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The colour is due to electronic transitions within each atom.

Electrons move up into high energy levels when heated in the fire.

The electrons then move back down into their original state upon cooling in the air around the fire.

When the electrons move down energy levels, specific amounts of energy are released, with the colour of the flame dependent on the wavelength of the light, which in turn depends on the distance (number of energy levels) that the electrons have to fall.

Try searching on YouTube for flame tests (I find "Mrericsully"'s videos to be quite good) for more similar reactions, particularly involving alkali earth metals

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