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What determines the harmfulness of radiation: Ionizing Power or Penetrating power?
Ionizing Power:When a radiation particle interacts with atoms, the interaction can cause the atom to lose electrons and thus become ionized. Because of the large mass of the alpha particle which is nothing but a Helium nucleus, it has the highest ionizing power and the greatest ability to damage tissue.
Penetrating Power:The capacity of a radiation beam to penetrate through a medium is its penetrating power. Because of the large size of alpha particles it can be stopped by a sheet of paper. Hence, bigger the size of radiation particles lesser is the penetrating power.

The following table gives a quantitative comparison of alpha beta and gamma particles in terms of their ionizing power and penetrating power.

We have understood that alpha particles have thehighest ionizing power and gammarays have thehighest penetrating power.So, which one do you think is more harmful?
Gamma rays are the most harmful source of External Radiation, as a gamma source lying close to you can cause radiation damage depending on the extent of exposure.Alpha rays are on the other hand are the most dangerous source of Internal Radiationif an alpha source manages to enter our body. Alpha particles can be easily blocked on the outside but once inside the body, it can be extremely dangerous.