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)

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)

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)

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)