The myth of radiation coming with a green glow probably comes from the use of radium salts in clock faces in the 19th and early 20th centuries. These salts would fluoresce with a green tint, and since they were energized by their own radiation, rather than from stored light, they would never dim.

That, plus of course the desire to show to the audience that something is dangerous. Highly radioactive substances will indeed glow in air or in water, but the glow appears blue to human eyes, not green. It also means radiation doses which are likely to be deadly unless observed through shielded glass or via a camera.