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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.

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]

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.