The radii are chosen so that the more distant hemisphere is much farther away than the half-life of the decaying nucleus, times the flight-time of the alpha ray.
And once inside the body, those alpha rays are efficiently lethal, damaging internal tissues and organs and -- as indicated above -- wreaking destructive havoc in the bones.
He had discovered the existence of alpha rays, beta rays, and gamma rays, and had proved that these were the consequence of the disintegration of atoms.
