An analyte in an excited state possesses an energy, E 2 , that is greater than its energy when it is in a lower energy state, E 1 . When the analyte returns to its lower energy state—a process we call relaxation—the excess energy, \(\Delta E\) \[\Delta E=E_{2}-E_{1} \nonumber\] is released. Figure 10.1.4 shows a simplified picture of this process. The amount of time an analyte, A , spends in its excited state—what we call the excited state's lifetime —is short, typically 10 –5 –10 –9 s for an electronic excited state and 10–15 s for a vibrational excited state. Relaxation of the analyte's excited state, A *, occurs through several mechanisms, including collisions with other species in the sample, photochemical reactions, and the emission of photons. In the first process, which we call vibrational relaxation or nonradiative relaxation, the excess energy is released as heat. \[A^{*} \longrightarrow A+\text { heat } \nonumber\] Relaxation by a photochemical reaction may involve simple decomposition \[A^{*} \longrightarrow X+Y \nonumber\] or a reaction between A * and another species \[A^{*}+Z \longrightarrow X+Y \nonumber\] In both cases the excess energy is used up in the chemical reaction or released as heat. In the third mechanism, the excess energy is released as a photon of electromagnetic radiation. \[A^{*} \longrightarrow A+h \nu \nonumber\] The release of a photon following thermal excitation is called emission and that following the absorption of a photon is called photoluminescence. In chemiluminescence and bioluminescence, excitation results from a chemical or a biochemical reaction, respectively. Spectroscopic methods based on photoluminescence are the subject of the next section and atomic emission is covered in Chapter 10.7 .