2015-08-21
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The power of fluorescence emission F is proportional to the radiant power is proportional to the radiant power of the excitation beam that is absorbed by the system. The equation below best describes this relationship.
(1)
Since 
f K” is constant in the system, it is represented at K’. The table below defines the variables in this equation.
| Variable | Definition |
| F | Power of fluorescence emission |
| P0 | Power of incident beam on solution |
| P | Power after transversing length b in medium |
| K” | Constant dependent on geometry and other factors |
| f
| Quantum efficiency |
Table 9. Definitions of all the variables defined in the Fluorescence Emission (F) in Equation 1.
Fluorescence emission (F) can be related to concentration (c) using Beer’s Law stating:
(2)
Where 
is the molar absorptivity of the molecule that is fluorescing. Rewriting Equation 2 gives:
(3)
Plugging this Equation 3 into Equation 1 and factoring out P0 gives us this equation:
(4)
The MacLaurin series could be used to solved the exponential term.
(5)
Given that 2.303 
= Absorbance <0.05, all the subsequent terms after the first can be dropped since the maximum error is 0.13%. Using only the first term, Equation 5 can be rewritten as:
(6)
Equation 6 can be expanded to the equation below and simplified to compare the fluorescence emission F with concentration. If the equation below were to be plotted with F versus c, a linear relation would be observed.
(7)
If c becomes so great that the Absorbance > 0.05, the higher terms start to become taken into account and the linearity is lost. F then lies below the extrapolation of the straight-line plot. This excessive absorption is the primary absorption. Another cause of this negative downfall of linearity is the secondary absorption when the wavelength of emission overlaps the absorption band. This occurs when the emission transverse the solution and gets reabsorbed by other molecules by analyte or other species in the solution, which leads to a decrease in fluorescence.
