Talk:Rutherford scattering/Archive 1

No Pictures??
Every other language has nice graphics, but the English version does not. — Preceding unsigned comment added by 141.213.67.134 (talk) 18:08, 10 March 2012 (UTC)
 * Well, WP:SOFIXIT!! Give example of "other language." If the pictures are on Commons for the other languages you read, just stick them in the same places, here. We'll fix captions so the English is good. S  B Harris 18:45, 10 March 2012 (UTC)

Errors in article
The section "Details of calculating nuclear size" doesn't seem to match what Rutherford actually did (see the link to his paper at the bottom of the article). The calculation doesn't make much sense anyway, since:
 * (1) It assumes without justification that the alpha particles don't penetrate the nucleus
 * (2) It only deals with particles that are colliding head-on with the nucleus (Rutherford's actual calculation considers deflection by an angle)
 * (3) It makes the "size of the nucleus" dependent on the velocity of the alpha particles. Rutherford was interested in how spread out the nuclear charge was in the atom, which has nothing to do with the velocity of the alpha particles (which aren't even part of the atom)
 * (4) It makes no mention of the small number of large angle deflections, contradicting the claim earlier in the article that this piece of data was how Rutherford knew the nucleus was small.
 * (5) At best, it could only be an upper bound estimate -- but there's no reason to think it's a good one unless the alpha particles have nearly the energy they'd need to penetrate the nucleus. No justification is given for this assumption.

Either the section needs to be removed, or reworked to address these issues. Either way, unless someone can show it's what Rutherford actually did, it's not relevant to this article. The cited paper of Rutherford's gives an estimate of b (not the estimate given in the article, since Rutherford used a different value of the nuclear charge) but it doesn't claim that b is the size of the nucleus. It just argues that the nucleus is small and localized to the center of the atom, based on various calculations showing that this assumption matches the data on what fraction of particles were deflected by various angles.

Reply: Yes, the mentioned section is indeed wrong, in particular the calculation. The particle is definitely *not* at rest at the point closest to the nucleus, it only has tangential velocity.


 * Actually, I'm quite sure that at closest approach, the alpha particle momentarily has a velocity of 0. Also, if I'm not mistaken, what the article is calculating is the distance of closest approach. ie, the closest distance between an alpha particle and a gold nucleus colliding head on, which then gives the upper bound for the size of the nucleus. So it seems to make sense if you read it carefully. No? Cjsk 13:02, 19 November 2006 (UTC)

The 'closest approach' calculation discussed here is used in A-level textbooks, e.g. Advancing Physics A2 students book, published by Institute of Physics. If anything, the section ought to be titled 'Details of calculating an upper limit on nuclear size' (or something similar but less clunky), thus making it clear that the positive charge in the atom is concentrated within a sphere with a radius much smaller than an atomic radius (Rutherford's original point). This bit of physics in indeed a key one, which is taught from GCSE level upwards in the UK. In the A level physics specification for the course that I teach (OCR B) it says that "Candidates should be able to demonstrate a qualitative understanding of the α-particle scattering experiment and the evidence this provides for the existence, charge and small size of the nucleus." Variations on the experiment include using foil with atoms with smaller nuclear charge (e.g. Al, less large-angle scattering predicted and seen) & using slower α-particles (using mica absorbers, greater deflection predicted and seen). More modern variations of this technique use a beam of electrons directed at a target - the scattering intensity versus angle curve has a minimum in it due to diffraction (unlike the monotonic curve predicted by pure inverse-square Coulomb scattering). JimChampion 22:32, 27 November 2006 (UTC)

Actually, perhaps the section would sit better in the Geiger-Marsden experiment article. This page should be to do with Rutherford scattering (Coulomb scattering). Needs an explanation of the predicted shape of the cross section versus angle graph. JimChampion 22:40, 27 November 2006 (UTC)


 * Agree that what is calculated here by Rutherford in 1911 is "upper limit for nuclear size" for large nuclei. As he knew. Obviously the particles can be stopped before they hit the nucleus if they aren't going fast enough (this is the case for typical 5 MeV alphas and gold-- the potential and kinetic energy to get in as far as you can is easy to calculate) and if that happens (no nucleus hit, but just field repelling), you see a nice smooth angular distribution that goes right up to as close to total 180 degree backscatter, as you can measure it. This is what Rutherford actually saw for gold. So he knew very well he probably wasn't hitting the actual nucleus, or the scattering function would have departed from the smooth curve calculated by pure elastic Coulombic repulsion, at the highest backscatter angles, and it never did for the gold foil experiment. Historically it is interesting that Rutherford (being no fool) did have his grad students in 1919 try the same thing with hydrogen and alphas, and found indeed that they departed from the 1/r potential Coulomb scattering curve, suggesting that they HAD in a sense hit (clunk) against the mechanical (or nuclear force) barrier which did NOT have a 1/r form. That radius where non-coulombic behavior showed up, came out to be something like 3.5 fm for alpha-on-H scatter. Which Rutherford reported, even though at the time he knew neither the alpha or the H radius, though it was reasonable that (at the same nuclear density) one radius was 4^(1/3) of the other. So if you postulate R as radius of a proton and R * 4^(1/3) fm radius of an alpha, you should get R for the total minimal radius of impact as R [1+4^(1/3)] = 2.59 R. Rutherford got a departure from Coulombic scattering at 3.5 fm, which suggests R for the proton is 3.5/2.59 = 1.35 fm. Pretty good for 1919! (Our modern value is 1.2 fm or so). So far as I can tell, THIS 1919 value is the really best first guess at how "large" nuclei and protons "are." You can read about it on page 239 of Pais' Inward Bound (a really good book on 20th century physics history). S  B Harris 03:09, 23 December 2006 (UTC)

Q.In the section "Details of calculating nuclear size" How can the unit of mass be "eV"...? — Preceding unsigned comment added by 165.132.5.87 (talk) 18:10, 18 June 2015 (UTC)

Charge of Particles
It might be useful to add a hint about the charges of the particles in the formula for the differential cross section (i.e. multiply it with $$(Z_1 Z_2)^2$$). —Preceding unsigned comment added by 129.240.80.209 (talk) 10:09, 3 June 2008 (UTC)

particle at rest debate
To Cjsk: umm, sorry, i simply read over the words "for head on collisions". Then the particle will indeed be at rest at the point of closest approach. But isn't it sort of the whole point that the alpha-particles get highly deflected? - 80.143.112.3 16:31, 6 January 2007 (UTC)


 * Yes, but think of that rare totally head on collision where impact parameter is zero (like a metiorite headed straight for Earth). Only with a repulsive force. They get to a closest approach with potential 1/2 mv^2 = q^2/r, and then (whoosh) the alpha is repelled, staight back the way it came, like a billiard ball hitting a bowling ball elastically. So it's scattered back with MAXIMAL deflection-- straight back and with (nearly) the same energy (there's some momentum transfer, but with the large M difference between alphas and gold, not much). It's hard to see those events because they are so rare, but for near-grazing paths, where the cross section is larger because there's more area, it becomes more probable, and yet still with high deflections. At some point, the scattering area gets too big for these, because at high impact parameters-- the closest approach for the alpha path if there was no interaction-- the interaction potential "sideways" becomes larger than the one for "back"). But before that point is reached, there's an angle of maximal numbers of particles seen (this is due, like all these things, to maximizing an equation with two terms). Rutherford could calculate this angle in simple terms of nuclear charge. Interesting, note that the math is just the same if the nucleus is positive or negative. If it's negative, the whole thing looks like gravity, and all you lose is the EXACT head on collisions in which the particles would presumably stick. But with the really dense nucleus, you'd never see those (or if they disappeared out of your dataset, you'd never notice). The rest of the time near-head-on-collisions would look like a spaceship making a hairpin hyperbolic orbit turn around a neutron star (same density as an atomic nucleus), as close as it could go, without hitting it (as in that Larry Niven story, if you've read it). From outside, it would look just about like a collision, but not quite (you couldn't see the hairpin, and the path back would be nearly the same as the path in). Tides would be bad at minimum approach, but alphas wouldn't care. S  B Harris 18:03, 6 January 2007 (UTC)

Nonworking link
Link to Geiger and Marsden paper does not workYehoshua2 (talk) 04:15, 6 December 2009 (UTC)

elastic scattering
Agreed, energy is conserved, but surely the velocity of the particle is not. The scattering serves to change the direction of motion of the particle, doesn't it? —Preceding unsigned comment added by Andrew imperial (talk • contribs) 20:58, 10 December 2009 (UTC)

Infinite density at Θ=0?
So the cross section turns out to be proportional to this, right? csc^4(Θ/2) Csc^4 is infinite at Θ=0, so how does this not lead to an infinite density at the center? For confirmation, Wolfram Alpha gives the integral of csc^4(x) as -1/3 cot(x) (2+csc^2(x)), which is also infinite for x=0.  Λυδ α  cιτγ  03:23, 20 December 2012 (UTC)


 * The cross section does tend to infinity as the deflection angle goes to zero. Of course. What is the total cross section of a star or a naked nucleus, with a coulombic field around it? Infinite! Anything that goes past will be deflected, and the smaller the deflection, the farther away that can happen. So the gravitational cross section of our Sun is infinite. Now, this is not true of an atom, ONLY because at large distances and small angles its bare charge is screened by electrons (which the Rutherford equation doesn't take into account). So real atoms (unlike naked Rutherford nuclei) really have finite cross sections to alphas. But again, not from this equation, which doesn't take that screening into account. There really is a "singularity" there, for tiny, tiny deflection angles, tending to zero deflection. The cross section there for that should go to infinite. In this model, it does (in reality, for real atoms, it doesn't). This model fails for very, very small deflection angles and only works well for particles that penetrate fairly closely to the nucleus so they see its full charge. S  B Harris 05:24, 20 December 2012 (UTC)


 * I see! Awesome, thanks for the explanation.  Λυδ α  cιτγ  06:13, 20 December 2012 (UTC)