Relationship between Absorption Intensity and Fluorescence Lifetime of Molecules

TLDR

Fluorescence lifetime equations that relate to absorption intensity are strictly applicable only to atomic systems with sharp transitions. This paper derives a modified formula for fluorescence lifetime that should be valid for broad molecular bands with strongly allowed transitions. The authors compute lifetimes using this formula and compare them with measured lifetimes of various organic molecules in solution. The results agree within experimental error for most molecules, and the authors discuss the formula’s limitations for weak or forbidden transitions.

Abstract

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 1/τ0=2.880×10−9n2〈ν̃f−3〉Av−1(gl/gu) ∫ εdlnν̃,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.