Editing Rutherford scattering experiments (section)

==Experiments==
===Alpha particle scattering: 1906 and 1908 experiments===
Rutherford's first steps towards his discovery of the nature of the atom came from his work to understand alpha particles.<ref name=Baily2013/>{{rp|17}}<ref name="Barrette2021"/>{{rp|435}}
In 1906, Rutherford noticed that alpha particles passing through sheets of mica were deflected by the sheets by as much as 2 degrees. Rutherford placed a radioactive source in a sealed tube ending with a narrow slits followed by a photographic plate. Half of the slit was covered by a thin layer of mica. A magnetic field around the tube was altered every 10 minutes to reject the effect of beta rays, known to be sensitive to magnetic fields.<ref name=LeoneRobotti2018>{{Cite journal |last1=Leone |first1=M |last2=Robotti |first2=N |last3=Verna |first3=G |date=May 2018 |title='Rutherford's experiment' on alpha particles scattering: the experiment that never was |url=https://iopscience.iop.org/article/10.1088/1361-6552/aaa353 |journal=Physics Education |volume=53 |issue=3 |pages=035003 |doi=10.1088/1361-6552/aaa353 |bibcode=2018PhyEd..53c5003L |issn=0031-9120|url-access=subscription }}</ref> The tube was evacuated to different amounts and a series of images recorded. At the lowest pressure the image of the open slit was clear, while images of the mica covered slit or the open slit at higher pressures were fuzzy. Rutherford explained these results as alpha-particle scattering<ref name=Heilbron1968/>{{rp|260}} in a paper published in 1906.<ref name=Rutherford1906a>{{Cite journal |last=Rutherford |first=E. |date=August 1906 |title=XIX. Retardation of the α particle from radium in passing through matter |url=https://zenodo.org/records/1430810 |journal=The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science |language=en |volume=12 |issue=68 |pages=134–146 |doi=10.1080/14786440609463525 |issn=1941-5982}}</ref> He already understood the implications of the observation for models of atoms: "such a result brings out clearly the fact that the atoms of matter must be the seat of very intense electrical forces".<ref name=Rutherford1906a/>{{rp|145}}<ref name="Baily2013">{{Cite journal |last=Baily |first=C. |date=January 2013 |title=Early atomic models – from mechanical to quantum (1904–1913) |url=http://link.springer.com/10.1140/epjh/e2012-30009-7 |journal=The European Physical Journal H |language=en |volume=38 |issue=1 |pages=1–38 |doi=10.1140/epjh/e2012-30009-7 |arxiv=1208.5262 |bibcode=2013EPJH...38....1B |issn=2102-6459}}</ref>

{{anchor|1908 experiment}}
[[File:Geiger1908.jpg|upright=1.5|thumb|This apparatus was described in a 1908 paper by Hans Geiger.  It could only measure deflections of a few degrees.]]
A 1908 paper by Geiger, ''On the Scattering of α-Particles by Matter'', describes the following experiment. He constructed a long glass tube, nearly two metres long.  At one end of the tube was a quantity of "[[Radon-222|radium emanation]]" (R) as a source of alpha particles.<ref name=Baily2013/>{{rp|20}}  The opposite end of the tube was covered with a phosphorescent screen (Z).  In the middle of the tube was a 0.9&nbsp;mm-wide slit.  The alpha particles from R passed through the slit and created a glowing patch of light on the screen.  A microscope (M) was used to count the scintillations on the screen and measure their spread.  Geiger pumped all the air out of the tube so that the alpha particles would be unobstructed, and they left a neat and tight image on the screen that corresponded to the shape of the slit.  Geiger then allowed some air into the tube, and the glowing patch became more diffuse.  Geiger then pumped out the air and placed one or two gold foils over the slit at AA.  This too caused the patch of light on the screen to become more spread out, with the larger spread for two layers.<ref name=Baily2013/>{{rp|20}}   This experiment demonstrated that both air and solid matter could markedly scatter alpha particles.<ref name=Geiger1908>[[#refGeiger1908|Geiger (1908)]]</ref><ref name=Baily2013/>{{rp|20}} 
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===Alpha particle reflection: the 1909 experiment===
{{anchor| 1909 experiment}}
The results of the initial alpha particle scattering experiments were confusing. The angular spread of the particle on the screen varied greatly with the shape of the apparatus and its internal pressure. Rutherford suggested that Ernest Marsden, a physics undergraduate student studying under Geiger, 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.<ref name=Baily2013/>{{rp|23}} Although this fraction was small, it was much larger than the Thomson model of the atom could explain.<ref name=Heilbron1968/>{{rp|264}}

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These results where published in a 1909 paper, ''On a Diffuse Reflection of the α-Particles'',<ref name=GeigerMarsden1909/> where Geiger and Marsden described the experiment by which they proved that alpha particles can indeed be scattered by more than 90°. In their experiment, they prepared a small conical glass tube (AB) containing "radium emanation" ([[radon]]), "radium A" (actual radium), and "radium C" ([[bismuth]]-214); its open end was sealed with [[mica]].  This was their alpha particle emitter.  They then set up a lead plate (P), behind which they placed a fluorescent screen (S).  The tube was held on the opposite side of plate, such that the alpha particles it emitted could not directly strike the screen.  They noticed a few scintillations on the screen because some alpha particles got around the plate by bouncing off air molecules.  They then placed a metal foil (R) to the side of the lead plate. They tested with lead, gold, tin, aluminium, copper, silver, iron, and platinum. They pointed the tube at the foil to see if the alpha particles would bounce off it and strike the screen on the other side of the plate, and observed an increase in the number of scintillations on the screen. Counting the scintillations, they observed that metals with higher atomic mass, such as gold, reflected more alpha particles than lighter ones such as aluminium.<ref name=GeigerMarsden1909/><ref name=Baily2013/>{{rp|20}}

Geiger and Marsden then wanted to estimate the total number of alpha particles that were reflected.  The previous setup was unsuitable for doing this because the tube contained several radioactive substances (radium plus its decay products) and thus the alpha particles emitted had varying [[Range (particle radiation)|ranges]], and because it was difficult for them to ascertain at what rate the tube was emitting alpha particles.  This time, they placed a small quantity of radium C (bismuth-214) on the lead plate, which bounced off a platinum reflector (R) and onto the screen.  They concluded that approximately 1 in 8,000  of the alpha particles that struck the reflector bounced onto the screen.<ref name=GeigerMarsden1909/> By measuring the reflection from thin foils they showed that the effect due to a volume and not a surface effect.<ref name=LeoneRobotti2018/> When contrasted with the vast number of alpha particles that pass unhindered through a metal foil, this small number of large angle reflections was a strange result<ref name=GilibertiLovisetti/>{{rp|240}} that meant very large forces were involved.<ref name=LeoneRobotti2018/>
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===Dependence on foil material and thickness: the 1910 experiment===
[[File:Geiger-1910-fig1.GIF|upright=1.5|thumb|This apparatus was described in 1910 paper by Geiger.  It was designed to precisely measure how the scattering varied according to the substance and thickness of the foil.]]
A 1910 paper<ref name=Geiger1910>[[#refGeiger1910|Geiger (1910)]]</ref> by Geiger, ''The Scattering of the α-Particles by Matter'', describes an experiment to measure how the most probable angle through which an alpha particle is deflected varies with the material it passes through, the thickness of the material, and the velocity of the alpha particles. He constructed an airtight glass tube from which the air was pumped out.  At one end was a bulb (B) containing "radium emanation" ([[radon]]-222).  By means of mercury, the radon in B was pumped up the narrow glass pipe whose end at A was plugged with [[mica]].  At the other end of the tube was a fluorescent [[zinc sulfide]] screen (S).  The microscope which he used to count the scintillations on the screen was affixed to a vertical millimetre scale with a vernier, which allowed Geiger to precisely measure where the flashes of light appeared on the screen and thus calculate the particles' angles of deflection. The alpha particles emitted from A was narrowed to a beam by a small circular hole at D.  Geiger placed a metal foil in the path of the rays at D and E to observe how the zone of flashes changed. He tested gold, tin, silver, copper, and aluminium. He could also vary the velocity of the alpha particles by placing extra sheets of mica or aluminium at A.<ref name=Geiger1910/>

From the measurements he took, Geiger came to the following conclusions:<ref name="BelyaevRoss2021"/>{{rp|5}}
* the most probable angle of deflection increases with the thickness of the material
* the most probable angle of deflection is proportional to the atomic mass of the substance
* the most probable angle of deflection decreases with the velocity of the alpha particles

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{{Anchor|1911_paper}}

=== Rutherford's ''Structure of the Atom'' paper (1911) {{anchor|Rutherford's Structure of the Atom paper}} ===
{{See also| #Rutherford scattering}}
Considering the results of these experiments, Rutherford published a landmark paper in 1911 titled "The Scattering of α and β Particles by Matter and the Structure of the Atom" wherein he showed that single scattering from a very small and intense electric charge predicts primarily small-angle scattering with small but measurable amounts of backscattering.<ref name=GilibertiLovisetti/>{{rp|252}}<ref name="Rutherford 1911"/> For the purpose of his mathematical calculations he assumed this central charge was positive, but he admitted he could not prove this and that he had to wait for other experiments to develop his theory.<ref name="Rutherford 1911"/>{{rp|688}}

Rutherford developed a mathematical equation that modelled how the foil should scatter the alpha particles if all the positive charge and most of the atomic mass was concentrated in a point at the centre of an atom.
From the scattering data, Rutherford estimated the central charge ''q<sub>n</sub>'' to be about +100 units.<ref name=Rutherford1911/>

Rutherford's paper does not discuss any electron arrangement beyond discussions on the scattering from Thomson's plum pudding model and Nagaoka's Saturnian model.<ref name=Heilbron1968/>{{rp|303}} He shows that the scattering results predicted by Thomson's model are also explained by single scattering, but that Thomson's model does not explain large angle scattering. He says that Nagaoka's model, having a compact charge, would agree with the scattering data. The Saturnian model had previously been rejected on other grounds. The so-called [[Rutherford model]] of the atom with orbiting electrons was not proposed by Rutherford in the 1911 paper.<ref name=Heilbron1968/>{{rp|304}}

===Confirming the scattering theory: the 1913 experiment===
In a 1913 paper, ''The Laws of Deflexion of α Particles through Large Angles'',<ref name=GeigerMarsden1913/> Geiger and Marsden describe a series of experiments by which they sought to experimentally verify Rutherford's equation. Rutherford's equation predicted that the number of scintillations per minute ''s'' that will be observed at a given angle ''Φ'' should be proportional to:<ref name="BelyaevRoss2021"/>{{rp|11}}
# cosec<sup>4</sup>{{sfrac|''Φ''|2}}
# thickness of foil ''t''
# magnitude of the square of central charge ''Q<sub>n</sub>''
# {{sfrac|1|(''mv''<sup>2</sup>)<sup>2</sup>}}

Their 1913 paper describes four experiments by which they proved each of these four relationships.<ref name=Barrette2021>{{Cite journal |last=Barrette |first=Jean |date=2021-10-02 |title=Nucleus-nucleus scattering and the Rutherford experiment |url=https://www.tandfonline.com/doi/full/10.1080/03036758.2021.1962368 |journal=Journal of the Royal Society of New Zealand |language=en |volume=51 |issue=3–4 |pages=434–443 |doi=10.1080/03036758.2021.1962368 |bibcode=2021JRSNZ..51..434B |issn=0303-6758|url-access=subscription }}</ref>{{rp|438}}

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To test how the scattering varied with the angle of deflection (i.e. if ''s'' ∝ csc<sup>4</sup>{{sfrac|''Φ''|2}}). Geiger and Marsden built an apparatus that consisted of a hollow metal cylinder mounted on a turntable.  Inside the cylinder was a metal foil (F) and a radiation source containing radon (R), mounted on a detached column (T) which allowed the cylinder to rotate independently.  The column was also a tube by which air was pumped out of the cylinder.  A microscope (M) with its objective lens covered by a fluorescent zinc sulfide screen (S) penetrated the wall of the cylinder and pointed at the metal foil. They tested with silver and gold foils. By turning the table, the microscope could be moved a full circle around the foil, allowing Geiger to observe and count alpha particles deflected by up to 150°. Correcting for experimental error, Geiger and Marsden found that the number of alpha particles that are deflected by a given angle ''Φ'' is indeed proportional to csc<sup>4</sup>{{sfrac|''Φ''|2}}.<ref name=GeigerMarsden1913/>

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Geiger and Marsden then tested how the scattering varied with the thickness of the foil (i.e. if ''s'' ∝ ''t''). They constructed a disc (S) with six holes drilled in it.  The holes were covered with metal foil (F) of varying thickness, or none for control.  This disc was then sealed in a brass ring (A) between two glass plates (B and C).  The disc could be rotated by means of a rod (P) to bring each window in front of the alpha particle source (R). On the rear glass pane was a zinc sulfide screen (Z). Geiger and Marsden found that the number of scintillations that appeared on the screen was indeed proportional to the thickness, as long as the thickness was small.<ref name=GeigerMarsden1913/>

Geiger and Marsden reused the apparatus to measure how the scattering pattern varied with the square of the nuclear charge (i.e. if ''s'' ∝ ''Q''<sub>''n''</sub><sup>2</sup>).  Geiger and Marsden did not know what the positive charge of the nucleus of their metals were (they had only just discovered the nucleus existed at all), but they assumed it was proportional to the atomic weight, so they tested whether the scattering was proportional to the atomic weight squared. Geiger and Marsden covered the holes of the disc with foils of gold, tin, silver, copper, and aluminium. They measured each foil's stopping power by equating it to an equivalent thickness of air. They counted the number of scintillations per minute that each foil produced on the screen. They divided the number of scintillations per minute by the respective foil's air equivalent, then divided again by the square root of the atomic weight (Geiger and Marsden knew that for foils of equal stopping power, the number of atoms per unit area is proportional to the square root of the atomic weight). Thus, for each metal, Geiger and Marsden obtained the number of scintillations that a fixed number of atoms produce. For each metal, they then divided this number by the square of the atomic weight, and found that the ratios were about the same.  Thus they proved that ''s'' ∝ ''Q''<sub>''n''</sub><sup>2</sup>.<ref name=GeigerMarsden1913/>

Finally, Geiger and Marsden tested how the scattering varied with the velocity of the alpha particles (i.e. if ''s'' ∝ {{sfrac|1|''v''<sup>4</sup>}}).  Using the same apparatus, they slowed the alpha particles by placing extra sheets of [[mica]] in front of the alpha particle source.  They found that, within the range of experimental error, the number of scintillations was indeed proportional to {{sfrac|1|''v''<sup>4</sup>}}.<ref name=GeigerMarsden1913/>
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===Positive charge on nucleus: 1913===
In his 1911 paper ([[#1911 paper|see above]]), Rutherford assumed that the central charge of the atom was positive, but a negative charge would have fitted his scattering model just as well.<ref name=AIP3>{{harvnb|AIP}}</ref>  In a 1913 paper, Rutherford declared that the "nucleus" (as he now called it) was indeed positively charged, based on the result of experiments exploring the scattering of alpha particles in various gases.<ref name=RutherfordNuttal1913/>

In 1917, Rutherford and his assistant William Kay began exploring the passage of alpha particles through gases such as hydrogen and nitrogen. In this experiment, they shot a beam of alpha particles through hydrogen, and they carefully placed their detector—a zinc sulfide screen—just beyond the range of the alpha particles, which were absorbed by the gas. They nonetheless picked up charged particles of some sort causing scintillations on the screen. Rutherford interpreted this as alpha particles knocking the hydrogen nuclei forwards in the direction of the beam, not backwards.<ref name=AIP3>{{harvnb|AIP}}</ref>