In particle physics, the quantum yield (denoted Φ) of a radiation-induced process is the number of times a specific event occurs per photon absorbed by the system.
Φ ( λ ) = number of events number of photons absorbed {\displaystyle \Phi (\lambda )={\frac {\text{number of events}}{\text{number of photons absorbed}}}}
Applications
Fluorescence spectroscopy The fluorescence quantum yield (FQY) is defined as the ratio of the number of photons emitted to the number of photons absorbed.
Φ = number of photons emitted number of photons absorbed {\displaystyle \Phi ={\frac {\text{number of photons emitted}}{\text{number of photons absorbed}}}}
Fluorescence quantum yield is measured on a scale from 0 to 1.0, but is often represented as a percentage. A quantum yield of 1.0 (100%) describes a process where each photon absorbed results in a photon emitted. Substances with the largest quantum yields, such as rhodamines, display the brightest emissions; however, compounds with quantum yields of 0.10 are still considered quite fluorescent. Quantum yield is defined by the fraction of excited state fluorophores that decay through fluorescence:
Φ f = k f k f + ∑ k n r {\displaystyle \Phi _{f}={\frac {k_{f}}{k_{f}+\sum k_{\mathrm {nr} }}}}
where
Φf is the fluorescence quantum yield, kf is the rate constant for radiative relaxation (fluorescence), knr is the rate constant for all non-radiative relaxation processes. Non-radiative processes are excited state decay mechanisms other than photon emission, which include: Förster resonance energy transfer, internal conversion, external conversion, and intersystem crossing. Thus, the fluorescence quantum yield is affected if the rate of any non-radiative pathway changes. The quantum yield can be close to unity if the non-radiative decay rate is much smaller than the rate of radiative decay, that is kf > knr. Fluorescence quantum yields are measured by comparison to a standard of known quantum yield. The quinine salt quinine sulfate in a sulfuric acid solution was regarded as the most common fluorescence standard, however, a recent study revealed that the fluorescence quantum yield of this solution is strongly affected by the temperature, and should no longer be used as the standard solution. The quinine in 0.1M perchloric acid (Φ = 0.60) shows no temperature dependence up to 45 °C, therefore it can be considered as a reliable standard solution.
Experimentally, relative fluorescence quantum yields can be determined by measuring fluorescence of a fluorophore of known quantum yield with the same experimental parameters (excitation wavelength, slit widths, photomultiplier voltage etc.) as the substance in question. The quantum yield is then calculated by:
Φ = Φ R × I n t I n t R × 1 − 10 − A R 1 − 10 − A × n 2 n R 2 {\displaystyle \Phi =\Phi _{\mathrm {R} }\times {\frac {\mathit {Int}}{{\mathit {Int}}_{\mathrm {R} }}}\times {\frac {1-10^{-A_{\mathrm {R} }}}{1-10^{-A}}}\times {\frac {{n}^{2}}{{n_{\mathrm {R} }}^{2}}}}
where
Φ is the quantum yield, Int is the area under the emission peak (on a wavelength scale), A is absorbance (also called "optical density") at the excitation wavelength, n is the refractive index of the solvent. The subscript R denotes the respective values of the reference substance. The determination of fluorescence quantum yields in scattering media requires additional considerations and corrections.
FRET efficiency Förster resonance energy transfer efficiency (E) is the quantum yield of the energy-transfer transition, i.e. the probability of the energy-transfer event occurring per donor excitation event:
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