They don’t – radio waves have no adverse effect. No more than visible light, anyways.
It’s UV and up. These are ionizing radiation. See, for the most part, atoms can only interact with one photon at a time. So, no matter how many photons you have, they only really interact one at a time with atoms.
So, if one photon does not carry enough energy to break molecules apart, then it will not cause harm (except through heating, like in a microwave). However, higher-energy radiation has enough energy to break molecules apart in each individual photon, and so it causes damage on the cellular level, shredding DNA and other important parts of your cells.
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