Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 921
τ N. Since Γ = τ N –1, then Γ = 2.5 x 10 8 s –1 . Using the
definition of the quantum yield in eq. 25.1 the nonradiative
decay rate is given by
k nr Γ Q O Γ
Q O
122.5 10 8 s 1
(25.5)
This value of k nr is reasonable because k nr must be significantly
larger than Γ to account for the low value of
Q O = 0.02.
In the presence of SIF the quantum yield increases
4.8-fold to Q m = 0.096. This quantum yield is related
to the total decay rate by
Q m Γ T
Γ T k nr
(25.6)
so that
ΓT Qm knr 1.3 10
1 Qm 9 s1 (25.7)
The radiative decay rate due to the metal is given by
Γ m = Γ T – Γ = 1.05 x 10 9 s. Hence Γ m /Γ = 4.7.
If only 10% of the Rose Bengal is affected, then the
apparent quantum yield (Q A ) is related to the quantum
yield near the SIF and in solution as
Q A 0.90Q O 0.10Q m
(25.8)
Using Q A = 0.096, then Q m = 0.78. The value of Γ T
can be calculated from eq. 25.7, so that Γ T = 4.34 x
10 10 s –1 , and then Γ m = 4.32 x 10 10 s –1 . If only 10% of
the RB population is affected by the SIF, then Γ m /Γ =
173.