= Kasha's rule
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\b[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.<Characterization of electronic transitions in complex molecules by Michael Kasha>[Discussions of the Faraday Society 9, 14–19; printed pp. 14–15]{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 $S_2$ is
$$
\Phi_{2r}=\frac{k_{2r}}{k_{21}+k_{2r}+k_{2x}}.
$$
With 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.
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