Rutherford's experiment on the scattering of $$\alpha$$-particles, conducted between 1908 and 1913, was groundbreaking in the field of atomic physics. In this experiment, Rutherford and his colleagues, Hans Geiger and Ernest Marsden, aimed a beam of alpha particles (which are positively charged particles) at a thin gold foil and observed their scattering patterns using a fluorescence screen.

The results were surprising and led to a dramatic shift in the understanding of the atomic structure. Most of the alpha particles passed straight through the gold foil, a few were deflected at large angles, and a very small number were deflected backward. This was in stark contrast to the expectations based on the plum pudding model of the atom that was prevalent at the time, which proposed that the atom was a diffuse cloud of positive charge with electrons embedded throughout.

The only way Rutherford could explain the observed scattering patterns was by proposing that the atom consists of a tiny, dense nucleus that contains all of its positive charge and most of its mass. This nucleus is surrounded by a cloud of electrons, which occupies the rest of the atom's volume but contributes negligibly to its mass. The alpha particles were mostly passing through the empty space of the atom, but when they came close to the dense nucleus, they were deflected by its positive charge.

Therefore, Rutherford's experiment showed for the first time that the atom has a nucleus, making the correct answer:

Option C: nucleus.