*sigh*
Radiation does not work that way. It is not a particle that you stick in your pocket. You fly in a jet and you have more radiation hit you. When you land you're not walking around radioactive. That radiation hit what it was going to hit and kept going.
Sigh...
And what it hits is how it kills life. Radiation does not kill like a gun. It splits the DNA of your cells so it can no longer reproduce. You die because your old cells die and don't get replaced.
Expose a candy bar to radiation to sterilize it and eat it 5 minutes later without any impact as if you never ate it.
Nuclear radiation consists almost entirely of alpha particles, beta particles and gamma rays. Matter is considered radioactive if it contains unstable atomic nuclei that will decay into these and other products in the process of losing resting mass energy.
Alpha particles are, in essence, the nucleus of a Helium+4 atom: two protons and two neutrons. Alphas produced by alpha decay are fairly slow and do not contain a great deal of energy. They can be stopped by a piece of paper or your skin. However, alphas produced by fission can have much greater energy and will easily pass through your body as well as a great deal of shielding. Alpha emitters (ie, a piece of matter that emits alpha particles) such as plutonium, can do an enormous amount of damage if ingested as they are very effective at ionizing and thus killing tissue. A speck of plutonium dust you can barely see, if swallowed or inhaled, will kill you dead.
Beta particles are simply electrons or positrons (an electron with a positive charge) and are weaker than alpha particles. Then can still ionize tissue, but not as badly as alpahs.
Gamma radiation is simply very high power electromagnetic radiation (eg photons such as those carrying heat, visible light, RF, X-rays, etc). They are just past X-rays in energy content (ie, frequency) and the two are not always clearly delineable. Gamma radiation is ionizing, but not as dangerously as alpha or beta particles, despite the fact that it has much greater penetrating power.
Irradiated food is treated with ionizing electromagnetic radiation (gamma, X-ray or electron beam). The purpose is to slow or stop spoilage by elimination of bacterial agents. Insect pests may also be controlled, but not by killing them as the required dose would be too high. Insects are simply rendered sterile by exposure to low doses and cannot reproduce. Different foods have different tolerances from irradiation and regulatory controls differ from country to country. Germany allows only the irradiation of dried herbs and with a small dose while Brazil allows the irradiation of any food stuff at any dose.
It is physically impossible for electromagnetic irradiation to produce radioactivity in exposed foods. Irradiation can produce chemical changes in foods that can alter taste, appearance and nutritional content. But so does every other method of food preservation (freezing, cooking, salting, etc). The changes wrought by irradiation are demonstrably LESS than those produced by any other means of preservation though at high doses it can produce unique radiolytic (from radiation) products that act as oxidizing radicals. However, there is a common confusion between the risk of radicals in the body and radicals ingested as the latter are destroyed by the digestive process.
Numerous food safety organizations around the world have studied the effect of irradiation on foods and unanimously find the results more than acceptable. The trade-off between spoiled foods vs edible foods with slight changes comes down, objectively, on the side of preservation.
Irradiation will prevent a candy bar from gifting you with unwanted active pathogens, but it will have no impact whatsoever on the candy's ability to make you fat and put you at risk for dental caries.