Talk:Rutherford scattering experiments

Maths

@Mikhail Ryazanov: 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)

@Mikhail Ryazanov: 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)

@Chetvorno: 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

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

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)

@Leyo: 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

@Ajrocke and Johnjbarton: 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)

@Johnjbarton: 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"?

1. Thomson and Crowther used multiple scattering from (point) electrons, that is not discussed in the article,
2. The hyperphysics-based scattering discussed in the article is based on glazing incidence on a sphere. It uses the Thomson atom radius.
3. The 1911 paper discussed in "Rutherford mathematically models the scattering pattern" uses point scattering.
4. 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)

@Johnjbarton: 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, 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

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)

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

@Johnjbarton: 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)

@Johnjbarton: 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)

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

Since the electrons are extremely light

I keep taking claims like this out of the article, but they keep coming back:

• Since the electrons are extremely light, their influence can be neglected and the atom can be modeled as a heavy sphere of positive charge.

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.

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)

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

Then deflection angle Θ can be expressed as:

$${\begin{aligned}\Theta &=2\theta _{0}-\pi =2\arctan b\kappa \\&=2\arctan {\frac {Z_{1}Z_{2}e^{2}}{4\pi \epsilon _{0}mv_{0}^{2}b}}.\end{aligned}}$$

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

1. change the section title to "A mathematical look at Rutherford scattering" or similar.
2. Use radius like 10-30fm. Viola scattering per Rutherford's model!
3. 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)

A different hyperphysics slide

"The Thomson Model of the Atom" says

• 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.

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)