Physics answer: Sunburns are caused by ultraviolet light, a wavelength of light just outside of human vision. All light is a form of electromagnetic radiation.
Infrared has a long wavelength, and it’s just below visual spectrum range. This is considered ‘heat’ wavelength and can cook the upper most layer of skin. The skin absorbs this wavelength and there isn’t really enough specific energy to damage the DNA. Think of the ‘red’ lights at a restaurant used to keep the food warm.
Ultraviolet is above the visual spectrum of light, and has enough energy to pass into the upper layers of skin cells. The wavelength is small enough to get into the cells and start messing with things, sometimes killing or mutating it. (I assume this is why sunburns peel.) Welding can cause UV from the intense white hot welding arc. Welders wear hoods and sleeves to protect from this artificial sunburn.
High energy, short wavelength (eg: x-ray, gamma) radiation can penetrate through to the deeper cells, like organs, and affect DNA, leading to severe mutations and possibly death. (Other posts cover this fairly well.) This can be from a radioactive element – cesium being a common industrial source, or an X-ray tube designed to emit specific high energy waves that will penetrate all but dense metals.
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