Relationship between Absorption Intensity and Fluorescence Lifetime of Molecules

The equations usually given relating fluorescence lifetime to absorption intensity are strictly applicable only to atomic systems, whose transitions are sharp lines. This paper gives the derivation of a modified formula $${\text{1/τ}}_0{\text{=2.880×10}}^{\text{−9}}{n}^2{\mathrm{〈\nu ̃}}_f^{\text{−3}}{〉}_{\mathrm{Av}}^{\text{−1}}{\mathrm{(g}}_l{\mathrm{/g}}_u){\displaystyle \int }\mathrm{\epsilon d}\ln \mathrm{\nu ̃,}$$ which should be valid for broad molecular bands when the transition is strongly allowed. Lifetimes calculated by this formula have been compared with measured lifetimes for a number of organic molecules in solution. In most cases the values agree within experimental error, indicating that the formula is valid for such systems. The limitations of the formula and the results expected for weak or forbidden transitions are also discussed.