# What exactly was the Rutherford model of the atom?

I was recently doing research on the "Rutherford model" of the atom. I found that there seem to be three different accounts of Ernest Rutherford's theory circulating online:

1. Electrons move move randomly in the space around the nucleus. Like here.
2. Electrons orbit the nucleus in rings each containing many electrons. This model appears to be identical to that proposed by Japanese physicist Hantaro Nagaoka (This paper argues that Nagaoka's model has been widely mischaracterized as "Saturnian" when in fact it features a small nucleus and allows for the possibility of rings not lying in the same plane.).
3. The number of electrons in a neutral atom is equal to the atom's atomic number. Electrons orbit the nucleus along solitary paths (or with a partner) like planets orbiting the sun. Like here. This model is very similar to the Bohr model, except that it lacks Bohr's requirement of fixed, discrete orbits. It is what most people think of when they hear the term and is often anachronistically represented as having featured a nucleus containing separate protons and neutrons, even though the structure of the nucleus had not yet been determined.

Which of these is the "Rutherford model?" Did Rutherford propose all three of them (or some subset thereof) at different points in his career? If not, then why is he being given credit for a model/models which he didn't come up with?

• "Consider an atom which contains a charge ±Ne at its centre surrounded by a sphere of electrification containing a charge ±Ne supposed uniformly distributed throughout a sphere of radius R." E. Rutherford, The Scattering of α and β Particles by Matter and the Structure of the Atom, Philosophical Magazine Series 6, vol. 21 May 1911, p. 669-688 lawebdefisica.com/arts/structureatom.pdf Oct 6 '20 at 8:42
• Interestingly, when I was in high school, I think both my chemistry and physics texts (if not, then certainly the physics text) mentioned Sommerfeld's ellipse modification of Bohr's model, which is not mentioned in your #1, and yet Nagaoka's 1904 model is mentioned in your #1 and I'm certain this was nowhere mentioned in my high school texts. Oct 6 '20 at 13:03

"The Rutherford planetary model" was not exactly... anything, it was a vague umbrella term. The inspection of Rutherford's 1911 paper shows that Rutherford did not propose even one of the three OP versions. What he did propose, that there is a positively charged nucleus, does not distinguish among them. He did assume that the electron cloud was spherical, but that was not set in stone. That was it, and he was not much more specific in the book Radioactive substances and their radiations (1913) two years later. But one can hardly expect historical accuracy from the loose pop-sci snippets such as the ones linked. For a more accurate account see Rutherford, Nagaoka, and the nuclear atom.

Most of the 1911 paper is devoted to ruling out the then dominant "plum pudding" model of Thomson. Continuous distribution of the positive charge over the entire atom was inconsistent with the scattering experiments, and Rutherford had to shrink it to the central nucleus to explain them. He does not say much about electrons because their influence on scattering (beyond balancing the charge) is negligible. Indeed, he does not even say definitively that the nucleus is positively charged:

"Consider an atom which contains a charge $$±Ne$$ at its centre surrounded by a sphere of electrification containing a charge $$±Ne$$ [N.B. in the original publication, the second plus/minus sign is inverted to be a minus/plus sign] supposed uniformly distributed throughout a sphere of radius $$R$$, $$e$$ is the fundamental unit of charge, which in this paper is taken as $$4.65\times10^{-10}$$ E.S. unit. We shall suppose that for distances less than $$10^{-12}$$ cm. the central charge and also the charge on the alpha particle may be supposed to be concentrated at a point. It will be shown that the main deductions from the theory are independent of whether the central charge is supposed to be positive or negative. For convenience, the sign will be assumed to be positive. The question of the stability of the atom proposed need not be considered at this stage, for this will obviously depend upon the minute structure of the atom, and on the motion of the constituent charged parts."

Near the end Rutherford did approvingly quote Nagaoka's "Saturnian model" (he knew of Perrin's 1901 planetary model as well, mentioned in the 1913 book). But here again he is non-committal as to how electrons are distributed in it, experiments could not resolve that:

"It is of interest to note that Nagaoka has mathematically considered the properties of the Saturnian atom which he supposed to consist of a central attracting mass surrounded by rings of rotating electrons. He showed that such a system was stable if the attracting force was large. From the point of view considered in his paper, the chance of large deflexion would practically be unaltered, whether the atom is considered to be disk or a sphere."

The last remark concerns the only supposed difference between "the Rutherford model" and Nagaoka's. That Nagaoka was committed to a disk is indeed disputable, but then it is not like Rutherford was really committed to a sphere. As to why he gets the credit, it is similar to Newton being credited for the inverse square law, which many speculated about before him. Nagaoka's model was a mathematical speculation, and there was a host of other models besides, including planetary ones. Rutherford convinced people that something like it was real, at least as far as having a nucleus was concerned.

Bohr in his 1913 paper refers to that same 1911 paper for "the Rutherford's model" and confirms this attitude. As can be seen from his remarks, what mattered was only that the model was nuclear, and discussing what electrons were doing there was moot because any version of it was classically unstable. Contrary to what Rutherford thought about Nagaoka's model, and in contrast to Thomson's model:

"According to this theory, the atoms consist of a positively charged nucleus surrounded by a system of electrons kept together by attractive forces from tile nucleus; the total :negative charge of the electrons is equal to the positive charge of the nucleus. Further, the nucleus is assumed to be the seat of the essential part of the mass of the atom, and to have linear dimensions exceedingly small compared with the linear dimensions of the whole atom. The number of electrons in an atom is deduced to be approximately equal to half the atomic weight. Great interest is to be attributed to this atom-model; for, as Rutherford has shown, the assumption of the existence of nuclei, as those in question, seems to be necessary in order to account for the results of the experiments on large angle scattering of the $$\alpha$$ rays.

...The principal difference between the atom-models proposed by Thomson and Rutherford consists in the circumstance that the forces acting on the electrons in the atom-model of Thomson allow of certain configurations and motions of the electrons for which the system is in a stable equilibrium; such configurations, however, apparently do not exist for the second atom-model."

• In older times it was said that paper never refused ink. Now it is the internet. There is so much historically incorrect stuff out on the web that any serious scholar should consult the original work if they wish to get a true picture. Fortunately, it is also available online. Oct 6 '20 at 14:43
• Thank you, this is very helpful. :) Oct 8 '20 at 0:42

The Nagaokan model was suggested by Nagoaka and who called it the Saturnian model. He proposed it in 1904, contra Thomsons 'plum pudding' model. It might have been more accurately called the planetary model.

In fact, Rutherford credited Nagaoka with the model in his paper of 1911 where he elaborated on his experimental work that showed Nagaoka was justified in his theoretical description of the atomic structure, as far as it was known then.

Neither Nagoaka nor Rutherford called the model after themselves. It was upto their contemporaries and later generations to assign credit where credit is due.