Quantised energy levels in atoms

An electron bound inside an atom can't have just any energy — it's restricted to a specific ladder of discrete levels, unlike a free particle, which can have any energy at all on a continuous scale.

Jumping between rungs of that ladder is how atoms interact with light. An electron absorbs a photon and jumps to a higher level only if that photon's energy matches the gap between levels exactly — not more, not less. Drop back down to a lower level, and the atom emits a photon carrying away precisely that same energy difference.

This is why heated elements produce sharp, distinctive spectral lines instead of a smooth rainbow of colour: since each element's electrons have their own particular ladder of energy levels, the photon energies — and therefore the exact colours — they can emit or absorb are unique to that element, working almost like a fingerprint.