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Here: https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiments Some calculations were done to show how JJ Thomson's model predicts alpha particles will be mostly undeflected by the gold foil. There they used the charge of an alpha particle and charge of a gold atom in their calculations, how did they know that?

Did they assume Van den Broek's hypothesis that nuclear charge = atomic number or through some other way? Also they could also have found q/m ratio of alpha particle using a setup similiar to JJ Thomson's cathode ray experiment where he found q/m ratio of electron but I assume that they didn't know the masses of the atoms?

Update:- Wikipedia had this, I dont know how I missed it.

The calculations above use modern measurements, but Rutherford had sufficiently accurate estimates. He assumed that the radius of atoms in general to be on the order of $10^{−10}$ m (perhaps after reading Jean Perrin's studies on Brownian motion[7]) and the positive charge of a gold atom to be about 100 times that of hydrogen (100 e).[8] He knew that gold has an atomic weight of 197. From an experiment in 1906, Rutherford measured alpha particles to have a charge of 2 e and an atomic weight of 4, and alpha particles emitted by radon to have velocity of 1.70×107 m/s.[9] Jean Perrin in 1909 measured the mass of hydrogen to be 1.43×10−27 kg,[10] and if alpha particles are four times as heavy as that, they would have an absolute mass of 5.72×10−27 kg.

I'll look into the papers further

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As for the properties of $\alpha$-particles, there is some information in Rutherford's Nobel lecture:

"Strutt (Lord Rayleigh) in 1901 and Sir William Crookes in 1902 suggested that they might possibly prove to be projected particles carrying a positive charge. I independently arrived at the same conclusion from consideration of a variety of evidence. If this were the case, the $\alpha$-rays should be deflected by a magnetic field. Preliminary work showed that the deflection was very slight if it occurred at all. Experiments were continued at intervals over a period of two years and it was not until 1902, when a preparation of radium of activity 19,000 was available, that I was able to show conclusively that the particles were deflected by a magnetic field, though in a very minute degree compared with the $\beta$-rays. This showed that the $\alpha$-rays consisted of projected charged particles while the direction of deflection indicated that each particle carried a positive charge. The $\alpha$-particles were shown to be deflected also by an electric field and from the magnitude of the deflection, it was deduced that the velocity of the swiftest particles was about 2.5 x $10^9$ cm per second, or one-twelfth the velocity of light, while the value of $e/m$ – the ratio of the charge carried by the particle to its mass – was found to be 5,000 electromagnetic units."

As for the charge of the gold nucleus, it was deduced from the results of scattering of $\alpha$-particles. Several arguments were offered (Rutherford, E.(1911) 'LXXIX. The scattering of $\alpha$ and $\beta$ particles by matter and the structure of the atom', Philosophical Magazine Series 6, 21: 125, 669 — 688), for example,

(a) In the paper of Gelger and Marsden (loc. cit.) on the diffuse refiexion of $\alpha$ particles falling on various substances it was shown that about ~ 1/8000 of the $\alpha$ particles from radium C falling on a thick plate of platinum are scattered back in the direction of the incidence. This fraction is deduced on the assumption that the $\alpha$ particles are uniformly scattered in all directions, the observations being made for a deflexion of about 90$^{\circ}$. The form of experiment is not very suited for accurate calculation, but from the data available it can be shown that the scattering observed is about that to be expected on the theory if the atom of platinum has a central charge of about 100 $e$.

While platinum is close to gold in terms of atomic mass and nucleus charge, there are also some estimates for gold in the same work.

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  • $\begingroup$ In rutherford's lecture link I didn't understand how he found the charge from what you said so im reading the whole thing. he said at the start "Shortly after his discovery of the radiating power of uranium by the photographic method." what is the photographic method? is it a fluorescent screen? $\endgroup$
    – Saif
    Commented Dec 10, 2023 at 10:39
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    $\begingroup$ @Saif : see the description at en.wikipedia.org/wiki/Henri_Becquerel , in the section "Experiments". A photographic plate protected from light by thick black paper was exposed by uranium salts. $\endgroup$
    – akhmeteli
    Commented Dec 10, 2023 at 12:18
  • $\begingroup$ @Saif : "I didn't understand how he found the charge" Without looking further into Rutherford's papers, I suspect the experiments with motion of $\alpha$-particles in electric and magnetic fields provide both the charge and velocity as the electric and magnetic forces depend differently on the velocity. $\endgroup$
    – akhmeteli
    Commented Dec 10, 2023 at 12:30

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