Fluorescence Quantum Yield
Relative fluorescence quantum yield against a reference standard: Φ = Φ_ref (F_s/F_ref)(f_ref/f_s)(n_s/n_ref)² with absorbed fractions f = 1 − 10^−A, compared with the absorbance-ratio approximation.
Quantum Yield Φ_s
0.6454
64.5 %, absorptance form
Absorbance-Ratio Approximation
0.6825
A_ref/A_s in place of f_ref/f_s: +5.75 %
Absorbed Fractions f = 1 − 10^(−A)
0.1087 / 0.2057
sample / reference
Refractive-Index Factor (n_s/n_ref)²
1.000
A ≤ 0.1: inner-filter effects small
Φ_s = Φ_ref · (F_s / F_ref) · (f_ref / f_s) · (n_s² / n_ref²), f = 1 − 10^(−A)
F is the integrated, spectrally corrected emission, measured with the same excitation wavelength, slit widths and geometry for sample and reference. f is the fraction of excitation light absorbed; the common A_ref/A_s form is its small-absorbance limit and errs when the two absorbances differ.
Keep A ≲ 0.1 (1 cm cell) so that the excitation is uniform through the cell and reabsorption of the emission is negligible; the absorptance does not correct for either. Recommended standards and their yields are reviewed by Brouwer (2011).
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Comparative method for dilute solutions measured under identical conditions: same excitation wavelength, geometry and detection, isotropic emission, no inner-filter effects or reabsorption.
- Würth C., Grabolle M., Pauli J., Spieles M., Resch-Genger U. (2013). Relative and absolute determination of fluorescence quantum yields of transparent samples. Nat. Protoc. 8, 1535–1550. doi:10.1038/nprot.2013.087
- Brouwer A. M. (2011). Standards for photoluminescence quantum yield measurements in solution (IUPAC Technical Report). Pure Appl. Chem. 83, 2213–2228. doi:10.1351/PAC-REP-10-09-31
- Melhuish W. H. (1961). Quantum efficiencies of fluorescence of organic substances: effect of solvent and concentration of the fluorescent solute. J. Phys. Chem. 65, 229–235 (quinine sulfate 0.546). doi:10.1021/j100820a009