Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

Appendix D 272
Final solutions for [B ()]:
i.e.
[B ()] = − 1 [A] 0
2 − 1
× − 2 + 1 [A] 0
2 − 1
− 1
= 1 [A] 0
2 − 1
− 1 − 1 [A] 0
2 − 1
× − 2
[B ()] = 1 [A] 0
1 − 2
× ¡ − 2 − − 1 ¢
(C.63)
(C.64)
(C.65)
• In the time-resolved fluorescence measurements, we observe
() ∝ [A ()] + [B ()]
(C.66)
with some unknown factor accounting for the (lower) transition probability of
state B, i.e., the fluorescence-time profile () is
() =[A] 0
− 1 + 1 [A] 0
1 − 2
× ¡ − 2 − − 1 ¢
=[A] 0
− 1 + 1 [A] 0
1 − 2
× − 2 − 1 [A] 0
1 − 2
× − 1
= µ
1 [A] 0
× − 2 + [A]
1 − 0
−
1 [A] 0
× − 1
2 1 − 2
= 2 × − 2 + 1 × − 1
(C.67)
(C.68)
(C.69)
(C.70)
This is the same result as would be obtained by a fit toasumoftwoexponentials
with the rate constants 1 = 1 + 1 and 2 , i.e., time constants
1 =( 1 + 1 ) −1 and 2 = 2 .