= Photochemical quantum yield
{title2=$\Phi$}
The \b[photochemical quantum yield] measures the number of specified chemical events per excitation <photon> absorbed by the system. For an integrated product measurement,
$$
\Phi(\lambda)=\frac{N_{\mathrm{product}}}{N_{\mathrm{absorbed\ photons}}}
=\frac{n_{\mathrm{product}}}{n_{\mathrm{absorbed\ photons}}}.
$$
Counts $N$ or amounts of substance $n$ must be used consistently. State the product or reactant-change event, excitation wavelength and experimental conditions. A wavelength-specific yield strictly refers to monochromatic excitation.<IUPAC Compendium of Chemical Terminology, fifth edition (Gold Book) by International Union of Pure and Applied Chemistry>[Entry Q04991: definition, integral/differential quantum yield and monochromatic-excitation note; https://goldbook.iupac.org/terms/view/Q04991/plain .]{ref}
Absorbed and incident light are different denominators. Under the simple transmission model, the fraction absorbed at <absorbance> $A$ is $1-10^{-A}$. If $10\,\mathrm{\mu mol}$ of photons arrive at a sample with $A=1$, then $9\,\mathrm{\mu mol}$ are absorbed, neglecting reflection and scattering. Formation of $3\,\mathrm{\mu mol}$ of the chosen product gives $\Phi=1/3$; dividing by incident exposure instead gives $0.30$. These are invented bookkeeping values, not a measured reaction yield.<IUPAC Compendium of Chemical Terminology, fifth edition (Gold Book) by International Union of Pure and Applied Chemistry>[Entry Q04991: absorbed-flux correction in the differential expression.]{ref}
A measurement therefore combines two calibrations: quantify the chemical change and determine absorbed photon exposure. A differential yield uses the reaction rate divided by <absorbed photon flux>; an integrated yield averages the specified change over an exposure. Changing absorption as products accumulate can make those quantities differ.
<Photoisomerization> supplies one application, but the definition requires the chosen event rather than an assumption that every absorbed photon makes one permanent product. A yield for chemical conversion also differs from a <fluorescence quantum yield>, which counts emitted photons. The numerical example does not impose a universal upper bound on every possible definition of a photochemical event.
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