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How do emission spectra reveal the energy levels of atoms and molecules?

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A horizontal gradient bar displays the visible light spectrum from violet to red, labeled with corresponding frequency in terahertz, wavelength in nanometers, and photon energy in electron volts. — light When white light is spread apart by a prism or a diffraction grating, the colours of the visible spectrum appear. The colours vary according to their wavelengths. Violet has the highest frequencies and shortest wavelengths, and red has the lowest frequencies and the longest wavelengths.

Emission spectra reveal the discrete energy levels of atoms and molecules because these systems exist in specific quantum states with well-defined energies.12

When atoms or molecules are excited—typically via flames, electrical discharges, or collisions—they are promoted to higher energy states. As these particles spontaneously relax back to lower energy levels, they release the excess energy as electromagnetic radiation in the form of a photon. The energy of this photon ( $E$ ) corresponds exactly to the difference between the two energy levels ( $Δ E = E_{u p p e r} - E_{l o w e r}$ ).134

Because the relationship between photon energy and frequency ( $ν$ ) is defined by the equation $E = h ν$ (where $h$ is Planck’s constant), the frequency and wavelength of the emitted light are directly determined by the atom's internal energy structure. By measuring these characteristic spectral lines, scientists can work backward to map the unique energy levels of a given atom or molecule, effectively using the spectrum as a "fingerprint" for identification.154