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When the alpha particle find its way to your inside body so that it can interact directly from inside
alpha particles have week penetrating power that can be stopped with a thin paper of few centimeters in air and no way to penetrate the skin, but gamma rays have strong penetrating power of the human body
Inhalation of alpha partcle or any other ways like swallowing alpha source to the body.
Dear Mohammed,
that's right! Alpha particle will be more dangerous than gamma ray when the alpha particle entered inside the human body by ingestion, injection or inhalation. That's only the way to get Alpha particle more dangerous than gamma ray for us since its penetration is very low and can be stopped by a thin piece of paper.
Best Regards
Ayman