Which phenomenon describes the release of energy when electrons fall back to a lower energy state?

The release of energy when electrons fall back to a lower energy state is accurately described by photon emission. When an electron in an atom or a semiconductor absorbs energy, it can move to a higher energy level, creating an excited state. As it returns to its original, lower energy state, the electron must release the excess energy it had gained. This energy is typically emitted in the form of a photon, which is a particle of light. The process of photon emission is fundamental in various optoelectronic devices, such as light-emitting diodes (LEDs) and lasers, where controlled photon release is essential for their operation.

Phonon emission refers to the release of vibrational energy in a crystal lattice and does not involve electromagnetic radiation. Atomic ionization involves the complete removal of an electron from an atom, a process that requires energy input rather than energy release. Electron transfer generally refers to the movement of an electron from one atom or molecule to another, which may or may not involve a change in energy states and is a broader concept not specifically focused on the release of energy as described in the question. Thus, photon emission is the most accurate and relevant term for this phenomenon.