Why does each chemical element produce a characteristic spectrum?

Each chemical element produces a characteristic spectrum because of its unique electronic structure, which is determined by the number and arrangement of electrons surrounding its nucleus.1

According to quantum mechanics, electrons within an atom can only exist in specific, discrete energy levels. When an atom is excited—for example, by heat or an electrical discharge—its electrons move to higher energy states. As these electrons spontaneously return to lower energy levels, they release the excess energy as photons of [electromagnetic radiation].2345

The energy of each emitted photon is exactly equal to the difference between the two energy levels involved in the transition, defined by the relationship $E=h\nu$, where $h$ is Planck’s constant and $\nu$ is the frequency of the light. Because every element has a distinct set of allowed energy levels, the specific frequencies of light emitted act as a unique "fingerprint" or spectral line series, allowing for the identification of the element.35