Copper, like most metals, oxidizes in the presence of air. Iron is a common example when it rusts.
The oxides of copper further react with water, carbon dioxide, and other gasses floating around to create the signature green color also known as a patina. The green is due to how those compounds interact with the light. Color is basically what doesn’t get absorbed and is instead bounced back to your eyes. If you think about the molecules like a coffee filter, they hold back all the colors (coffee grounds) that don’t make the greenish color (coffee).
Your question is, at it’s heart, about how materials get their color.
It’s down to electrons. There are complex rules that govern how far electrons can go around the nucleus of atoms.
When light hits an atom, it really hits the top most (called valence) electron. When this electron absorbs the light photon, it gets energized and jumps away from the nucleus into a higher orbit.
After some time, the electron emits another light photon. This could have the same energy (and thus, same color) as the one it absorbed; thus falling back to it’s original orbit.
It’s also possible that the electron emits a photon of lower energy (and different color) and fall into an intermediate orbit.
It’s also possible that the electron was already in a slightly higher orbit (electrons are in the lowest possible orbit only if the temperature is absolute zero, or -273.15 Celsius. Since real world can never get that cold, electrons are generally in a higher orbit). Thus, absorbing the photon makes it go even higher and it ends up emitting a photon of higher energy (and color) than the one it absorbed. Incidentally, scientists use this method, called laser cooling to cool substances to very close to absolute zero.
The electrons in neutral copper atom emit brownish red photons.
The electrons in oxidized copper ions emit greenish blue photons.
This attributes to their color.
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