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How do quantum energy levels create discrete spectral lines?

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Discrete spectral lines are created by the movement of electrons between specific, allowed quantum states within an atom or molecule. According to quantum mechanics, these systems possess only certain definite energy levels, rather than a continuous range of energies.12

When an atom transitions between these levels, it must gain or lose an exact amount of energy equal to the difference between the two states.12
* Emission: An electron moving from a higher-energy state to a lower-energy state releases the excess energy as a photon.12
* Absorption: An atom absorbs a photon of a specific energy to move from a lower-energy state to a higher-energy state.12

Because the energy of the emitted or absorbed photon is defined by the relationship $E = h ν$ (where $h$ is Planck’s constant and $ν$ is frequency), only specific frequencies—and thus specific wavelengths—are possible. These discrete wavelengths appear as distinct spectral lines when observed through a spectroscope, serving as a unique signature for the elements or molecules involved.123