Photochemical quantum yield ($\Phi$)

The photochemical quantum yield measures the number of specified chemical events per excitation photon absorbed by the system. For an integrated product measurement,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.^[ref]

Absorbed and incident light are different denominators. Under the simple transmission model, the fraction absorbed at absorbance $A$ is $1-10^{-A}$. If $10\mu \mathrm{mol}$ of photons arrive at a sample with $A=1$, then $9\mu \mathrm{mol}$ are absorbed, neglecting reflection and scattering. Formation of $3\mu \mathrm{mol}$ 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.^[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.

Absorbed photon flux is the rate at which a specified sample absorbs photons. Number-based flux counts photons per second; amount-based flux counts moles of photons per second. The absorbed rate differs from the incident rate and supplies the denominator of a rate-based photochemical quantum yield. For monochromatic light passing through a homogeneous absorbing sample,where $q_0$ is incident photon flux and $A(\lambda )$ is the decadic absorbance at the excitation wavelength. Reflection and scattering must be absent or accounted for before transmission loss is interpreted entirely as absorption.^[ref]

For example, $q_0=2\mu \mathrm{mol}{\mathrm{s}}^{-1}$ and $A=0.30$ giveA product-formation rate of $0.20\mu \mathrm{mol}{\mathrm{s}}^{-1}$ would then give photochemical quantum yield approximately $0.20/0.998=0.200$, whereas division by incident flux gives $0.10$. The two calculations answer different questions.

The distinction also matters during an experiment: if absorbance changes as a reactant is consumed, one initial flux value cannot represent the whole exposure. Absorbed photon amount is the time integral of the absorbed rate. If the numerator is a change of concentration per second, divide the total absorbed amount rate by the illuminated sample volume as well. A photon rate, a rate per unit area and a rate per unit volume have different dimensions; the word flux alone should not conceal that distinction.^[ref]