspectives of Modern Physics, p. 109

Note that this is the ref that was used by the Hyperphysics site. However that site attempts to condense the entire derivation down to one slide. The missing parts have been filled in incorrectly.

The content is still not correct but @Kurzon keeps reverting my changes. I'm done with this. Johnjbarton (talk) 15:08, 14 July 2024 (UTC)

Ok I will take a closer look at the Beiser book. Kurzon (talk) 18:51, 14 July 2024 (UTC)

The only thing I reverted was you writing R as R(t). I don't feel it's necessary and Beiser doesn't do it. I understand it's frustrating to see your edits reverted but this is overreacting. Kurzon (talk) 19:53, 14 July 2024 (UTC)

The presentation was incorrect about exactly the integration variable. Making the functional dependence explicit is the best way to avoid this. Johnjbarton (talk) 21:34, 14 July 2024 (UTC)

$$\int \limits {\frac {kq_{a}q_{g}}{R^{2}}}\cdot \cos \varphi \cdot \mathrm {\mathrm {d} } t$$

So you're saying that unless you make it clear that R and phi are functions of t, a reader might mistakenly resolve the integral to

$${\frac {kq_{a}q_{g}}{R^{2}}}\cdot \cos \varphi \cdot t+C$$

Is that your complaint? Kurzon (talk) 22:10, 14 July 2024 (UTC)

No, I am saying that an editor may create a version like this one with limits in angles and integration in time. Johnjbarton (talk) 22:14, 14 July 2024 (UTC)

Ah, now I understand. Well spotted. Kurzon (talk) 22:29, 14 July 2024 (UTC)

OK, is it better now? Kurzon (talk) 22:40, 14 July 2024 (UTC)

Make things easy

@Johnjbarton: I don't want to offend you but your way of explaining things is hard to understand. I went to pains to lay out all the steps to make things easy to understand for a high school student. We don't have to be faithful to Beiser as long as we produce something that is correct. Kurzon (talk) 08:10, 18 July 2024 (UTC)

I also do not want to offend, but your version was incorrect and also not easier to understand. Consequently we do need to be faithful to Beiser unless we can agree. My suggestion is that you restore my Beiser based version and then let's discuss what parts you think are difficult to follow and find better ways to explain them. Johnjbarton (talk) 15:25, 18 July 2024 (UTC)

Formatting of math blocks.

Unfortunately math formatting has issues. As far as I understand it, the best compromise for web and mobile is to use

• <math display="block">...</math>

This adds the correct space above and below the math if placed in a paragraph. If extra blank lines are added, extra vertical space appears in the article. I assume that the extra blank lines are to make the math stand out in the editor? Maybe a format like

• <math display="block">
• ...
• </math>

with no extra lines would be useful? Johnjbarton (talk) 22:12, 18 July 2024 (UTC)

NeE

@Johnjbarton: I'm confused about Rutherford use of NeE whereas I used kqQ, with k being the Coulomb constant and the charges expressed in Coulombs. How would you rewrite Rutherford's equation to use modern conventional variables? Kurzon (talk) 18:13, 19 July 2024 (UTC)

I added a paragraph to address this, please take a look.

Unfortunately "modern conventional" for electrostatics depends on where you look and what is "modern". For a long time cgs held the field, then MKS. The SI system was changed as recently as 2019. And these are mostly application or engineering-focused works. Physics theory usually adopts natural units. Rutherford's use of the variable 'b' is similar: by expressing lengths in units of 'b', the formula are simpler and the units only come in one time. Johnjbarton (talk) 21:47, 19 July 2024 (UTC)

If we take e = 4.65×10⁻¹⁰ esu, then NeE with a gold atom is 3.41×10⁻¹⁷. But kqQ, where q and Q are in Coulombs, is 1.82×10⁻²⁶. I don't understand. Kurzon (talk) 22:31, 19 July 2024 (UTC)

I guess that 3.4×10⁻¹⁷ will be in dyne-cm², in CGS units. 1 dyne is 1×10⁻⁵ Newtons (per wikipedia anyway) and 1 m is 1×10² cm so I get 3.4×10⁻²⁶N*m²

For kqQ, where q and Q are in Coulombs, 8.987×10⁹ N·m²/C² * 1.26×10⁻¹⁷ C * 3.20×10⁻¹⁹ C so about 3.7×10⁻²⁶N*m² (numbers copied from article)

Did I mention how great it is to have units only come in one time ;-) Johnjbarton (talk) 23:19, 19 July 2024 (UTC)

Units.

@Kurzon I deliberately used Rutherford's formulas as presented in his paper to ensure verifiability. As we discussed in other topics here, the units for electromagnetism are not standardized universally; adopting any one convention makes understanding the sources harder. I'm not against changing the formulas to one consistent approach if we can do it in a way that addresses this concern.

Things that I think would help address this concern would include:

• explicit discussion of units and their appearance in historical work.
• footnotes on each conversion (I generally disagree with footnotes but this is one case where I think they make sense.
• a specific reliable reference or references as the standard agreed, called out.
• limited use of specific values to avoid clutter.
• consistency throughout.

Most modern physicists use natural units because all the extra k's and $1/4\pi \epsilon _{0}$ stuff is not physics. But I understand that textbooks are fascinated with units so I'm ok with picking one. Johnjbarton (talk) 15:49, 20 July 2024 (UTC)

Possible references:

• Kibble 5th ed uses SI units, $F={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}r_{12}^{2}}}$ (not k)
  • Kibble, T. W. B.; Berkshire, F. H. (2004). Classical mechanics (5 ed.). London : River Edge, NJ: Imperial College Press ; Distributed by World Scientific Pub. ISBN 978-1-86094-424-6. OCLC 54415965. Page 8.
• Hand and Finch use natural units.
  • "It is common practice in physics to chose units to simplify the formula..." page 85.
  • Hand, L. N., & Finch, J. D. (1998). Analytical Mechanics. Cambridge: Cambridge University Press.
• Goldstein 3rd edition uses cgs $F={\frac {ZZ'e^{2}}{r^{2}}}$ Page 109
  • Goldstein, Herbert; Poole, C. P.; Safko, J. L. (2001). Classical Mechanics (3rd ed.). Addison-Wesley. ISBN 978-0-201-65702-9.

By the way, the use of k is common force and potential problems as meaning "whatever constants". So it's not a standard notation for Coulomb's constant AFAIK. Johnjbarton (talk) 16:38, 20 July 2024 (UTC)

I proposed to use Kibble as the reference for units. Two options however:

1. Put $\left({\frac {q_{Au}q_{\alpha }}{4\pi \epsilon _{0}}}\right)$ in front of most equations or
2. define $F={\frac {k}{r^{2}}},\ k=\left({\frac {q_{Au}q_{\alpha }}{4\pi \epsilon _{0}}}\right)$ and use k everywhere.

Johnjbarton (talk) 22:07, 20 July 2024 (UTC)

Legacy + Reception.

An edit by @22merlin made me realize that we did not properly integrate the Legacy section during the merge. I think we want the Summary to have a wrap up eg Legacy, but the Summary now needs to include the scattering topic a bit more. So I will move some of the Reception content towards Legacy rather than the other way around. Johnjbarton (talk) 21:07, 20 July 2024 (UTC)

Ok I think this is mostly fixed up. The Reception section is merged into Legacy. The Legacy section needs a few more references. Also

• The astronomer Arthur Eddington called Rutherford's discovery the most important scientific achievement since Democritus proposed the atom ages earlier.

is unclear: Which achievement? Johnjbarton (talk) 21:59, 20 July 2024 (UTC)

Rutherford's scattering experiments with light nuclei.

Around 1917 Rutherford did more more experiments with alpha particle scattering, ultimately leading to the discovery of the proton. I guess these are covered in Proton but we need to mention this aspect in Legacy. A good ref is already used in the article:

• Barrette, J. (2021). Nucleus-nucleus scattering and the Rutherford experiment. Journal of the Royal Society of New Zealand, 51(3–4), 434–443. https://doi-org.wikipedialibrary.idm.oclc.org/10.1080/03036758.2021.1962368 Johnjbarton (talk) 22:48, 20 July 2024 (UTC)

Cloud chamber image.

The cloud chamber image of Rutherford scattering was removed in an edit summarized: This image screws up the layout on desktop Instead of removing something like this for a minor reason, please post the issue and we can find a way to fix it.

In general wikipedia pages do not render perfectly. Removing content to fix layout will on be a temporary fix and it won't impact most readers.

I added the image back with more concise text. The rendering is fine for the moment. Johnjbarton (talk) 00:53, 24 July 2024 (UTC)

Is that cloud chamber image even useful? Does it tell us anything the diagram above it can't? Kurzon (talk) 11:52, 24 July 2024 (UTC)

Yes, the image does three things:

1. Historically significant independent experimental evidence
2. Direct visual experimental demonstration of scattering angle
3. Introduction of alternative particle physics arenas beyond gold foil scattering.

I thought about also adding an image related to particle accelerators. The primary legacy of Rutherford's scattering experiments was in the physics of scattering. Johnjbarton (talk) 16:47, 24 July 2024 (UTC)

If you can pad out the Legacy section a bit, that would solve the layout issues. Kurzon (talk) 17:56, 24 July 2024 (UTC)

The Geiger Marsden section in Summary

The section "Rutherford, Geiger, and Marsden" is, as I understand it, intended to explain the the gold-foil backscattering result of 1909. Due to recent changes it no longer does this. It ends with a comment about uranium sources. Johnjbarton (talk) 16:41, 24 July 2024 (UTC)

Johnjbarton's writeup of Rutherford's math

@Johnjbarton: I'm confused. In a diagram you use $\varphi$ as one of the polar co-ordinates of the alpha particle but later on you use $\phi$ for the scaterring angle. Your diagram also uses the Greek letter rho for the impact parameter, not p. Double-check Rutherford's paper. Kurzon (talk) 13:02, 27 July 2024 (UTC)

Rutherford uses $\phi$ for the "angle of deviation". He never uses polar coordinates for the particle because he jumps directly to "the eccentricity is $\sec \theta$". I used another source as cited to try to explain this jump, and that source used polar coordinates with $\varphi$. To further distinguish these I used $\varphi '$.

To me Rutherford's diagram looked like a rho but once I went through the math detail I realized it was p. I'll fix that. Johnjbarton (talk) 03:26, 28 July 2024 (UTC)

Oh Christ, this terrible and I'm fed up. The notation you use is inconsistent with the rest of the article and inconsistent with modern convention. I suggest you translate all your equations from Rutherford's notation to modern notation. We don't have to be that faithful to Rutherford's paper as long as we get the physics right. Use $\theta$ for the scattering angle and $\varphi$ for the angle between $r$ and $r_{A}$ and b for the impact parameter. Fix this yourself or I'll do it myself and you might not like how I butcher things. Kurzon (talk) 11:07, 28 July 2024 (UTC)

I changed the URLs for Rutherford's 1911 paper to a PDF scan of the original. The re-typed versions we previously used have some copy errors. Kurzon (talk) 17:03, 27 July 2024 (UTC)

Thanks, good move. Johnjbarton (talk) 03:11, 28 July 2024 (UTC)

Newtonian model for scattering from Thomson atomic model.

Once again I removed the Newtonian model for scattering from the Thomson atomic model.

1. The content appears in the article on Thomson's model, Plum pudding model.
2. Historically the case against Thomson was not made using these approaches.
3. Any discussion of a Newtonian mechanics approach to scattering is in my opinion bad physics. Force based models have not been used in atomic physics since before the time of Rutherford; energy based models are used. Force based methods are more complex (because the energy approaches already include the integrals) and do not work in quantum problems.
4. The description is lengthy and detracts from the topic of the article, which is scattering from Rutherford's model.

I think the material works well in Plum pudding model because Thomson did not provide a detailed account of scattering from the positive sphere. In addition, the source for this material, Beiser, presents it as Thomson-model scattering. A short WP:SUMMARY section could be included or we could expand the discussion of the historic case against Thomson's model.

I was originally against any presentation of a force based scattering. I did not oppose the presentation of the force-based model of Rutherford scattering as a compromise, but now I wonder if that was a good choice. Johnjbarton (talk) 03:59, 28 July 2024 (UTC)

I am fine with deleting that stuff once we fix the notation issues in your stuff. Kurzon (talk) 16:45, 28 July 2024 (UTC)

Request for comment: presenting Rutherford's 1911 paper in Rutherford's way.

As of this version the section Atomic model in Rutherford's crucial 1911 paper presented the 1911 paper using Rutherford's notation. @Kurzon has changed the formulas to arbitrary and confusing notations. I proposed to revert these changes and leave the original notation. I am asking for the input of other editors so we don't go back and forth on this issue. Johnjbarton (talk) 22:29, 28 July 2024 (UTC)

Use Rutherford 1) Any notation is arbitrary, 2) This paper is a classic, 3) Using Rutherford's notation allows a simple narrative, 4) Using Rutherford's notation makes verification straightforward. Johnjbarton (talk) 00:57, 29 July 2024 (UTC)

How many readers are going to even read the original paper? If they make that effort, it shouldn't be too hard for them to translate the notation. Kurzon (talk) 06:29, 29 July 2024 (UTC)

 Done I concede the issue. Johnjbarton (talk) 22:16, 30 July 2024 (UTC)

@Headbomb: Could you comment on this? Rutherford used p for the impact parameter, but p is more often used for momentum these days. Kurzon (talk) 11:54, 29 July 2024 (UTC)

I don't get this insistence on following Rutherford's paper. I find the article has become an overall downgrade from what it used to be just a month or so ago. And I find impact parameter b to be much clearer (and modern) because it can't be confused with momentum. Headbomb {t · c · p · b} 12:09, 29 July 2024 (UTC)

Although I respect Johnjbarton's expertise, his sense of presentation leaves something to be desired. Kurzon (talk) 12:55, 29 July 2024 (UTC)

Per the Wikipedia code of conduct WP:CIVIL keep your personal comments to yourself and discuss the article content here. Johnjbarton (talk) 15:51, 29 July 2024 (UTC)

There is nothing incivil about Kurzon's comments. Headbomb {t · c · p · b} 16:05, 29 July 2024 (UTC)

I disagree. I have ignored his insults in the past but seems to have been a mistake. There is no reason to post an insulting personal opinion about my abilities. Johnjbarton (talk) 16:50, 29 July 2024 (UTC)

You're a little sensitive, I meant no offense. Kurzon (talk) 20:18, 29 July 2024 (UTC)

Rather than more unfounded claims about my character, the traditional response is an apology. Johnjbarton (talk) 21:30, 29 July 2024 (UTC)

Alright I'm sorry. Kurzon (talk) 03:05, 30 July 2024 (UTC)

Thanks. Johnjbarton (talk) 16:02, 30 July 2024 (UTC)

A month ago the article was factually incorrect and based on WP:OR. If you have specific concerns, please be specific. Johnjbarton (talk) 15:53, 29 July 2024 (UTC)

I've changed p to b, swapped phi and theta to be consistent with other diagrams in this article and others, and made a few more changes. Tell me what still remains incorrect. Once we've sorted this all, I'll be happy to delete the stuff I adapted from Hyperphysics. Your historically-relevant stuff is better (it also gave me a reason to brush up on hyperbolic geometry, thanks for that). Kurzon (talk) 15:05, 30 July 2024 (UTC)

Using b for impact parameter is common in my experience, and using p for momentum is of course a widespread convention. Physicists are also more inclined to use $\theta$ for the angle from the axis, and $\phi$ for the azimuthal angle (as noted in our Spherical coordinate system article). I think it makes sense to follow the modern conventions; anyone taking the time to look up Rutherford's original paper will be competent enough to make a few letter substitutions. XOR'easter (talk) 21:46, 30 July 2024 (UTC)

Why the Thomson model was wrong

@Johnjbarton: A week or so ago you complained that the material I put on the Thomson model was wrong somehow. I think we should do a section on it, and I invite you to lay it out, since you understand the history better. Kurzon (talk) 18:14, 30 July 2024 (UTC)

Our treatment of the case against the Thomson model is spread out in the article. It is discussed in "Legacy", "Comparison to JJ Thomson's results" and some implicit parts of the experiment. Perhaps we need to rearrange the content to address the Thomson model head on.

I am opposed to a mythological discussion of how the Rutherford experiments devastated Thomson's model. It's not what happened. That's half the reason I'm against a scattering theory section on Thomson model; the other half is its distraction from the article main content.

Rutherford's scattering model deposed Thomson's scattering model, but the physics community did not understand the power of scattering models at the time. So the implications for atomic models did not sink in. In addition, Rutherford's atomic model had no electrons, it's not a replacement.

Do you think it would help to subdivide the Legacy section into "Particle scattering" and "Demise of the Thomson model"? That would draw attention to the two aspects and give them focus. The latter section could include more modern perspective. Johnjbarton (talk) 18:45, 30 July 2024 (UTC)

Let me study the matter a little further until I fully understand what you're talking about. Kurzon (talk) 11:33, 31 July 2024 (UTC)

r min

@Johnjbarton: In one part of the article, $r_{\text{min}}$ is defined as

$r_{\text{min}}={\frac {kq_{a}q_{g}}{{\tfrac {1}{2}}mv_{0}^{2}}}$

but in another part it's

$r_{\text{min}}=-{\frac {kq_{a}q_{g}}{{\tfrac {1}{2}}mv_{0}^{2}}}$

Which is it? Kurzon (talk) 16:25, 31 July 2024 (UTC)

Well r_min can't be negative. I removed the minus. But this copyedit fail means we may have a sign error in the other equations. Johnjbarton (talk) 16:31, 31 July 2024 (UTC)

Did RUTHERFORD make mistake? Look, I'll retype what he put in his own paper:

${\frac {1}{2}}mV^{2}={\frac {1}{2}}mv^{2}-{\frac {NeE}{SA}}$

$v^{2}=V^{2}(1-{\frac {b}{SA}})$

and on a following page $b={\frac {2NeE}{mu^{2}}}$

That's his stuff. Now I'm going to do my own rearranging:

${\frac {1}{2}}mV^{2}+{\frac {NeE}{SA}}={\frac {1}{2}}mv^{2}$

$V^{2}+{\frac {NeE}{{\frac {1}{2}}mSA}}=v^{2}$

Help me I'm going mad. Kurzon (talk) 17:06, 31 July 2024 (UTC)

@Johnjbarton, Headbomb, and XOR'easter: Did Rutherford make a mistake in his conservation of energy equation? This is what he wrote in his 1911 paper:

${\frac {1}{2}}mV^{2}={\frac {1}{2}}mv^{2}-{\frac {NeE}{SA}}$

V is the velocity of the alpha particle at the start and v is it's velocity at the point of closest approach A. I figure that as the alpha particle approaches A, it should LOSE energy, not gain it as the equation suggests. Should it instead be like this?

${\frac {1}{2}}mV^{2}={\frac {1}{2}}mv^{2}+{\frac {NeE}{SA}}$

Kurzon (talk) 19:37, 31 July 2024 (UTC)

I agree with your reasoning if we assume $NeE>0$ and SA positive. Rutherford did not now the charge on the nucleus and the value of SA could depend on the branch of the hyperbola. Earlier in the paper he has head-on energy balance (where SA is b)

$${\frac {1}{2}}mu^{2}=NeE\cdot \left({\frac {1}{b}}-{\frac {3}{2R}}+{\frac {b^{2}}{2R^{3}}}\right)$$

If we neglect the 2nd and 3rd terms as he does, then the potential energy term is positive:

$${\frac {1}{2}}mu^{2}={\frac {NeE}{b}}$$

BTW we should either use $u$ (initial) in our form of this equation or $V$ (approaching nucleus from afar) but not $v$ (apse velocity) as currently set. Johnjbarton (talk) 19:53, 31 July 2024 (UTC)

OK, I chose to change the energy equation rather than redefine r_min. Kurzon (talk) 20:19, 31 July 2024 (UTC)

I think this change is fine, but Rutherford was not mistaken. If you use the other sign and follow through the derivation you get an equation relating $b/r_{\text{min}}$ to $-\theta$, which is just the other half of the angles in the table or the bottom of the diagram. Both sets of angles are observed in the experiment: the two results are indistinguishable. This is what Rutherford meant when he said "The deductions of the experiment so far considered are independent of the sign of the central charge..." Johnjbarton (talk) 23:51, 31 July 2024 (UTC)

The eccentricity of a hyperbola can be calculated

Two or three times I have tried to fix this. Each time @Kurzon removes it.

We have a paragraph that starts

• The eccentricity of a hyperbola can be calculated ...

My immediate reaction is "wait what"? What is this "eccentricity" thing? Where did it come from? How is this all related to the problem?

My solution was simply to start the paragraph with a sentence about eccentricity, hyperbola, and the geometry of the problem:

---

Any hyperbola can be written in polar coordinates $(r,\varphi )$ with the origin at the center as

$$r={\frac {1}{\sqrt {e^{2}\cos ^{2}\varphi -1}}}.\,$$

where $e$ is the eccentricity. Comparing Fig. 1 to the geometry of a hyperbola shows that SO is the focal distance and OA is the length of the semi-major axis. The eccentricity, e, is the focal distance divided by the length of the semi-major axis or ⁠SO/OA⁠.

---

I think something like this is essential. Johnjbarton (talk) 22:44, 31 July 2024 (UTC)

But you don't use that formula for anything here, it serves no purpose. All we need is ⁠SO/OA⁠ = sec Phi. Kurzon (talk) 01:47, 1 August 2024 (UTC)

A historical narrative for why the scattering result surprised Rutherford

@Johnjbarton: You rejected the stuff I previously wrote for Why the Thomson model was wrong. Let's talk about a more historically accurate one, then.

I looked through the 1968 paper by Heilbron you shared with me and on page 270 he addresses beta particle scattering in the Thomson model, offering two equations:

$\tan(\varphi /2)=(e_{1}e_{2})/(m'v^{2}p)$

and

$\sin ^{2}(\varphi /2)=(1+p^{2}m'^{2}v^{4})/e^{4})^{-1}$

The first one is pretty much what we produced in the article, in your write-up of Rutherford's equations and my write-up of the Hyperphysics/Beiser stuff. The second one confuses me. I'm not sure where to go from here. I found a 1906 paper by Thomson which Heilbron says is important.

https://gilles.montambaux.com/files/histoire-physique/Thomson-1906.pdf

Kurzon (talk) 10:37, 1 August 2024 (UTC)

@Kurzon I'm confused by your questions.

First "why the scattering result surprised Rutherford". Rutherford worked on scattering for probably 30 years so I'm unsure what result you have in mind, but I suppose it relates to the invented-history around the often repeated cannon ball quote and Geiger-Mardsen's results.

The 1909 Geiger-Mardsen result obviously did not surprise Rutherford: he proposed the experiment. Most experiments confirm existing ideas and so it was in this case per Heilbron and other references. However, the cannonball comment (many years after the fact) does make sense of the events between 1906 and 1909, during which time Rutherford and Geiger did many scattering experiments under the influence of Thomson's atom model. Their results did not make sense given the model. The results in around 1908 were to demonstrate that alpha particles scattered at all: that was surprising given Thomson's model. Hence the title of Geiger paper "On the Scattering of α-Particles by Matter". So yes Rutherford was overall "surprised" by the scattering results, but not by the Geiger-Mardsen result per se.

As discussed in Plum pudding model, Thomson's scattering model had three parts: 1) electron-electron Coulomb scattering (your formula above) 2) positive sphere (largely ignored by Thomson), 3) multiple scattering. The third one was essential. Let me repeat it: the multiple scattering in Thomson model was essential. Without multiple scattering Geiger's 1908 results invalidate Thomson's model. Crowther's work was exactly on this issue. Geiger's thickness dependence experiments aimed at testing the multiple scattering. That is why Rutherford's 1911 paper focuses on multiple scattering as discussed in the section "Comparison to JJ Thomson's results". He invalidates multiple scattering most of all.

But this kind of invalidation in 1911 is very weak. The experiments are crude. The sources are diffuse and poorly understood. They don't know what alpha and beta particles really are. They don't know what atoms or solids really are. One bit of new evidence against the only atomic model existing does not instantly elevate an alternative.

Most especially Thomson had established that his model had potential to explain chemistry via arrangement of the electrons. In comparison, Rutherford's model explained some experiments Geiger did which no one else performed and few understood. Rutherford's model had no electrons and the only existing model for electrons with a compact positive core was the already dismissed Saturnian model. So the 1911 paper was really only of interest to physicists like Wilson interested in scattering.

Thomson's model was not "wrong" until Bohr added new the electron model to Rutherford's nucleus. During this time it was not like Thomson's model was widely used. The very existence of atoms was still being debated.

The scattering formula in Thomson's "On the number of corpuscles in an atom" is a minor step in his analysis of absorption. Historically absorption, related to Geiger's thickness experiments, was critical in understanding the physics. However modern texts make more of Coulomb scattering because it is simpler. I don't know what trig relations connect the tangent and sin forms in Heilbron's paper on 270, but as far as I can make out Heilbron is just trying to explain where the sin formula in Thomson's paper could have come from. I don't think it is otherwise significant. Johnjbarton (talk) 17:21, 1 August 2024 (UTC)

I think I'm getting what you say. On the plum pudding article, and in Beiser, its says that the odds of a particle being deflected by more than 90 degrees after 10,000 collisions is negligible. But what about ten million collisions? If an atom contains many thousands of electrons instead of just a hundred or fewer, then the plum pudding model could produce strong deflection of alpha particles. Kurzon (talk) 16:07, 2 August 2024 (UTC)

Yes, that is one example of the many poorly known issues at the time. Geiger spent a lot of time on thickness dependence experiments for this reason. By doubling the thickness you double the number of collisions and can create a graph. Crowther had done this for beta scattering and used it to support Thomson, but his data was inaccurate for a critical range, affecting the conclusion (this from Heilbron) around p279. Johnjbarton (talk) 17:19, 2 August 2024 (UTC)

OK if I wanted to rewrite the stuff in the plum pudding model article to make it more historically accurate, what should I do? Kurzon (talk) 18:06, 2 August 2024 (UTC)

I think the plum pudding model is pretty good now. We could add a paragraph on how the beta scattering results only apparently supported Thomson's model. Beta scattering was much less sensitive to the effects Rutherford saw with alpha particles, beta scattering turns out to be quite complex, and Crowther's experiments were inaccurate in just the range that showed important effects. If you think this would be valuable I can find the refs.

Heilbron spends much of his 1968 article discussing how Rutherford had to address Crowther's results after 1906. That is, the dramatic reduction in the number of electrons discovered by Thomson did not eliminate the multiple scattering concept. They did not have good data on scattering by angle as implied by our scattering model presentations. They had a narrow cone of angles and variation with material and thickness. Within this range of data Thomson's model works. It was only the large angle scattering and careful work with thicknesses done by Geiger that showed the model fails. The quality data for this came out in Geiger's 1913 paper. Johnjbarton (talk) 16:19, 3 August 2024 (UTC)

The first three paragraphs of the Heilbron 1968 paper summarize the role of multiple scattering. Johnjbarton (talk) 18:18, 3 August 2024 (UTC)

Explicit interjection of link to (trivial) trig page

Several times @Kurzon adds something like:

• This next part makes several references to Wikipedia's list of trigonometric identities.

Why? This is among the most trivial bits of related material, not a major issue that needs to be called out. Each and every use of a trig identity can be link inline in the text. This is out of character for the article or article in general. I will keep removing this. Johnjbarton (talk) 17:49, 1 August 2024 (UTC)

I think it's useful to students to have this resource pointed out. You take this knowledge for granted. Kurzon (talk) 18:47, 1 August 2024 (UTC)

First this is not a textbook. Second an injected explicit link like this is lazy and not helpful to any readers, especially students. There are hundreds of formula on that page.

Any step in the article which is not clear to a typical reader should be clarified. An explicit link followed later by a series of obscure steps does not clarify.

To this point, you removed my description of secant which, in my opinion, is obscure for readers. Most readers will understand sin, cos, tan, maybe cot, but the rest are rarely used. My original version had links for steps. When you add new trig steps, add the appropriate links. An explicit statement that "reader, you need to learn a hundred or so trig identities to follow this" is not helpful. Johnjbarton (talk) 19:01, 1 August 2024 (UTC)

In fact I can't figure out the section that discusses the OA SA $\Phi$ geometry now. Johnjbarton (talk) 19:14, 1 August 2024 (UTC)

Writing this article (and I wrote most of it) was a learning process for me, I didn't take physics in college. I think that makes me well equipped to empathize with the laymen. I remember the parts where I stumbled. So maybe I should write the explanation and you should check it to see if I got the physics right. I wasn't aware that Wikipedia even had a list of trigonometric identities until I started studying Rutherford's work, and that was one of many stumbling blocks I had to overcome. I want to make that block easier for those who come after me. Kurzon (talk) 20:08, 1 August 2024 (UTC)

I don't see the connection. The explicit link to the overall page does not aid in understanding. If you don't know that trig identities exist, the explicit link sentence is a completely mysterious interjection. If you do know the exist, the list of 100 does not help.

The links like cotangent double angle formula lead you directly to the appropriate section.

I don't understand why you would be against that. And the OA SA geometry would be much clearer if we use sin/cos/tan and triangle sides. People who take trig learn the "opposite over hypotenuse" rules but not the reciprocal functions like secant/cosecant. Johnjbarton (talk) 21:10, 1 August 2024 (UTC)

What do you think of it now? Kurzon (talk) 16:43, 7 August 2024 (UTC)

I'm unsure which aspect you are asking about. The wikilinks for trig are fine now. I think the derivation of the SO SA bits could be a bit clearer with a dedicated diagram showing the right triangles, but I don't think this is essential.

I think overall the article is in excellent condition. Perhaps neither one of us is happy with the process but we can be proud of the net result. Johnjbarton (talk) 16:56, 7 August 2024 (UTC)

Oh come on, don't you have an appetite for argument? Kurzon (talk) 19:55, 7 August 2024 (UTC)

Feedback on current state

@Headbomb and Materialscientist: Johnjbarton is satisfied with this article, how about you guys? Kurzon (talk) 08:13, 11 August 2024 (UTC)

Unsourced statements

@Gog the Mild and SchroCat: Which unsourced statements did you have in mind? Kurzon (talk) 08:45, 15 August 2024 (UTC)

It sounds obvious, but the ones without citations at the end. These are more obvious when the sentence at the end of the paragraph - check out those paragraphs which don't have a citation at the end (both paras of the Alpha particles section, two of those in the Rutherford, Geiger, and Marsden section), etc. - SchroCat (talk) 08:56, 15 August 2024 (UTC)

Man, FA process is not worth this. Kurzon (talk) 11:41, 15 August 2024 (UTC)

Quite possibly not, but it is something required of every FA, indeed of every article; we are just a bit more formal about it at FAC. See WP:WHYCITE and WP:PROVEIT. Note "Any material lacking an inline citation to a reliable source that directly supports[b] the material may be removed and should not be restored without an inline citation to a reliable source" which is policy. Any drive-by editor could delete all of the statements in question, irrespective of the article's FAC/FA status, and if you can't be bothered to add citations there would be nothing you could do about it. Gog the Mild (talk) 11:57, 15 August 2024 (UTC)

I assume that the abbreviation in the above content "FA" means Wikipedia:Featured articles Johnjbarton (talk) 15:21, 15 August 2024 (UTC)

@SchroCat says

• "It sounds obvious, but the ones without citations at the end."

Can you help me understand "the ones"? Sentences? paragraphs? sections?

• "...Alpha particles section..."

? The whole article is about about alpha particles, can you narrow this down? Johnjbarton (talk) 15:12, 15 August 2024 (UTC)

@Gog the Mild says in an edit summary:

• Needs more citations. See talk page

But I don't see any additional information in the Talk page. Where would I look? Johnjbarton (talk) 15:14, 15 August 2024 (UTC)

The second comment of this section. Ie [2]. Gog the Mild (talk) 15:21, 15 August 2024 (UTC)

Kurzon, It's not necessarily about the FA process: it's about an article that doesn't even reflect the core policy of Wikipedia:Verifiability.

Johnjbarton The two unsourced sentences that stand out for me in the Alpha particles section are "Protons and neutrons had yet to be discovered, so Rutherford knew nothing about the structure of alpha particles." and "The scattering of alpha particles was expected to be similar. Rutherford's team would show the scattering model to be incorrect because the model of the atom was incorrect." Every piece of information needs to be supported by a reliable source (that's the verifiability policy), and these are the obvious ones there. The entire first paragraph of the Scattering theory section is also unsourced, as is the quote calling Rutherford the "the father of nuclear physics". These are the obvious ones that stand out and are examples only, rather than an exhaustive summary. Cheers - SchroCat (talk) 15:24, 15 August 2024 (UTC)

(edit conflict) Taking just the section "Alpha particles and the Thomson atom", the following statements are not cited:

• Protons and neutrons had yet to be discovered, so Rutherford knew nothing about the structure of alpha particles.
• The scattering of alpha particles was expected to be similar.
• Rutherford's team would show the scattering model to be incorrect because the model of the atom was incorrect.

The whole first paragraph of "Scattering theory and the new atomic model" is uncited.

There are many other cases.

Gog the Mild (talk) 15:30, 15 August 2024 (UTC)

You are going to think that we are being awkward, but if you are still considering FAC - and I hope you are - you will not wish to put in a load of work to get over one hurdle, to then fall at the next similar one. You need where possible to use modern sources and/or sources by third parties. There are various reasons for this, including "it is a thorough and representative survey of the relevant literature." Gog the Mild (talk) 15:43, 15 August 2024 (UTC)

@Gog the Mild

• "You need where possible to use modern sources and/or sources by third parties."

I don't understand what you are saying. Is this a paraphrase of WP:PSTS? So by "third parties" you mean secondary sources? Johnjbarton (talk) 16:03, 15 August 2024 (UTC)

Partly yes, it is a reference to PSTS, partly it refers to the part of the FAC criteria I quote. Certainly if this comes back to FAC I would be querying every cite to Rutherford, Geiger or Marsden, or older than about 30 years as to whether each is, in context, a HQ RS secondary source. And overall the article needs to be a thorough and representative survey of the relevant literature. There is a plentiful modern(ish) literature on this, it needs to be reflected in the article - over and above PSTS. Gog the Mild (talk) 16:19, 15 August 2024 (UTC)

@Gog the Mild

• There is a plentiful modern(ish) literature on this

If you have any good secondary references please let me know. Johnjbarton (talk) 17:08, 15 August 2024 (UTC)

@Gog the Mild @SchroCat I have addressed each item you listed and many more. Of course I cannot address:

• "There are many other cases."

If you add Template:cn markers in the article I will fix them.

I would like to remove the Template:more footnotes tag. Johnjbarton (talk) 23:43, 16 August 2024 (UTC)

OK, I've added several more using the {{citation needed span}} template. Unfortunately this doesn't work with the maths template or markup, so I've had to leave that out and just focus on the text elements. Much of the maths will also have to be supported, given it's showing us what's in the textbooks. I hope this all helps! - SchroCat (talk) 14:28, 17 August 2024 (UTC)

The math stuff shouldn't require citations for every paragraph since it's not facts but mathematical reasoning. Anyone with a maths or physics degree can verify the maths without sourcing. Kurzon (talk) 14:36, 17 August 2024 (UTC)

I would argue that it does need it. Although you may be right, not everyone who reads this article will have a maths or physics degree. Think: if this gets to FA, it will appear on the main page where a large number of people will read it - the vast majority won't have maths or physics degrees, and the only thing that gives them comfort that the material is correct is the little blue superscript number at the end of it showing it's supported by a reliable source. - SchroCat (talk) 14:43, 17 August 2024 (UTC)

@SchroCat Thanks! I have add refs for your marks.

• "Unfortunately this doesn't work with the maths template or markup..."

Simply placing Template:citation needed aka Template:cn on the end of the line preceding a formula works as this is where a citation would be set. Johnjbarton (talk) 17:28, 17 August 2024 (UTC)

I have added more than 30 refs in the last few days. Again I ask @Gog the Mild to remove the Template:more footnotes. I don't think it serves any purpose. The criteria:

• "This template indicates that the article cites a sufficient number of reliable sources, but uses an inappropriate combination of inline citations and general references. All material in articles must be verifiable, but outside of featured articles and good articles Wikipedia does not require the use of inline citations except to support direct quotations, material that has been challenged or is likely to be challenged and contentious material about living persons."

does not apply as far as I can tell. Johnjbarton (talk) 23:44, 19 August 2024 (UTC)

Major unexplained changes.

@Kurzon is making significant changes with no explanation. We've worked hard on this article and I don't agree with the changes. Johnjbarton (talk) 15:23, 16 August 2024 (UTC)

Shouldn't we show some equations for the Thomson scattering? Anyway, there is an issue I'd like you to help me with on the plum pudding model Talk page. Kurzon (talk) 17:51, 16 August 2024 (UTC)

• Shouldn't we show some equations for the Thomson scattering?

We should have at most a summary of the content in Plum pudding model. You have deleted the scattering model content in that article so I cannot understand why you would want to increase it here. Johnjbarton (talk) 18:12, 16 August 2024 (UTC)

Well we can leave this argument for another time. Kurzon (talk) 18:48, 16 August 2024 (UTC)

Multiple scattering Rutherford's paper

@Johnjbarton: In his 1911 paper, Rutherford explains how Thomson's equations can't be adapted to explain his experimental data and he mentions multiple scattering. Kurzon (talk) 11:05, 18 August 2024 (UTC)

Yes, and that is what the article says. Johnjbarton (talk) 15:31, 18 August 2024 (UTC)

The plum pudding stuff should be here

@Johnjbarton, Headbomb, and Materialscientist: We really ought to move the stuff about why the plum pudding model was wrong from the Inconsistency_of_the_plum_pudding_model article to this one. They go together. Kurzon (talk) 16:13, 20 August 2024 (UTC)

I disagree completely. Instead we should fix the content in Plum pudding model so it no longer focuses on "wrong" but focuses on the article topic, Thomson's model of the atom and his evidence to support it. I have already tried to do that and was reverted. Chronologically, historically, and logically each model is developed against the evidence at hand. When new evidence emerges, new models are forced to be created. Attempting to describe Thomson's scattering model by assuming Geiger/Marsden results is not going to make sense. When Thomson wrote his 1910 paper there was no large angle scattering data as far as he was concerned. Once we present Thomson's model the way he presented it, then we can have a short summary of the Rutherford's team's new results. Johnjbarton (talk) 16:37, 20 August 2024 (UTC)

Yeah, wasn't that what I did? Kurzon (talk) 08:43, 21 August 2024 (UTC)

Why do you disagree? Kurzon (talk) 17:34, 24 August 2024 (UTC)

@Kurzon Content primarily about the plum pudding model belongs in the plum pudding model article. It's up to you to justify what is an illogical partial merger.

Thomson's atom model was not refuted by scattering theory. New experimental evidence built the case for a compact nucleus and Bohr showed how a quantized orbit could explain spectra. Thompson's scattering model is historically important in supporting his atom model and by being first. It belongs where it is. Johnjbarton (talk) 22:04, 24 August 2024 (UTC)

I'm honestly baffled as to why you don't agree with what I tried to do, because I don't disagree with the historical narrative you just gave me. Kurzon (talk) 03:13, 25 August 2024 (UTC)

The title of this Topic is "The plum pudding stuff should be here". But we have an article about Plum pudding model. Why would we move that content in to this article?

The only reason you have given, is that you want "stuff about why the plum pudding model was wrong". We already have two paragraphs of background discussing the plum pudding model, a section Alpha particles and the Thomson atom, a subsection Comparison to JJ Thomson's results, and two other places where the comparison is discussed. That is more than enough stuff, or even a bit too much. On the other hand we have very little about other nuclear models. Johnjbarton (talk) 16:11, 25 August 2024 (UTC)

I guess because before you came along (at my request) this article had a section with some maths on why the Thomson model was wrong, and I want to restore that. Kurzon (talk) 17:36, 25 August 2024 (UTC)

I have reorganized the Plum Pudding model article to combine the two 1910 discussions, place the content in chronological order, and fix up the section heading to match. I think more can and should be done but that discussion should be on the Talk page of that article. Johnjbarton (talk) 23:51, 24 August 2024 (UTC)

More refs added

I added 2 refs and reworded a sentence based on Template:cn notations by @AirshipJungleman29. Please review to ensure I addressed the issues. Johnjbarton (talk) 02:43, 22 August 2024 (UTC)