# Quantum yield

The quantum yield (Φ) of a radiation-induced process is the number of times a specific event occurs per photon absorbed by the system.

## Applications

The quantum yield for the decomposition of a reactant molecule in a decomposition reaction is defined as:

$\Phi ={\frac {\rm {\#\ molecules\ decomposed}}{\rm {\#\ photons\ absorbed}}}$ Quantum yield can also be defined for other events, such as fluorescence:

$\Phi ={\frac {\rm {\#\ photons\ emitted}}{\rm {\#\ photons\ absorbed}}}$ Here, quantum yield is the emission efficiency of a given fluorophore.

## Examples

Quantum yield is used in modeling photosynthesis:

$\Phi ={\frac {\rm {\mu mol\ CO_{2}\ fixed}}{\rm {\mu mol\ photons\ absorbed}}}$ In a chemical photodegradation process, when a molecule dissociates after absorbing a light quantum, the quantum yield is the number of destroyed molecules divided by the number of photons absorbed by the system. Since not all photons are absorbed productively, the typical quantum yield will be less than 1.

Quantum yields greater than 1 are possible for photo-induced or radiation-induced chain reactions, in which a single photon may trigger a long chain of transformations. One example is the reaction of hydrogen with chlorine, in which as many as 106 molecules of hydrogen chloride can be formed per quantum of blue light absorbed.

In optical spectroscopy, the quantum yield is the probability that a given quantum state is formed from the system initially prepared in some other quantum state. For example, a singlet to triplet transition quantum yield is the fraction of molecules that, after being photoexcited into a singlet state, cross over to the triplet state.

The fluorescence quantum yield is defined as the ratio of the number of photons emitted to the number of photons absorbed. 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:

$\Phi =\Phi _{\mathrm {R} }\times {\frac {\mathit {Int}}{{\mathit {Int}}_{\mathrm {R} }}}{\frac {1-10^{-A_{\mathrm {R} }}}{1-10^{-A}}}{\frac {{n}^{2}}{{n_{\mathrm {R} }}^{2}}}$ where $\Phi$ 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, and n is the refractive index of the solvent. The subscript R denotes the respective values of the reference substance.