How did Rutherford conclude that most of the mass distribution was concentrated in a central nucleus? I read this link
How did Rutherford conclude that most of the mass (as well as the positive charge) was concentrated in the nucleus?
And understand from it that the scattering pattern is consistent with an alpha particle colliding with a much more massive particle.
Like a billiard ball colliding with a bowling ball, there will be a fraction on billiard balls that bounce back. (unlike two billiard ball collisions where a head on collision never results in a reflection back - unless the impacting billiard ball has a lot of backspin which we ignore in this experiment because alpha particles don’t have backspin)
But why did he conclude that there was only one such particle?
And why did he conclude that it was at the center?
I know that sounds stupid and someone will bring up a symmetry argument. But consider that the distance between the origin of the alpha particle and its collision >>> diameter of massive object it is colliding with. So where the massive object really is in its neighborhood is really unknown. And if you don’t know where it is in its neighborhood, who is to say that the next collision did not occur in a different region of the neighborhood? So the massive particle may have had its one ‘orbit’ or random motion? Or that the next collisions occurred with another massive particle or particles entirely?
 A: There are a few arguments which are part of the answer. 


*

*The assumption of a distributed charge over the atom (Thomson model) is discarded due to the fact that the scattering would only be at very low angles and most of the $\alpha$ particles would pass the thin film almost undisturbed. 

*To have some large scattering angles one needs a "hard" center. And also heavy since the film could be gold (for example) with many nucleons. It was known that the electrons would be lighter and therefore the center of mass would be mostly in the nucleus, and the reduced mass of the system is just the mass of the $\alpha$ particle and the recoil of the nucleus small. 

*Then the nucleus would be the smart choice for the origin of the coordinate system to study the process, since it does not move much and it is the center of mass.

*There is an assumption of spherical symmetry for the charge distribution around the origin in the nucleus but this is because one can assume the nucleus is point-like.  This is tested afterwards; indeed, in the experiment one can ask the minimum distance between the projectile and the nucleus. If the $\alpha$ particle penetrates the nucleus the scattering would also be either non-elastic or involve some other process.  This did not happen, the minimum distance (derived with energy considerations) would be consistent with a point-like charge also centered at the center of mass and also therefore point-like. 

*The other  thing is that the hypothesis and calculations were consistent with the data of the ratio of scattered particles at a given angle, atomic number and so on. 
This is an example of a hypothesis which leads to a calculation for the cross section and then the contrast with data, which was extremely close to the calculation leaving little room for other assumptions. 
A: It was the large angle scattering that at convinced Rutherford that most of the mass of an atom is contained in the nucleus and the interaction was via the Coulomb force.
In the first set of experiments the incoming alpha particle only interacted with the nucleus via the Coulomb force and never got close enough to actually “touch” the nucleus so Rutherford could only give an upper limit to the size of the nucleus.  
Subsequent experiments with lower atomic number nuclei lead to discrepancies between theory and experiment at large angles of scattering ie at closest approach to the nucleus of the alpha particles.  Rutherford was interpreted the discrepancy as being due to the alpha touching the nucleus an interacting with it via a different force.  Such experiments enabled him to estimate the size of the nucleus.  
Much later it was Robert Hofstadter who used electron diffraction to investigate the structure of the nucleus.
