A fluorescent dye dissolved in water absorbs most strongly at

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra · Molecular structure and spectra

Deriving the Spectrum, Ch Electronic spectra of diatomic molecules

Problem

555\,\mathrm{nm}

. Collisions with solvent molecules remove vibrational energy on a picosecond timescale, far faster than the nanosecond fluorescence lifetime, so emission always starts from

v' = 0

of the excited state (Kasha's rule). The Stokes shift for this dye, defined as the wavenumber drop from absorption to emission, is

800\,\mathrm{cm^{-1}}

. ((a)) Explain, using the vertical-absorption, relaxation and vertical-emission picture, why the emission wavelength must be longer than

555\,\mathrm{nm}

rather than equal to it. ((b)) Predict the wavelength of the emission maximum.

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