How can Rutherford conclude that most of the atom's mass (as opposed to charge) was concentrated in a central nucleus?

Question

I don't understand how Rutherford can conclude from his scattering experiments that the nucleus's mass is concentrated in the center. I can see why the experiments suggest that the charge is concentrated at the center, and can also see why they suggest that the atom's mass is much bigger than the alpha particle's mass, but I don't see how the logic goes for the mass distribution.

To illustrate, why can't the nucleus be a hollow sphere with most of the mass in (uncharged) surface of the sphere and a small point charge in the center? The alpha particle should still be able to scatter off such a construct, since the electric force dominates the interaction and the surface of the sphere could be permeable (c.f. the Thomson model, where the atom is permeable).

I am looking for an explanation as to why we can deduce the mass distribution from the Rutherford scattering experiments.

Related: How did Rutherford conclude that most of the mass distribution was concentrated in a central nucleus? and How did Rutherford conclude that most of the mass (as well as the positive charge) was concentrated in the nucleus? However, none of the answers to either question address this in detail.

Answer 1

It looks like the answer is that he didn't. He only constrained the charge distribution. Mass distribution is not constrained.

Source

In comparing the theory outlined in this paper with the experimental results, it has been supposed that the atom consists of a central charge supposed concentrated at a point, and that the large single deflexions of the $\alpha$ and $\beta$ particles are mainly due to their passage through the strong central field.

This shows he's only constraining the charge distribution.

He is aware he is dealing with an atom that's significantly more massive than alpha particles:

In cases where the mass of the deflecting atom (for example, hydrogen, helium, lithium) is not very different from that of the $\alpha$ particle, the general theory of single scattering will require modification, for it is necessary to take into account the movements of the atom itself (see section 4).

But at no point does he attempt to model how the mass is distributed in the atom. He models only the concentrated central charge, and acknowledges that it is possible that the charge moves, but it (and the stability of the atom) is not his concern right now:

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.

Answer 2

There are probably other models which could account for the scattering pattern that Rutherford observed - especially if the models allow a separation of charge and mass - but Rutherford chose the simplest possible model that could explain his observations. In this he was applying the principle of Occam's razor:

The simplest explanation is usually the correct one

which has also been paraphrased as

When you hear hoofbeats, think of horses not zebras

Answer 3

To illustrate, why can't the nucleus be a hollow sphere with most of the mass in (uncharged) surface of the sphere and a small point charge in the center? The alpha particle should still be able to scatter off such a construct, since the electric force dominates the interaction and the surface of the sphere could be permeable (c.f. the Thomson model, where the atom is permeable).

How can the mass be disembodied from the point charge? If so, what holds the mass to the charge? Why would the parts of the hollow sphere not fly apart from each other, especially when bombarded with alpha particles?

The permeable bits of a Thomson model atom get crashed and fly apart when high energy particles attack them. Permeability is just a problem when you think hard about this issue.