There are different models of the atom that have been improved and changed over the years.
Rutherford fired alpha particles at a thin metal foil. The result of Rutherford's experiment concluded that most of the atom's mass is concentrated in a small region and that the nucleus is positively charged because it repels alpha particles.
Alpha decay, beta decay and gamma radiation are used in smoke alarms, thickness control and radioactive tracers respectively. Alpha radiation has a short range but highly ionising, the opposite is true for gamma radiation.
Nuclear radius can be measured using high energy electron diffraction (which is more accurate) or the distance of cloest approach which equates the kinetic enegry of an alpha particle to the electric potential energy between the alpha particle and the nucleus.