Editing Fluorescence (section)

=== Lifetime ===
[[File:Jablonski Diagram of Fluorescence Only-en.svg|thumb|[[Jablonski diagram]]. After an electron absorbs a high-energy photon the system is excited electronically and vibrationally. The system relaxes vibrationally, and eventually fluoresces at a longer wavelength than the original high-energy photon had.]]

The fluorescence lifetime refers to the average time the molecule stays in its excited state before emitting a photon. Fluorescence typically follows [[first-order kinetics]]:
: <math> \left[S_1 \right] = \left[S_1 \right]_0 e^{-\Gamma t} </math>
where <math>\left[S_1 \right]</math> is the concentration of excited state molecules at time <math>t</math>, <math>\left[S_1 \right]_0</math> is the initial concentration and [[Gamma|<math>\Gamma</math>]] is the decay rate or the inverse of the fluorescence lifetime. This is an instance of [[exponential decay]]. Various radiative and non-radiative processes can de-populate the excited state. In such case the total decay rate is the sum over all rates:
: <math> \Gamma_{tot}=\Gamma_{rad} + \Gamma_{nrad} </math>
where <math>\Gamma_{tot}</math> is the total decay rate, <math>\Gamma_{rad}</math> the radiative decay rate and <math>\Gamma_{nrad}</math> the non-radiative decay rate. It is similar to a first-order chemical reaction in which the first-order rate constant is the sum of all of the rates (a parallel kinetic model). If the rate of spontaneous emission, or any of the other rates are fast, the lifetime is short. For commonly used fluorescent compounds, typical excited state decay times for photon emissions with energies from the [[Ultraviolet|UV]] to [[near infrared]] are within the range of 0.5 to 20 [[nanoseconds]]. The fluorescence lifetime is an important parameter for practical applications of fluorescence such as [[fluorescence resonance energy transfer]] and [[fluorescence-lifetime imaging microscopy]].