Analytical Chem istry - DePauw University

Chapter 10 Spectroscopic Methods615to the ground electronic state without emitting a photon. A related formof radiationless deactivation is an external conversion in which excessenergy is transferred to the solvent or to another component of the sample’smatrix.A final form of radiationless deactivation is an intersystem crossingin which a molecule in the ground vibrational energy level of an excitedelectronic state passes into a higher vibrational energy level of a lower energyelectronic state with a different spin state. For example, an intersystemcrossing is shown in Figure 10.48 between a singlet excited state, S 1 , and atriplet excited state, T 1 .Re l a x a t i o n b y Fl u o r e s c e n c eFluorescence occurs when a molecule in an excited state’s lowest vibrationalenergy level returns to a lower energy electronic state by emitting a photon.Because molecules return to their ground state by the fastest mechanism,fluorescence is observed only if it is a more efficient means of relaxationthan a combination of internal conversions and vibrational relaxations.A quantitative expression of fluorescence efficiency is the fluorescentquantum yield, F f , which is the fraction of excited state molecules returningto the ground state by fluorescence. Fluorescent quantum yields rangefrom 1, when every molecule in an excited state undergoes fluorescence, to0 when fluorescence does not occur.The intensity of fluorescence, I f , is proportional to the amount of radiationabsorbed by the sample, P 0 – P T , and the fluorescent quantum yieldI = kΦ ( P −P) 10.25f f 0 Twhere k is a constant accounting for the efficiency of collecting and detectingthe fluorescent emission. From Beer’s law we know thatPTbC= 10−ε 10.26P0where C is the concentration of the fluorescing species. Solving equation10.26 for P T and substituting into equation 10.25 gives, after simplifyingbCI = kΦ P − − ε0( 1 10 )ff10.27When ebC < 0.01, which often is the case when concentration is small,equation 10.27 simplifies toI = 2. 303kΦεbCP = kP ′ff 0 010.28where k′ is a collection of constants. The intensity of fluorescent emission,therefore, increases with an increase in the quantum efficiency, the source’sincident power, and the molar absorptivity and the concentration of thefluorescing species.Fluorescence is generally observed when the molecule’s lowest energyabsorption is a p p* transition, although some n p* transitions showLet’s use Figure 10.48 to illustrate howa molecule can relax back to its groundstate without emitting a photon. Supposeour molecule is in the highest vibrationalenergy level of the second electronic excitedstate. After a series of vibrationalrelaxations brings the molecule to thelowest vibrational energy level of S 2 , itundergoes an internal conversion into ahigher vibrational energy level of the firstexcited electronic state. Vibrational relaxationsbring the molecule to the lowestvibrational energy level of S 1 . Followingan internal conversion into a higher vibrationalenergy level of the ground state,the molecule continues to undergo vibrationalrelaxation until it reaches the lowestvibrational energy level of S 0 .