Yes.
X-rays can ionize atoms so you can get free H+, OH-, and O (2-) ions. Even if they do not recombine they are not dangerous in small amounts.
X-rays and gamma rays are used to irradiate food to kill bacteria and other microorganisms are is a safe procedure used all the time.
Object can become radioactive if they are hit by neutron radiation and the atoms in them are transmuted. The other way is by contamination ie physical transfer of radioactive atoms to it
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