Editing Rutherford scattering experiments (section)

===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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 | footer = This apparatus was designed to accurately measure the scattering pattern of the alpha particles produced by the metal foil (F). The microscope (M) and screen (S) were affixed to a rotating cylinder and could be moved in a full circle around the foil.<ref name=GeigerMarsden1913/>
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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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 | footer = This apparatus was used to measure how the scattering pattern varied in relation to the thickness of the foil, the atomic weight of the material, and the velocity of the alpha particles.  The rotating disc in the centre had six holes which could be covered with foil.<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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