Nuclear radiation generally consists of three kinds, which we call alpha, beta, and gamma.
Alpha rays can be blocked by a piece of paper, beta by tinfoil, and gamma only by very thick shielding: think meters of concrete or thick lead plates.
So alpha are not dangerous unless you eat them. Your skin easily blocks the rays.
Beta emitters are mostly fine unless you eat them or like, get them smeared on your skin or clothes.
Gamma rays are very dangerous. They are actually a high energy form of electromagnetic radiation. Much higher frequency than your cell phone. In addition to being hard to block, gamma rays are “ionizing” meaning they break chemical bonds when they are absorbed. This is very bad for you. In the short term, high doses can cause organ failure, and in the long term, even relatively small doses can cause cancer.
WiFi, in contrast, is lower frequency and doesn’t have the energy (per photon) to break chemical bonds. It’s in the same frequency band as a microwave oven. If you got hit by a super blast of WiFi radiation, it could heat you up, even burn you if there was enough. WiFi is not considered dangerous because having a mobile phone in your pocket, the heating you get from the radiation is small even compared with the waste heat from the battery and CPU.
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