Talk:Rutherford scattering experiments

Maths
Are you good at maths? What do you think of this modification to the equation? The lateral force F exerted on the alpha particle by the gold atom is not constant as the alpha particle crosses the space 2r, so I added something to the start to get the average force exerted. It's unnecessary for this article's needs, but is it correct? Kurzon (talk) 17:08, 31 March 2023 (UTC)

$$ \theta = \arctan \frac{\Delta p}{p} = \frac {2}{\pi} \cdot \left( \int_{-\frac {\pi}{4}}^{ \frac {\pi}{4}} \cos (x)\mathrm{d}x \right) \cdot k \frac{Q_\alpha Q_g}{r^2} \cdot \frac{2r}{v} \cdot \frac{1}{mv}$$


 * The actual correct expression can be seen in the article Impact parameter. But regarding Rutherford's motivation, it's enough to show that the expected scattering angle is very small, and thus the extremely simplified expression to estimate just the order of magnitude would be perfectly sufficient and more appropriate than anything with integrals and trigonometry (which is useless in the small-angle limit). — Mikhail Ryazanov (talk) 02:00, 1 April 2023 (UTC)

Hah. That's the story of my life. Just when I think I have gotten the hang of this math stuff, a real math swot comes along and shows me how utterly hopeless I am. It's the Dunning-Kruger effect. Kurzon (talk) 07:50, 1 April 2023 (UTC)

Now I'd like to do some maths for an alpha particle that goes right through the center of the gold atom. Have I got this right?



The amount of exerted by the gold atom on the alpha particle as the alpha particle approaches is given by

$$\int_{r}^{\infty } k \frac{Q_\alpha Q_g}{x^2} dx = \left [-k \frac{Q_\alpha Q_g}{x} \right ]_r^{\infty} = 2.5315 \times 10^{-16} ~\text{Joules}$$

where x is the distance between the alpha particle and the center of the atom.

The amount of work exerted on the alpha particle as it passes through the atom is given by

$$\int_{0}^{r } k \frac{Q_\alpha Q_g x}{r^3} dx = \left [ \frac{1}{2} k \frac{Q_\alpha Q_g x^2}{r^3} \right ]_0^{r} = 1.266 \times 10^{-16} ~\text{Joules}$$

The total amount of work is 3.797 x 10-16 J.

The initial kinetic energy of the alpha particle is given by

$$E_\alpha = \frac{1}{2} m v^2 = \frac{1}{2} \times 6.645 \times 10^{-27} \times (1.53 \times 10^7)^2 = 7.7776 \times 10^{-13} ~\text{Joules}$$

So the Thomson gold atom does not transfer enough energy into the alpha particle to bring it to a halt, never mind send it flying back to the emitter. Kurzon (talk) 15:20, 10 June 2023 (UTC)

You have a PhD in chemistry. Did I get the above stuff right? Kurzon (talk) 15:54, 27 June 2023 (UTC)

Ref list
1st reference in auto-generated references list doesn’t actually link to the reference in the bibliography. Anyone with a deeper knowledge of wiki templates - is this something specific to this page or is it a wider issue with the template itself? 3nt0 (talk) 00:30, 21 March 2024 (UTC)

Feedback
What do you guys think of the math I used when explaining the plum pudding model in the Summary section? Kurzon (talk) 08:15, 15 May 2024 (UTC)


 * I assume you are referring to the impulse-based scattering angle and the work calculations.
 * I'm not a fan of math in physics articles, essentially because math is a language and this is the English language Wikipedia. If we have math all of the terms need to be connected to the physics.
 * The article has a diagram of a Thompson sphere showing 7 electrons. This would make the sphere electrically neutral outside of the sphere, contradicting the math shown. I'm skeptical that this equation has any relationship to the historical experiment.
 * What is the physical nature of the impulse approximation? An average approximate force is applied over a fixed time interval. The force is calculated when the alpha particle is at the glancing edge of the Thompson sphere; the corresponding time interval is the diameter of the Thomson sphere divided by the speed of the alpha particle.  I don't see any of this in the article.
 * The form of the scattering equation looks like an engineer wrote it. A physicist would express the charge as 2 and 79 and use atomic units. Notice that seeing "79" immediately raises the question about the missing electrons.
 * I have similar comments about the work calculations. The Thompson sphere exerts no force (its neutral) so I don't understand how the numbers work out. Johnjbarton (talk) 15:51, 15 May 2024 (UTC)
 * The electrons have so little mass that they get pushed aside. Kurzon (talk) 16:05, 15 May 2024 (UTC)
 * http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/rutsca3.html This is where I got the math. I didn't pull it out of my butt. Kurzon (talk) 16:52, 15 May 2024 (UTC)
 * Please take a look at Rutherford's 1911 paper:
 * Ernest Rutherford (1911). "The Scattering of α and β Particles by Matter and the Structure of the Atom". Philosophical Magazine. Series 6. 21 (125): 669–688. doi:10.1080/14786440508637080
 * In the first part of the paper he describes the alternative theory for scattering from the Thomson atomic model. That theory is a series of individual scattering events (from the electrons), not a model like the one described on hyperphysics.
 * Note that the impulse model works for Rutherford's atom. In the region close to the nucleus the force from the uniform electron density will be negligible compared to the nuclear force as the alpha particle zooms by.
 * I'll look for other sources. Johnjbarton (talk) 17:53, 15 May 2024 (UTC)
 * But my stuff isn't wrong, is it? I can only guess what maths Rutherford actually scribbled in his notebook. Kurzon (talk) 19:24, 15 May 2024 (UTC)
 * As a model of a low-impact +2 particle scattering from a +79 sphere, the material is fine. However, no modern theory of the atom would use such a calculation, and I believe that if Rutherford had used it, Heilbron would have discussed it (Rutherford's notebooks are in the Library of Cambridge and were studied by Heilbron, see the first page of the history paper).
 * I did not look carefully but I believe the inline stopping-distance calculations are included in the 1911 Rutherford paper. Johnjbarton (talk) 21:21, 15 May 2024 (UTC)
 * Please take a look at
 * Heilbron, John L. "The Scattering of α and β Particles and Rutherford's Atom." Archive for History of Exact Sciences 4.4 (1968): 247-307. https://www.jstor.org/stable/41133273
 * This paper is recommended by Abraham Pais in his book Inward Bound where he discusses Rutherford scattering.
 * The Heilbron paper is a long, detailed historical analysis. (In the section called "The Diffuse Reflection of (alpha) particle", Heilbron points out that Rutherford's team knew about strong backscattering of alpha particles before the famous Marsden/Geiger experiment.) In the section "Consolidation of the "Manchester Approach" to Scattering" Heilbron writes:
 * Still, as the year 1910 opened, there existed but one plausible quantitative scattering theory, Thomson's treatment of 1906, and that applied specific only to β particles. There is no reason to doubt that its basic assumption, hypothesis of multiple scattering, was then accepted at Manchester.
 * Of course we are very unlikely to find a source that says the hyperphysics scattering calculations are incorrect, but historically it's clear that such a model was not used. I think the hyperphysics site is wrong, but we don't need to argue it if we follow the historic sources. Johnjbarton (talk) 18:50, 15 May 2024 (UTC)
 * I took a quick look through that paper you linked and damn do I have my work cut out for me. Kurzon (talk) 21:04, 15 May 2024 (UTC)
 * Selecting material from these very detailed histories is challenging. You're doing great work, thanks. Johnjbarton (talk) 21:09, 15 May 2024 (UTC)
 * The Thomson scattering équation seems to want me to treat the atom as a point, not a sphere that the alpha particle can pass through. Kurzon (talk) 14:15, 16 May 2024 (UTC)
 * I'm unsure what you mean by "the Thomson scattering equation"?
 * Thomson and Crowther used multiple scattering from (point) electrons, that is not discussed in the article,
 * The hyperphysics-based scattering discussed in the article is based on glazing incidence on a sphere. It uses the Thomson atom radius.
 * The 1911 paper discussed in "Rutherford mathematically models the scattering pattern" uses point scattering.
 * There is also Thomson scattering but that is scattering of light from a charged particle.
 * Rutherford's 1911 paper showed that the nucleus was so tiny compared with the atom that putting all of the charge at a point was accurate enough. One can't use the impulse-based approximation in this model. Johnjbarton (talk) 15:33, 17 May 2024 (UTC)
 * You've got to get back to me on this. Since this was your idea, why don't YOU come up with a possible calculation that Rutherford might have made to show that the Thomson atom cannot cause large deflections? Kurzon (talk) 05:58, 17 May 2024 (UTC)
 * Thomson proposed multiple small scattering from electrons. To get large angles with multiple small scattering you need many collisions. But Rutherford knew that the vast majority of the alpha particles go straight through the foil: the biggest probability is no collision. That means the probability of one collision is small and two collisions is very tiny. Thus you can't get large deflections. This is what Rutherford says on page 385 of his 1911 paper, using 1/1000 for one collision and 1/1,000,000 for two. Johnjbarton (talk) 17:16, 17 May 2024 (UTC)

When I look through the papers on Rutherford scattering I keep getting back to the original equation I put in myself. Kurzon (talk) 16:44, 17 May 2024 (UTC)


 * Then cite those papers! Johnjbarton (talk) 17:07, 17 May 2024 (UTC)

Contemporary theories of atomic structure
The section "Contemporary theories of atomic structure" is incorrect in several ways, but in my opinion the entire approach of the section is off the mark. Both Thomson and Rutherford were experimentalists, really genius-level experimentalists. We should be discussing their ideas in terms of the experiments they designed, not the calculations or theories. Johnjbarton (talk) 15:45, 16 May 2024 (UTC)


 * The following text is in the article, citing a Cambridge physics site
 * Both the negative and positive charges within the Thomson atom are spread out over the atom's entire volume, and Rutherford had calculated that this volume was too large for strong deflection to happen. According the Coulomb's Law, if this sphere were to be smaller yet with the same amount of charge, the electric field at its surface would be much more intense.
 * The linked page says nothing like this at all.
 * There is no evidence in any source I have read that "Rutherford had calculated that this volume was too large" before the Geiger Mardsen experiments. Rutherford was an experimentalist: he was trying ideas in the lab to test models of the atom. He didn't know about the strong deflections before they were observed! (Well he knew something was amiss which is why he suggested the experiment to Mardsen). Johnjbarton (talk) 17:29, 17 May 2024 (UTC)

Another good reference.
Another good reference is Niaz emphasizes the critical role of large angle single-scattering as evidence against Thomson atom. To achieve large scattering angles you need a strong force, not possible with multiple scattering from electrons as proposed by Thomson. Johnjbarton (talk) 00:46, 17 May 2024 (UTC)
 * Niaz, Mansoor. "From cathode rays to alpha particles to quantum of action: A rational reconstruction of structure of the atom and its implications for chemistry textbooks." Science Education 82.5 (1998): 527-552. http://websites.umich.edu/~chemstu/content_weeks/F_06_Week4/Thompson_Rutherford_Bohr.pdf

Summary is not.
This article has two major sections: "Summary" and "The Experiments". Please take a look at the article over all and ask yourself: "What if we just deleted the Summary"? In my opinion the article would be instantly improved.

The Summary section is not a "summary" but an entire article: a pre-experiment, result, legacy. It does not summarize but rather randomly repeats.

If we want the material in the Summary we should integrate the material into the corresponding sections of the main article "The experiments".

In fact I think should remove the layer called "The experiments" altogether as redundant with the title. So the article would start with Background as the first major section. The current Summary/Contemporary would merge with Background, minus the parts that aren't background. The current Summary/Outcome and Summary/Legacy would be last in the article. @Kurzon what do you think of this idea? Johnjbarton (talk) 18:32, 17 May 2024 (UTC)


 * I figured I would do a short article and then in the second section I would go into more detail. Kurzon (talk) 19:03, 17 May 2024 (UTC)
 * Ok then I guess I am reporting that such a plan has not worked out. The "short article" is too long and detailed. It's less clear than the "more detail" part of the article. Johnjbarton (talk) 19:21, 17 May 2024 (UTC)
 * Yeeesh, you remind me of my college chemistry professor. I want to make this topic accessible to the layman, so I open with something easy then go into more detailed stuff. Kurzon (talk) 19:51, 17 May 2024 (UTC)
 * Hah, thanks for the compliment ;-)
 * A "Summary" that was accessible would be fine. It would include no math. The context it described would be broader than Thomson's atom because the lay reader may not even know that atoms were unknown at that time. It would explain what "scattering" means and why it was so critical. The legacy section would be focus entirely on the tiny size of the nucleus. Is that what we want? Johnjbarton (talk) 23:56, 17 May 2024 (UTC)

Multiples/ multiplier
I had initially used the word "multiple" myself but after thinking carefully I figured it should be multiplier. 6, 9, 12 are multiples of 3, but if we say x=3 and express those numbers as 2x, 3x, and 4x, then 2, 3, and 4 are the multipliers. Kurzon (talk) 15:31, 18 May 2024 (UTC)


 * The sentence was:
 * In 1908, Rutherford was trying to precisely measure the charge of alpha particles in absolute units (as opposed to multiples of the charge on a hydrogen ion).
 * As we both questioned it I thought to re-write it. But then I read the paragraph and realized the bigger problem. The "charge of alpha particles in absolute units" isn't something Rutherford was looking for. So I reworked the paragraph and now we don't need to worry about multiples. Johnjbarton (talk) 17:22, 18 May 2024 (UTC)

Balancing kinetic with potential energy.
The section "A mathematical look at the Thomson model" has a kind of stopping distance calculation based on work and integrals. Rutherford gets the same point across much more simply by balancing the incoming kinetic energy with the potential energy increase as the alpha particle approaches the nucleus head on. On the third page of his 1911 paper, the third equation gives the KE on the right side and the PE on the left. Since the PE is in terms of a stopping distance b and radius R this approach seems clearer to me. Johnjbarton (talk) 02:40, 19 May 2024 (UTC)

I remember that equation and I didn't understand it. I would appreciate it if you held my hand and walked me through all the steps by which Rutherford arrived at that equation, and how to use it. Kurzon (talk) 09:11, 19 May 2024 (UTC)


 * I added content to Rutherford_scattering concerning this result. Please check. Johnjbarton (talk) 17:30, 22 May 2024 (UTC)

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

Since the electrons are extremely light
I keep taking claims like this out of the article, but they keep coming back: Electrons are light but the 79 electrons in the gold atom have exactly and precisely the same charge as the 79 protons. If you neglect their influence you have to neglect the protons. You can't just pick one. The gold atom cannot be modeled as a heavy sphere of positive charge.
 * Since the electrons are extremely light, their influence can be neglected and the atom can be modeled as a heavy sphere of positive charge.

The impulse model for small angle scattering works because 1) the atomic sphere is filled with negatively charged electrons, 2) the positive charge is tiny compared to the negative charge, 3) the alpha particle penetrates the negative charge sphere and approaches the positive charge. The penetration is the reason the electrons can be neglected. This is what Rutherford says on page 382 of his 1911 paper. Johnjbarton (talk) 15:34, 19 May 2024 (UTC)


 * But in that paper he is modelling an atom with a nucleus, not the Thomson plum pudding model. Kurzon (talk) 16:11, 19 May 2024 (UTC)
 * Thomson model is electrically neutral since gold is neutral. In Thomson's compound or multiple scattering theory the alpha particle only interacts with the electrons. Rather than neglecting them he neglects the positive pudding (for the same reason Rutherford neglects the electrons: too diffuse during the close encounter of the collision). Since the electrons are so light, Thomson needs multiple collisions to get any measurable effect from his theory.
 * The impulse model for scattering works for Rutherford's atom because the nucleus is so small. How small? Very small, and you can get an estimate by using the model for small radii. At large radii the model gives too little scattering and it is physically incorrect. It does not make sense to attempt to justify the model that gives the wrong answer with incorrect physics.
 * That is why I added the "historical" paragraph you deleted. The only way the +79 sphere scattering model is worth discussing is to estimate the radius of the Rutherford nucleus. The impulse scattering for positive sphere was not used by Thomson or on Thomson atoms except to show that a nucleus that big gives unacceptable results. Johnjbarton (talk) 17:57, 19 May 2024 (UTC)
 * I remember reading somewhere that Thomson thought all the mass in the atom came from the electrons and therefore even a small atom needed to have thousands of electrons. Kurzon (talk) 17:59, 19 May 2024 (UTC)
 * Well that would make the small-angle impulse scattering from the positive pudding completely irrelevant and also incorrect. With no mass, the pudding can't resist the alpha particle force; 15 inch artillery shells vs tissue paper. Johnjbarton (talk) 18:07, 19 May 2024 (UTC)
 * I feel like there's a big chunk of information that you assume I know but which I actually don't and that's why you might be popping veins in your head (ah, this does take me back to college chemistry classes). Kurzon (talk) 18:28, 19 May 2024 (UTC)
 * The "popping veins" on my side comes from being unable to understand why an article on Rutherford scattering would invest so much space in applying Rutherford scattering to Thomson atom. It's not a combination that makes sense.
 * There is no such thing as a universal scattering model. Starting with the atomic model you can develop a scattering model.
 * Thomson imagined negative corpuscles in a background of positive jelly. So his scattering model brought the alpha particle close to the negative charge (so Coulomb force of the electron could be strong and the background negative charge neglected). The electron was light so he needed multiple scattering.
 * Rutherford imagined positive corpuscles (nuclei) in a background of negative charge cloud. So his scattering model brought the alpha particle close to the positive charge. The nuclei was massive so he only needed single scattering. (To be sure, he reasoned the opposite direction: he had evidence for single scattering and that requires concentrated force.)
 * For the impulse model it would make sense to ask: How big can the nucleus be and give results consistent with Geiger/Marsden? The impulse scattering model can do that and report a value close to nuclear radii. As part of that you could ask: How silly is the result if we increase nucleus to the size Thomson proposed (full atom)? That order of presentation would make sense.
 * When you apply Rutherford scattering to the Thomson model you are entering fairy-tale land, so you can ignore the constraint on Rutherford scattering that neglects the negative charge. Ignoring the constraint to show that the scattering fails even in that extreme case is fine. What is not fine is claiming that the constraint does not exist up front. Johnjbarton (talk) 19:02, 19 May 2024 (UTC)
 * Eh, ok. I wrote that the electrons have so little mass that the alpha particle will just brush them aside, but if the electrons are held firmly in place by the positive "jelly", then I suppose any electron in the atom would effectively have the same mass as the whole atom. Right? Kurzon (talk) 19:05, 19 May 2024 (UTC)
 * What I am trying to get across is that these considerations are not part of the scattering models. One could work on the full jelly dynamics but that is not what these physicist did. They observed scattering and reasoned that powerful forces were needed. With Coulomb force, that means small radius. Thomson thought the small radius was a small electron; Rutherford showed that the small radius was the small nucleus. At close range the complicated dynamics of the other charge averages to a small effect. There is no reason to invent a story for the parts that don't effect the result. You can't tell if you are right or wrong anyway. Johnjbarton (talk) 19:35, 19 May 2024 (UTC)
 * "Thomson thought the small radius was a small electron" — Did Thomson say this after Rutherford reported the extreme scattering (1909)? Kurzon (talk) 19:43, 19 May 2024 (UTC)
 * Yes, in fact the delay between the 1909 experiment and Rutherford's 1911 paper was caused by papers published by JA Crowther using Thomson multiple scattering in successful analysis of beta particle scattering. Rutherford had an explanation for the alpha particle results but he could not publish them until he could explain the beta scattering without multiple-electron-electron theory. Heilbron, John L. (1968). "The Scattering of α and β Particles and Rutherford's Atom" spends pages on this aspect beginning in the section "Inelastic β Scattering and Thomson's Second Theory" page 274.
 * I think it worth noting that Thomson discovered the electron and focused his work on it; Rutherford was the alpha particle guy. It just turned out that alpha particles were much better for studying the nucleus, a fact they didn't know, not having an understanding of atoms and particles. Johnjbarton (talk) 23:26, 19 May 2024 (UTC)
 * This might be worth mentioning in another part of the article, but not in the mathematical look section. Perhaps in the Rutherford's Structure of the Atom paper section. What I want to know is what Rutherford was thinking when he ran into problems with his Geiger counter back in 1908. He didn't think there should be any scattering of alpha particles at all. He was shocked that it was happening.  Why did he think that?  I'm going by what Hyperphysics did. Their worked example explicitly treats the atom as just a sphere of positive charge. Kurzon (talk) 23:55, 19 May 2024 (UTC)
 * Huh?
 * He didn't think there should be any scattering of alpha particles at all.
 * His experiments were based on scattering of alpha particles! He was not shocked. Many accounts of the Geiger/Mardsen result say Rutherford was shocked by the large angle scattering, but when you read the historical analysis you will see that story was created by Rutherford later, basically to emphasize how critical the large angle scattering was.
 * Rutherford's scattering calculations began in late 1910, see Heilbron 1968, pg 283. Before that only the electron scattering analyzed. And Rutherford's calculations needed to answer much more than simply that the Thomson positive radius too large. That was already clear from the KE vs PE comparison. Rutherford's calculation needed to predict the small angle scattering, the probability distribution with angle, and the beta scattering. See Heilbron pg 290. That is the historic math in the 1911 paper.
 * I think the hyperphysics site just put up something that would fit one slide related to Rutherford/Thomson. They did not pick the most important or historic math, just the one the could fit. Johnjbarton (talk) 02:24, 20 May 2024 (UTC)
 * I think you may right. I just reread Heilbron's history paper and he writes that back in 1906, Rutherford measured alpha particles being scattered by mica sheets by as much as 2 degrees. This is more than what my mathematical demonstration allows. I'll look into it. Kurzon (talk) 07:44, 20 May 2024 (UTC)
 * Look, why don't you just write some mathematical stuff yourself instead of browbeating me? Kurzon (talk) 10:13, 20 May 2024 (UTC)
 * Because I want to come to some agreement rather than just have an edit war. Johnjbarton (talk) 15:29, 20 May 2024 (UTC)
 * Just write a little something here in Talk, or your Sandbox. Kurzon (talk) 15:35, 20 May 2024 (UTC)

I've thought about stuff you said, what do you think of this: T"he Thomson atom is in practical terms uniformly neutral throughout its whole volume because its negative and positive charges are both evenly distributed, and therefore it ought to not deflect an alpha particle. But in the Rutherford atom, the charges are not evenly distributed. The alpha particle passes through a zone of negative charge which is inconsequential due to the minuscule mass of electrons, but then it encounters a zone of intense positive charge that is well anchored by its high mass—this is the nucleus, and it is therefore deflected strongly". Kurzon (talk) 11:17, 20 May 2024 (UTC)


 * Yes, that's fine. Johnjbarton (talk) 15:37, 20 May 2024 (UTC)
 * How then does a thick barrier absorb alpha particles, blocking a beam completely? Why don't the alpha particles go all the way through any thickness? Kurzon (talk) 15:46, 20 May 2024 (UTC)
 * Because thick barriers are not thin. Geiger's gold foils were 400 atoms thin. The probability that an alpha particle will hit a nucleus is small. But thousands such layers have high probability. Johnjbarton (talk) 17:05, 20 May 2024 (UTC)
 * I mean with a Thomson atom. If you have a sheet of Thomson atoms that is sufficiently thick, the alpha particles will all get absorbed.  Why? Kurzon (talk) 17:07, 20 May 2024 (UTC)
 * No one has a sheet of Thomson atoms so I don't understand the question. Johnjbarton (talk) 18:01, 20 May 2024 (UTC)

Okay I just looked at the Rutherford scattering article and saw this:


 * Then deflection angle $Θ$ can be expressed as:
 * $$\begin{align}

\Theta &= 2 \theta_0 - \pi = 2 \arctan b \kappa \\ &= 2 \arctan \frac{Z_1 Z_2 e^2}{4 \pi \epsilon_0 m v_{0}^2 b}. \end{align}$$

And this is what I put in this article:


 * $$\tan \theta = \frac{\Delta p_y}{p_x} < k \frac{q_\alpha q_g}{r^2} \cdot \frac{2r}{v} \cdot \frac{1}{mv}

= 0.000325$$

Aren't they kinda the same thing? Kurzon (talk) 17:59, 20 May 2024 (UTC)


 * Well they should have the same angular and radial dependence and same physical constants since they are both based on Rutherford scattering. And neither one should be applied to Thomson atoms which is the point I have been trying get across.
 * The Rutherford scattering formula fits the data for any radius around 10fm. You can say that it fails to fit the data for 100,000fm. What is incorrect is to describe these formula as models for scattering from Thomson atoms that don't work. A Thomson atom is not a Rutherford atom with radius of 100,000fm because both model involve a negative charge cloud with a 100,000fm radius. That is why I am objecting to the current content. The math is fine, the physics is not. Johnjbarton (talk) 20:16, 20 May 2024 (UTC)
 * I understand better. OK, now tell me about absorption. The Thomson atom can't scatter alpha particles, but a thick wall of them can absorb alpha particles. How does that work in theory? Kurzon (talk) 20:54, 20 May 2024 (UTC)
 * The Rutherford scattering is Elastic scattering, but a moving charge can lose energy by exciting electronic or vibrational modes in the solid. This was not understood at the time but esp. beta particle scattering was partly inelastic scattering. Then the particles lose energy and eventual just stop. They did not measure the outgoing energy so they had no way to know. But there were hints and theories. One of the histories points out that Rutherford was very lucky because natural alpha particles have the right energy to see lots of elastic scattering. (Just to be tedious but more correct, this isn't an issue with a thick wall of Thomson atoms but a consequence of normal atoms with different incoming particle mass and energy. That is why so many different scattering experiments have been done over the decades: different physics emerges from different probes.) Johnjbarton (talk) 21:20, 20 May 2024 (UTC)
 * Should I delete the whole mathematical section? Kurzon (talk) 21:46, 20 May 2024 (UTC)
 * I think you should
 * change the section title to "A mathematical look at Rutherford scattering" or similar.
 * Use radius like 10-30fm. Viola scattering per Rutherford's model!
 * Compare to a large radius, say 100,000fm. Scattering is small. "Even if the Thomson atom had no electrons its spread out positive charge could not scatter alpha particles."
 * This last one is the kind of extreme fairy-tale I mentioned earlier. Very common physics tactic. The difference from the current text is we are not claiming to calculate scattering from a Thompson atom, but merely showing that the Rutherford nucleus cannot be large and match the data.
 * We can take up the work vs PE-KE section after that. Johnjbarton (talk) 22:03, 20 May 2024 (UTC)
 * I guess you did not like my advice :-( Johnjbarton (talk) 02:24, 21 May 2024 (UTC)
 * I think I will reintroduce it in some form after I've had some time to figure things out. Kurzon (talk) 09:04, 21 May 2024 (UTC)

A different hyperphysics slide
"The Thomson Model of the Atom" says This is the dagger for the Thomson electron scattering hypothesis. It does not tell us what the alternative is, but it eliminates Thomson's model. Johnjbarton (talk) 22:19, 20 May 2024 (UTC)
 * The conservation of momentum and energy for an elastic collision dictate that the angle must be less than 90 degrees if the projectile is more massive than the target. But in the Rutherford scattering experiment, Geiger and Marsden showed that 1 in 8000 alpha particles scattered with angle >90 degrees.

Thomson positive sphere
The way I understand it, the positive sphere in the Thomson model also has most of the atom's mass. But I remember reading somewhere that Thomson thought all of the atom's mass is in the electrons, and even a small atom must have thousands of electrons. Is the positive pudding actually without mass? Kurzon (talk) 14:41, 21 May 2024 (UTC)


 * Thomson had several models that evolved as he did more experiments. In 1906 based on beta scattering he thought the atom may have 10,000 electrons. By 1910 the number was more like 100. Presumably the positive mass went in the opposite direction. Johnjbarton (talk) 15:34, 21 May 2024 (UTC)
 * See Heilbron 1968 pg 286 for this. Johnjbarton (talk) 15:35, 21 May 2024 (UTC)
 * I think I'm confused over conservation of momentum. (Man, I need to go back to the basics). In the calculations I showed in the article, does the mass of the atom matter?  As in, if it were an atom of hydrogen instead of gold, how would that affect the deflection angle theta? Kurzon (talk) 15:53, 21 May 2024 (UTC)
 * The hyperphysics version of the Rutherford model assumes the mass of the target (atom) is "infinite" rather than 50 times larger for gold. It won't work for hydrogen, the deflection will be much smaller. (That's why Thomson needed multiple scattering with the electrons). You can see that from the image: the incoming particle moves but the target atom does not and the mass of the atom does not come in to the formula.
 * An important effect of finite atom mass is the energy loss: each collision transfers some energy from the alpha particles. Rutherford treats this in his 1911 paper section 4, "Alteration of velocity in an atomic encounter" using Aluminum as the example.
 * Since Rutherford uses (hyperbolic) orbital mechanics I think the finite mass can be handled to first order by reducing the projectile mass. Again Heilbron discusses something like this in his discussion of scattering on page 270. Johnjbarton (talk) 16:55, 21 May 2024 (UTC)
 * This site:
 * https://www.sjsu.edu/faculty/watkins/scattering2.htm
 * derives the scattering with 'recoil' and concludes
 * "It only differs from the relation derived in the Rutherford analysis in which the target particle is presumed fixed by the term (1+m/M)³ in the denominator."
 * The site refs
 * W.S.C. Williams, Nuclear and Particle Physics, Clarendon Press, Oxford, 1991.
 * so that's a good sign, but I could find a copy to verify. Johnjbarton (talk) 17:27, 21 May 2024 (UTC)
 * How would you modify that equation to take conservation of momentum into account? Write it down here? Kurzon (talk) 17:39, 21 May 2024 (UTC)

anchored in space by its mass
In two places the article uses the metaphor of an "anchor" for inertia. I don't recall ever seeing this in a physics text. An "anchor" implies a tether between two points, one light and one fixed. But as far as we know there is no fixed point or tether. I don't think this metaphor is harmless but of course others may not agree. I've changed this before but it reappeared. Johnjbarton (talk) 18:03, 21 May 2024 (UTC)


 * If that's how you feel I will change it. Kurzon (talk) 18:08, 21 May 2024 (UTC)

Conservation of momentum
Is this a more accurate equation for the deflection of the alpha particle? Kurzon (talk) 14:48, 23 May 2024 (UTC)


 * I think the original formula is fine. 197/(197+4) is 2%. In the case of the Rutherford experiments, the value of r is not known. The errors from estimating r will be much larger than 2%.
 * The value of the impulse model is not accuracy but clarity. I'm thinking of copying part of the content here onto Rutherford scattering because that explanation is completely opaque to me. Johnjbarton (talk) 15:02, 23 May 2024 (UTC)
 * I not only ignored your advice but added the deflection caused by the electrons. Is it wrong? Kurzon (talk) 19:26, 23 May 2024 (UTC)
 * See, a point of confusion for me is that in Thomson's model, the electrons move around in the sphere, pushed and pulled around by the electrostatic forces of the sphere and the other electrons. So if an alpha particle passes by an atom, wouldn't the electrons be drawn towards the alpha particle?  If the electrons were firmly held in place like the sphere was a solid, then yeah your saying that the sphere is neutral makes total sense to me. Kurzon (talk) 20:32, 23 May 2024 (UTC)
 * Thomson's model, by his own words was incomplete. We're just guessing. If an alpha particle "passes by" an atom I would expect only inelastic interaction, excitation, not collision, it's a neutral atom. If the alpha particle passes through, we know what Thomson expected, he and Crowther's wrote several papers. They expected collisions with electrons. Yes the collision is attractive but that only changes the focus of the orbit. Unlike the nuclear case however the electron would be dramatically displaced because of its low mass. That's what it means to be "drawn towards the alpha particle".
 * A detailed, realistic model for scattering from a Thomson atom can't be created because the Thomson atom is not realistic. To create such a model you would try to come up with a potential energy surface for the alpha particle to travel on. The role of the electrons would be summarized in this energy surface. So the surface contains positive background and some kind of net effect for electrons. Scattering problems are all done this way because more than two particles is effectively impossible to solve. See Three-body problem. Johnjbarton (talk) 00:14, 24 May 2024 (UTC)

$$\tan \theta = \frac{\Delta p_y}{p_x} < k \frac{q_\alpha q_g}{r^2} \cdot \frac{2r}{v} \cdot \frac{1}{mv} \cdot \frac{\text{mass of gold atom}}{\text{mass of gold atom + alpha particle}} = 0.000319$$

Tiny atom?
Let's say the Thomson atom's radius was on the order of 10^-15 instead of 10^-10. Would there be alpha particle deflection? Or would there be none because it's still neutral? Kurzon (talk) 01:50, 24 May 2024 (UTC)


 * "None" at the levels detectable with ordinary equipment. In Thomson's model, the scattering particle enters the positive background and closely approaches an electron; in Rutherford's it's a negative background with close approach to the nucleus. I've not read Thomson's primary, only going by the secondary refs. Johnjbarton (talk) 03:13, 24 May 2024 (UTC)
 * I'm confused. You say the Thomson atom should cause no scattering because it's neutral, but you also say that if the alpha particle goes through the atom, it will experience faint scattering due to the electrons. These two things sound contradictory. Kurzon (talk) 08:25, 24 May 2024 (UTC)
 * From the outside the Thomson atom is neutral: it has no long range Coulomb force. Once the particle enters the atom it is in a sea of positive charge so it must have encountered some force to enter. This is neglected as too diffuse. Then it may, in this sea of positive charge, encounter an electron at close range where the 1/r effect causes the Coulomb force to grow. However, the electron suffers most from the interaction because the mass ratio is 1/8000.
 * The story for the Rutherford atom is largely the same, but with the nucleus being the target and the mass ratio favoring scattering of the alpha particle.
 * The penetration of the diffuse plus or minus cloud and the compact target (electron or nucleus) allows the alpha particle to approach the target closely and 1/r grows to give scattering. But the 1/r for a positive sphere the size of an atom never get large. The ratio of radii of atom vs nucleus (or electron) is 100,000. That is the big effect here. Johnjbarton (talk) 15:05, 24 May 2024 (UTC)

OK, on your advice I threw out most of the stuff I previous wrote. Kurzon (talk) 10:08, 24 May 2024 (UTC)

Tell me which of these you prefer:

https://en.wikipedia.org/wiki/Rutherford_scattering_experiments

https://en.wikipedia.org/w/index.php?title=Rutherford_scattering_experiments&oldid=1225419351

Kurzon (talk) 18:37, 24 May 2024 (UTC)


 * Well they both have issues which can be fixed. Overall I prefer the "Rutherford scattering" one as it is closer to the presentation in the 1911 paper featured in the article.
 * I have been working on Rutherford scattering. I think we should move the scattering model there and have a summary in this article. Johnjbarton (talk) 19:12, 24 May 2024 (UTC)
 * I think I'm going to do both approaches. I will put a historically accurate exposition in another part of the article. Kurzon (talk) 22:18, 24 May 2024 (UTC)

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)

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: 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".
 * ...treat it as having infinite mass and ignore the law of conservation of momentum.

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 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). A description of Rutherford's approach is in Rutherford_scattering. 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
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: 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)
 * Moving this to Background as this was not a deliberate attempt to measure alpha particle scattering


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

Your writeup
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 and should be on that Talk page. Johnjbarton (talk) 02:16, 8 June 2024 (UTC)

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. also has a great explanation. &#32; 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 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. &#32; 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:
 * 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. &#32; 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)
 * 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
Johnjbarton (talk) 15:22, 16 June 2024 (UTC)
 * 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.
 * 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.
 * 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.


 * "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. &#32; 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. &#32; 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
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?
I wrote this:

$$\bar F \cdot \mathrm dx = \int_{r}^{\infty } \frac{kq_a q_g}{x^2} \cdot \mathrm dx$$

Would it be better if I wrote:

$$\bar F \cdot \Delta x = \int_{r}^{\infty } \frac{kq_a q_g}{x^2} \cdot \mathrm dx$$ 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? Johnjbarton (talk) 14:40, 25 June 2024 (UTC)
 * 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.

Another unexplained removal
The following reference sentence was removed by @Kurzon without explanation. Why? Johnjbarton (talk) 14:42, 25 June 2024 (UTC)
 * Rutherford worked for almost 2 years before publishing his landmark 1911 paper with a new model for the atom.


 * 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
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 mβ and qβ are the mass and charge of an electron or beta particle. We will replace mβ and qβ with ma and qa 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)

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&deg; (when b = $7 m$).

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
 * $$r_\text{min} = \frac{1}{4\pi \epsilon_0} \cdot \frac{2 q_1 q_2}{mv^2}$$
 * 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)
 * $$\int\limits \frac{kq_a q_g}{R^2} \cdot \cos\varphi \cdot\mathrm \mathrm dt$$
 * 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
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 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 with no extra lines would be useful? Johnjbarton (talk) 22:12, 18 July 2024 (UTC)

NeE
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 = $4.65$ esu, then NeE with a gold atom is $3.41$. But kqQ, where q and Q are in Coulombs, is $1.82$. I don't understand. Kurzon (talk) 22:31, 19 July 2024 (UTC)
 * I guess that $3.4$ will be in dyne-cm2, in CGS units. 1 dyne is $1$ Newtons (per  wikipedia anyway) and 1 m is $1$ cm so I get $3.4$N*m2
 * For kqQ, where q and Q are in Coulombs, $8.987 N·m^{2}/C^{2}$ * $1.26 C$ * $3.2 C$ so about $3.7$N*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)
 * 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
 * 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:
 * Put $$\left(\frac{q_{Au} q_\alpha}{4\pi \epsilon_0}\right)$$ in front of most equations or
 * 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)
 * 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)