Plasma isn’t always purple but nitrogen plasma is and air is mostly nitrogen. (Oxygen to a degree adds to the color).
You get the same color when you ionize air in other ways, such as lightning discharge (don’t look directly at the lightning strike).
Each element has its own specific emission spectrum of color, based on the energy in the orbit of the electrons.
You can look at glowing stuff and tell what it is made up out of by looking at the color.
For air it is purple.
Plasma changes color depending on what gases are being plasmafied. Nitrogen plasma is the purple color you see, and since our atmosphere is mostly nitrogen, the lighter makes that purple color. It’s also the same color as lightning because it’s plasma made from the same atmosphere.
Neon lights are orange because neon plasma is orange (other color “neon” lights actually have different gasses in them) fluorescent lights get their distinct color from mercury vapor and one of the noble gases.
It all has to do with how the electrons are arranged around the atom. When electricity flows through the gas, it excites the electrons and they jump up to a higher energy level. They then drop back down, and give up that energy as light. Exactly how far they fall down determines the color of the light. Every element has a unique distance between its energy levels, which is why each element has a unique color when excited into a plasma.
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