I just watched a self-described "Integrative nutrition and life coach" make the claim that irradiated foods are somehow toxic, poisonous, and bad for you. (This, of course, came along with a healthy dose of conspiracy whaarglebaargle about "western medicine").
By now you know the drill: when someone in my network mutters embarrassingly unscientific nonsense, you guys end up getting either a physics lecture or a molecular biology lecture. Today it's physics.
We irradiate food for two reasons: to kill bacteria (like E. coli and salmonella), and to break down some of the enzymes (like polygalacturonase and phenolase) that cause fruits and vegetables to ripen and brown. Breaking down some portion of those enzymes doesn't halt the ripening process, but it can slow it down, increasing the shelf-stability of the food, thereby increasing safety and reducing waste.
The radioactive substance used to irradiate food is most often Cobalt-60. Cobalt-60 is toxic, but radionuclides never touch the food during the irradiation process. The attached photo is a chunk of Cobalt-60 I have at home (I use it as a gamma source for testing G-M tubes), and you can see that it is safely encased in a non-toxic plastic shield.
When Cobalt-60 decays to Nickel-60, the primary emissions are relatively low energy gamma rays. Part of my "woo peddler's" claims appear to be that Cobalt-60 irradiation will somehow render the food radioactive.
Induced radiation from high-energy (please note the "high-energy") gamma-ray exposure is certainly possible. In order for a gamma ray to induce an atom to become radioactive, it must strike the nucleus of that atom with enough energy to free a neutron. (Technically, in order to induce an atom to become radioactive, you'd usually have to free more than one neutron from the nucleus.). Helium has the lowest nuclear binding energy of any commonly encountered isotope; it would require a gamma ray strike carrying at least 8 MeV (that unit is "Million electron Volts) of energy in order to knock free a neutron.
The gamma rays that are the result of gamma decay in Cobalt-60 carry an energy of around 1.17 MeV.
Low-energy irradiation is a great way to increase the safety of the food supply. It won't make your food toxic, it won't make your food radioactive, and it won't give you extra limbs, cancer, or super-powers.
(I should note that if you were dumb enough to swallow Cobalt-60, the gamma rays are powerful enough to cause chemical (not nuclear) changes in your cells, and you would likely get cancer. Do not eat the radionuclides.