Radiation, either alpha particles or beta particles are sometimes called "ionizing radiation" and it wasn't just a cute name. Pierre Curie saw he could measure radiation given off from a substance by measuring the electrical conductivity between two separated plates. The radioactive particles, traveling through the air, would ionize the air, making it carry more charge. It'll do the same thing to living tissue ... and suddenly charged biomolecule, especially DNA, don't work the way they should. This is what makes alpha and beta particles dangerous to living things.