Just to clarify, when you say "Alpha Particles" and "Beta Particle" are not dangerous unless ingested, what you really mean is, "Alpha Particle EMITTERS" and "Beta Particle EMITTERS" are not too dangerous unless ingested. Once the Alpha Particle or Beta Particle is emitted by decay, it flys off with a given energy until it rams into somethinng (like your DNA). Now, if the emitter is outside your body, your skin will pretty much stop it and unless the source is particularly strong, you're in little danger. But, if you ingest the emitter, then as the Alpha and Beta Particles (Alpha is two protons and two neutrons, if memory serves correctly, basically equivalent to a fast moving helium nuclei with an extra neutron, Beta particles are fast moving, free electrons and positrons).
NOTE: I'm 100% sure you know all of the above and isn't meant to correct you, but, to help clarify for others who might not know. I felt that the way you said, "unless alpha and beta particles are ingested" could be misunderstood by someone who hasn't read about this subject much.