Ionizing radiation is "stopped" by passing the radiation through matter which becomes ionized.
By definition, ionizing radiation will ionize material that it passes through. Ionization involves transferring energy, so the entity doing the ionizing loses energy.
That is the simple answer. A closer look reveals greater complexity.
One needs to be clear about language to be accurate in the question and answer.
Normally when referring to ionizing radiation, one is referring to high energy particles that are causing the radiation. Normally, when we say such radiation is "stopped" we mean it is diminished to that the harmful effects are insignificant. One does not "stop" such radiation but rather one causes it to lose energy. There will always be a few stray particles with high energy even after the vast majority have lost so much energy that ionization has stopped occurring.
If one wants to "stop" ionizing radiation, then creating a large enough (thick enough) barrier will effectively reduce the radiation to insignificance. Of course, depending on the nature of the radiation, some materials may be more effective than others in removing the energy from the radiation. Though ionization, i.e. exicting or removing electrons of atoms, is an important energy loss process, there are also processes that involve the interaction of the ionizing radiation with the nuclei of the material through which it passes. Bremsstrahlung is one such process and so is simple transfer of kinetic energy from the incident particle to the particle in the material. These kinds of processes are larger or smaller depending on the mass and energy of the "ionizing radiation" and so an effective discussion of how well a material can "stop" ionizing radiation depends on the ionizing radiation itself.
Wearing protective clothing will reduce some forms of radiation and stop other forms all together, if there is a breach of radiation. Reducing the time handling a radioactive source or being in the vicinity will reduce exposure. And finally, storing the source in a thick lead casing should stop most forms, or will reduce strongly penetrating forms such as gamma.
The ONLY way to do that would be to live in a totally different universe, as this one has background radiation of many totally different types everywhere. However cosmological models suggest that all possible universes will have background radiation, so that option is probably out too.
Exposre from an external radiation source can be reduced by: # Decreasing the time of exposure, # Increasing the distance from the source, and # Placing shieldingbetween the source and the exposed person
Using radiation shields, working in glove boxes, using telemanipulators and hot cells, working with the minimum necessary quantity of material, observing working procedures, etc.
Time, Distance, and Shielding.
by shield
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Gamma Radiation
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