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Kasha's rule states that appreciable luminescence normally originates from the lowest excited electronic state of a given spin multiplicity. In the familiar molecular notation, fluorescence is usually associated with $S_1$ and phosphorescence with $T_1$, even when absorption initially prepares a higher state. The rule is a spectroscopic regularity, rather than a guarantee that all excited molecules emit.

Michael Kasha presented the underlying classification of electronic transitions in 1950, discussing the connection between radiationless conversion and the lowest emitting level.^[ref] Molecular internal conversion provides a route from a higher electronic state to a lower state of the same multiplicity before appreciable higher-state emission occurs.

An original rate-competition model makes the condition quantitative. For an initially populated $S_2$ state, let $k_{21}$ be conversion to $S_1$, $k_{2r}$ upper-state radiative decay and $k_{2x}$ other loss. The fraction emitting directly from $S_2$ isWith stipulated $k_{21}=10^{12}{\mathrm{s}}^{-1}$, $k_{2r}=10^8{\mathrm{s}}^{-1}$ and no other loss, this fraction is about $10^{-4}$. Fast conversion suppresses upper-state emission even though the molecule absorbs into that state. If conversion is slowed until it competes with radiation, appreciable higher-state emission becomes possible. These values illustrate kinetics, not universal molecular constants.

The rule concerns the emitting electronic state. It does not by itself assert an excitation-wavelength-independent fluorescence quantum yield; that is the separate Kasha-Vavilov rule. Competing photochemistry, intersystem crossing and state preparation can affect the number of emitted photons even when the eventual fluorescence band comes from $S_1$.

A proposed experimental test compares emission spectra after excitation into different absorption bands, correcting for absorbed photon counts and detector response. Similar emission-band shapes support a common emitting state, while time-resolved measurements test whether a fast relaxation precedes emission. A different band requires checking sample purity, distinct species and instrumental artifacts before assigning emission from a higher electronic state.

The rate argument also explains why a rigid drawing of one downward arrow is insufficient evidence. Measure which states are populated, how fast they exchange population and which transitions radiate. This connects an empirical rule with a falsifiable kinetic model, while preserving the distinction between a common behaviour and an exception-free law.

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.

Michael Kasha connected molecular light emission with the structure and competing relaxation of excited states. His 1950 paper formulated the spectroscopic regularity now called Kasha's rule: emission of a given spin multiplicity normally comes from the lowest excited level of that multiplicity.^[ref]

The argument involves rates, rather than a prohibition on preparing a higher excited state. In an original model, a higher state has radiative rate $k_r$ and competing molecular internal conversion rate $k_{ic}$. Its probability of emitting before conversion isChoosing $k_r=10^8{\mathrm{s}}^{-1}$ and $k_{ic}=10^{12}{\mathrm{s}}^{-1}$ gives approximately $10^{-4}$. Most molecules can therefore reach the lower state before emitting even when absorption initially populates the higher state. These are illustrative rates, not measured constants assigned to the 1950 paper. A rate competition also explains why the regularity has conditions and exceptions.

Kasha later coauthored the 1979 investigation with Pradeep K. Sengupta of 3-Hydroxyflavone and quercetin fluorescence. Comparing solution spectra, rigid low-temperature matrices, excitation spectra and isotope substitution supported formation of an emitting tautomer through excited-state proton transfer.^[ref] This distinguishes the electronic state initially reached by absorption from the molecular form that eventually emits. The lesson is experimental: emission colour and lifetime can identify competing pathways that a molecular formula alone cannot reveal.

A radiationless transition changes a system's electronic state without absorption or emission of a photon in that transition. Energy is redistributed among coupled degrees of freedom; it does not disappear. In molecular photophysics, the electronic change can populate vibrational motion before subsequent energy transfer to the surroundings.^[ref]

Molecular internal conversion connects electronic states of the same spin multiplicity, while intersystem crossing connects states of different multiplicity. These must be distinguished from vibrational relaxation within an electronic state and from nuclear internal conversion. A radiationless step need not instantaneously deliver all the electronic energy as heat to a solvent.

A simple competing-rate experiment illustrates why a dark channel can be inferred from light measurements. Suppose an emitting excited population loses members by fluorescence at rate $k_r$ and by nonfluorescent channels at total rate $k_{nr}$. With no population returning,These are the stated one-population assumptions of the fluorescence quantum yield model. For chosen rates $k_r=10^7{\mathrm{s}}^{-1}$ and $k_{nr}=4\times 10^7{\mathrm{s}}^{-1}$, the lifetime is $20\mathrm{ns}$ and the yield is $0.20$. A shorter lifetime here does not mean a larger radiative rate.

With a measured lifetime and yield, the model gives $k_r={\Phi }_f/\tau$ and $k_{nr}=(1-{\Phi }_f)/\tau$. Measuring only an emission intensity is less specific because it also depends on absorbed excitation and detection efficiency. Additional intermediate states, energy transfer or population return require a more complete model; the inferred missing fluorescence does not uniquely identify one radiationless mechanism.

Time-resolved emission paired with transient absorption can therefore test a proposed pathway: the first observes photons from an emitting state, while the second can reveal population in a state that does not emit in the monitored band. A mechanism must account for both signals and their time dependence.

Sequential excited-state population kinetics describes transfer from an initially prepared excited state into another excited state that subsequently decays. The measured rise and decay are consequences of both population flow and the detection model. A single fitted exponential function need not identify a unique molecular step.

Let upper-state loss rate be $a=k_{21}+k_{2x}$, lower-state loss rate $b$ and transfer rate $k_{21}$. Starting with $N_2(0)=N_0$, $N_1(0)=0$,For $a\ne b$,The transfer branching fraction is $k_{21}/a$. If upper-state loss has competing channels, not every initial excitation reaches the lower state.

The equal-rate limit is finite, although the displayed difference quotient looks singular. Taking $a\to b$ givesFor stipulated $a=b=k_{21}=1$ in consistent inverse-time units, the lower population peaks at $t=1$ with value $N_0/e$. The apparent denominator singularity is a numerical representation issue, not infinite population.

For unequal rates, the peak time isWith $a=10^{12}{\mathrm{s}}^{-1}$ and $b=10^8{\mathrm{s}}^{-1}$, it is about 9.21 ps. This differs from the upper-state time constant of 1 ps: a population maximum and a single-step time constant are not interchangeable observations.

An instrument-response limit in sequential population inference enters when observed fluorescence is a convolution of the radiative population signal with the instrument response, plus background. Temporal broadening can obscure a very fast rise. Spectral overlap can also mix upper- and lower-state contributions. A proposed analysis fits the response-convolved model to multiple assigned signals rather than interpreting an unresolved rise as an exact molecular rate.

For same-multiplicity electronic states, molecular internal conversion supplies one physical transfer mechanism. IUPAC defines it as a radiationless transition with vibrational excitation possible in the lower electronic state.^[ref] The equations above are original kinetic models; their parameters require experimental determination for the molecule and conditions studied.