Concentration Dependence of Fluorescence:
A spectrometer method can be put to quantitative analytical application only if the spectral characteristics like position, intensity of a width of the spectral band could be associative to the concentration of the analyte. Let us build a relationship between the fluorescence intensity and the concentration of the analyte. You would recall from the previous unit that, the fluorescence quantum efficiency, φf , is defined by the following expression.
φf = No. of photons emitted/ No. of photons absorbed = Intensity of fluorescen ce/ Intensity of absorption
=> φf = Pf/Pa
On rearranging this equation we get, Pf = ?f Pa
As Pa = P0 - Pt , we may write,
Pf = φf (P0 - Pt ) = φf P0 (1 - Pt/P0)
where,
Po = incident radiant power,
Pt = radiant power of emission spectra,
Pf = fluorescence power, and
φf = quantum yield of fluorescence.
As Pt = P0 e-εbc
You know that,
e-x=1-x/1!+x2/2!+x3/3!+x4/4!.........
Substituting the expansion word in the bracket of the above equation and simplifying, we get the following.
Pf = φf P0 εbc (1- εbc/2!+ (εbc)2/3!)
This, under the conditions of εbc = 0.05, (i.e., by ignoring higher terms) gets simplified to the following.
Pf = φf P0 εbc
According to Eq. the measured fluorescence signal is 0 if the analyte concentration is 0. The signal is a little number for low concentration. Therefore, for low analyte concentration, a fluorescence measurement entails unique a small signal from no signal. Compare it to the absorption spectroscopy where we required measuring a small difference among two large numbers; I and I0. The detection limit in the most favorable cases rarely exceeds 10-8 moles. Whereas, in fluorescence measurements under ideal conditions, the concentrations of the order of 10 -12 moles can be measured.
Keeping all other factors except concentration constant in Eq. 6.4, the final equation comes out to be:
Pf α c
Therefore, the fluorescence intensity of a sample can be used for the concentration determination of the analyte.