I have been taught that the mass of an atom is concentrated of an atom, this can be proved by invoking the fact that very few particles are deflected. However, unless I'm mistaken the deflection is due to electrostatic repulsion. Therefore, couldn't we instead say that the charge density varies with radius such that it's mostly in the Centre, whereas the mass density is very low, and spread out through out the atom and get the same result?

Note:- Rutherford's gold foil experiment = Geiger–Marsden experiments