Where did the myth that radiation glows green come from?

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Probably from radium, which was widely used in self-luminous paint starting in 1908. When mixed with phosphorescent copper-doped zinc sulfide, radium emits a characteristic green glow:

The use of radioluminescent paint was mostly phased out by the mid 1960s. Today, in applications where it is warranted (like spacecraft instrument dials and certain types of sensors, for example), the radiation source is tritium (radioactive hydrogen) or an isotope of promethium, either of which have vastly shorter half lives than radium.

In most consumer products, though, radioluminescence has been replaced by photoluminescence, phosphors that emit light of one frequency after absorbing photons of a difference frequency. Glow-in-the-dark items that recharge to full brightness after brief exposure to sunlight or a flourescent light only to dim again over a couple of hours are photoluminescent, and contain no radiation.

An aside on aging Radium:

By now, most radium paint manufactured early in the 20th century has lost most of its glow, but it’s still radioactive. The isotope of radium used has a half life of 1,200 years, but the chemical phosphor that makes it glow has broken down from the constant radiation—so if you have luminescent antiques that barely glow, you might want to have them tested with a Geiger counter and take appropriate precautions. The radiation emitted is completely harmless as long as you don’t ingest or inhale the radium—in which case it becomes a serious cancer risk. So as the tell-tale glow continues to fade, how will you prevent your ancient watch dial or whatever from deteriorating and contaminating your great, great grandchildren’s home, or ending up in a landfill and in the local water supply?

Even without the phosphor, pure radium emits enough alpha particles to excite nitrogen in the air, causing it to glow. The color isn’t green, through, but a pale blue similar to that of an electric arc.

This glow (though not the color) entered the public consciousness through this early illustration of its appearance in Marie Curie’s lab, and became confused with the green glow of radium paints.

The myth is likely kept alive by the phenomenon of Cherenkov glow which arises when a charged particle (such as an electron or proton) from submerged sources exceeds the local speed of light through the surrounding water.

So in reality, some radionuclides do glow (notably radium and actinium), but not as brightly or in the color people think. Plutonium doesn’t, no matter what Homer Simpson thinks, unless it’s Pu 238—which has such a short half life, it heats itself red hot.