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Absorbed-photon normalization in quantum-yield comparisons compares emitted events with the photons actually absorbed by the sample. The quantum yield uses absorbed photons as its denominator; equal incident optical power does not generally establish equal absorbed photon rates.^[ref]

For monochromatic incident power $P$, excitation wavelength $\lambda$ and absorbance $A$, the idealized absorbed photon flux isThis model assumes that the measured attenuation is attributed appropriately to absorption rather than unaccounted scattering or other optical losses. If background-corrected detected count rate is $D=\eta \Phi {\dot{N}}_{\mathrm{abs}}$, where $\eta$ includes the specified collection and detection efficiency, thenDifferent emission spectra or collection conditions can change $\eta$; treating it as equal requires justification.

An original example uses equal incident powers at 400 and 600 nm, with absorbed fractions $1/2$ and $3/4$. The absorbed photon rates have ratioIf count rates are 10,000 and 22,500 per second at equal detection efficiency, the inferred yield ratio is one. A raw brightness increase by 2.25 is entirely consistent with unchanged fluorescence quantum yield.

The weak-absorption approximation $1-10^{-A}\simeq (\log 10)A$ needs its stated range. At $A={\log }_{10}2$, the exact absorbed fraction is 0.5 while the approximation gives $\log 2\approx 0.693$. Using it here would overestimate absorbed photons by about 39 percent and underestimate the inferred yield.

NIST's primary fluorescence-calibration guide separately treats emission response, excitation-beam intensity and relative quantum-yield measurement, including refractive-index corrections in its comparison model.^[ref] Its framework motivates independently checking excitation and detection corrections. Inner filter effects, photobleaching and chemical changes can also defeat a naive comparison. Normalization corrects a specified measurement model; it should not force the Kasha-Vavilov rule to hold when corrected yields genuinely differ.

The effective area per target for absorbing incident radiation at a specified wavelength. For independent absorbers with number column $N$, the absorption optical depth is $\tau ={\sigma }_{\mathrm{abs}}N$. Absorption does not guarantee a particular chemical product; a channel's quantum yield is also needed in its photolysis rate coefficient.

The Kasha-Vavilov rule states that the quantum yield of luminescence is normally independent of excitation wavelength. IUPAC explicitly notes exceptions.^[ref] The statement concerns emitted photons per absorbed photon, not equal detector counts under equal incident optical power.

An original photon-accounting model writesfor monochromatic incident power $P$, wavelength $\lambda$ and absorbance $A$. Comparing raw fluorescence at different wavelengths without correcting incident photon number and absorbed fraction can therefore give a misleading yield comparison.

For equal incident powers and equal absorbed fractions at 400 and 500 nm, the absorbed photon rates have ratio $500/400=1.25$. A molecule obeying the rule with unchanged yield then emits 25% more photons per second under the 500 nm condition. Unequal raw emission is entirely consistent with equal emitted-per-absorbed-photon yield.

Absorbed-photon normalization in quantum-yield comparisons also needs detector-response correction. The observation system measures a selected fraction of an emission spectrum, not automatically all emitted photons. Keep excitation and emission spectral responses, sample geometry and optical density in the comparison.

The distinction from Kasha's rule is physical as well as verbal. Kasha's rule concerns the emitting electronic state. Suppose a wavelength-dependent fraction $f(\lambda )$ of absorbed excitations reaches the same emitting state, whose radiative and nonradiative rates are $k_r,k_{nr}$. ThenThe same emitting state and band shape can coexist with a wavelength-dependent yield if upstream branching changes. Fast molecular internal conversion can make the simple wavelength-independent approximation useful, but does not prove it for every system.

A proposed experiment compares corrected integrated emission with absorbed photon counts while checking concentration, chemical stability and competing absorption. A persistent excitation-dependent yield after those corrections is a scientific result to explain, rather than something to normalize away by assuming the rule in advance.

In a direct-beam model with an effective ozone cross section $\sigma$, removal of an overlying column $\Delta N$ multiplies the transmitted photodissociation flux by $e^{\sigma \Delta N}$. A real photodissociation coefficient integrates wavelength-dependent cross section, quantum yield and actinic flux, including scattering and the local radiation field.

The steady-state approximation for the excited singlet givesand that for the triplet givesCombining these with the quantum yield definition gives the more general expressionUnder the supplied limit $k_{\mathrm{ISC}}\gg k_F$, this becomesThe approximation is the near-unit triplet formation yield, not an assumption that phosphorescence is the only triplet loss process.

For one specified channel, the photolysis rate coefficient isIt depends on spectral actinic flux, absorption cross section, and channel quantum yield. Solar zenith angle, season, overhead absorbers, clouds and aerosol scattering affect the photon field; branching and collisional quenching affect the chemical yield. Absorption alone does not guarantee the desired dissociation.

Curve A is oxygen photodissociation; curve B is ozone photodissociation. Molecular oxygen needs relatively short-wavelength ultraviolet photons, which are strongly screened at lower altitudes, so its rate increases steeply with height. Ozone can dissociate using longer wavelengths that penetrate much further, producing the much larger, less height-sensitive rate shown by B. The plotted quantity is a first-order coefficient with units ${\mathrm{s}}^{-1}$, rather than a bimolecular rate constant.

The lost ozone-column photolysis shielding is $\Delta N=20(2.69\times 10^{16})=5.38\times 10^{17}\mathrm{molecules}\mathrm{c}{\mathrm{m}}^{-2}$, so its optical-depth decrement is $\sigma \Delta N=0.0538$. Under the stipulated effective-cross-section Beer-Lambert model, the transmitted photodissociation flux increases by $\exp (0.0538)$.

The short-lived oxygen singlet D atom satisfies $[\mathrm{O}({}^{1}D)]\simeq J_{{\mathrm{O}}_3}[{\mathrm{O}}_3]/(k_q[M])$ when quenching dominates. At fixed local ozone, water and air density, hydroxyl radical production is proportional to $J_{{\mathrm{O}}_3}$. ConsequentlyA linear optical-depth approximation would give $5.38\%$. A realistic calculation integrates the wavelength-dependent absorption cross section, quantum yield and actinic flux; clouds and multiple scattering modify the simple transmitted-beam model.

Ozone change can also alter the radiative temperature structure, water vapor and circulation, thereby changing the water reaction channel and the supply of ozone/precursors to the troposphere. If the held-fixed tropospheric ozone assumption is relaxed, altered ozone itself changes the photochemical source of oxygen singlet D atom. These are additional feedbacks, distinct from the isolated UV-transmission calculation above.

In a vertical-beam, effective-wavelength Beer-Lambert law approximation, the optical depth above altitude $z$ is $\tau (z)={\sigma }_{{\mathrm{O}}_2}{N}_{{\mathrm{O}}_2}(z)+{\sigma }_{{\mathrm{O}}_3}{N}_{{\mathrm{O}}_3}(z)$. Using centimetres consistently givesThe transmitted photon flux is proportional to $e^{-\tau }$. If the parent-gas absorption cross section and photodissociation yield are otherwise the same, they cancel in the ratio of photolysis rate coefficients:The corresponding fractions of the unattenuated beam are about $7.52\times 10^{-7}$ and $0.654$. Strong shielding by the overlying oxygen and especially ozone therefore makes destruction vastly faster higher in the stratosphere, even though the molecular absorption properties have not changed.

This numerical ratio uses the intended simplified radiation model. A real photolysis rate coefficient integrates wavelength-dependent actinic flux, absorption cross section and quantum yield. A nonvertical direct beam would use slant optical depth $\tau /\cos \theta$; diffuse scattering and the true solar spectrum would also matter. The supplied effective cross sections do not specify a unique broadband radiative-transfer calculation.

An exciton is a correlated electron–hole pair with a full wavefunction $\Psi ({\mathbf{r}}_e,{\mathbf{r}}_h)$. In strong confinement, a useful leading approximation is a product of lowest electron and hole envelope functions, followed by a Coulomb correction. A spherical hard-wall ground envelope is nodeless, proportional to $\sin (\pi r/R)/r$, and finite at the origin. Finite barriers produce exterior tails.

For a core-shell semiconductor nanocrystal with type-I band alignment, both conduction- and valence-band offsets confine the carriers mainly to the core. Their envelopes penetrate the shell but overlap less with external traps. Chemical surface passivation and spatial separation from defects can suppress nonradiative losses and increase photoluminescence quantum yield. Shell thickness, interfacial quality and strain must be controlled; a defective shell can introduce losses.

A larger shell band gap alone does not guarantee type-I alignment. A staggered type-II band alignment can move one carrier toward the shell, reduce electron–hole overlap and alter lifetime and emission energy. The sketch illustrates the conditional type-I case. In CdSe/ZnS experiments, optical spectra were combined with structural and compositional measurements to test shell-growth interpretations.^[ref]

Photochemistry studies chemical changes initiated or influenced by light. Absorption of a photon can prepare an electronically excited molecule, opening reaction pathways different from those available on its ground-state potential energy surface.^[ref]

The absorbed energy is $E=h\nu$, so changing wavelength changes both which species absorb and which states are reached. Photodissociation of molecular oxygen is an atmospheric example. Absorption alone does not guarantee chemical conversion: relaxation and competing reactions affect the quantum yield. A photon-initiated chain can produce more than one product event per absorbed photon, so a chemical quantum yield need not be at most one.

Photoluminescence is light emission following absorption of incident photons. The excitation first puts matter into excited states; subsequent relaxation can emit at a different wavelength. Fluorescence and phosphorescence are distinct forms whose timing and transition mechanisms differ.

An excitation source, sample, rejection filter and spectrometer form a simple experiment. Place collection optics away from the directly transmitted beam and suppress excitation light before measuring the emission optical spectrum. Recording an empty holder or solvent blank helps identify background. Emission intensity alone does not determine absorption or quantum yield, because collection geometry and nonradiative relaxation also affect the signal.

The first-order rate coefficient for a specified photodissociation channel. It integrates spectral actinic flux, absorption cross section and channel quantum yield. Absorption without dissociation does not contribute to that channel's rate. Its units are inverse time.

Official terminology entry S06004. Describes dependence of photophysical quantum yields on reagent concentration, including the linear dynamic-quenching relation underlying the Stern-Volmer equation.