A molecule is electronically excited from an S_0 state to an S_2* state with vib

Question

A molecule is electronically excited from an S_0 state to an S_2* state with vibrational excitation and can undergo 4 different decay pathways: fluorescence back to S_0, intramolecular vibrational energy redistribution, internal conversion to S_1, and collisional relaxation. The fluorescence lifetime has been measured to be 50 ns, and the rate constant for collisional relaxation and IVR are 2.0 times 10^4 and 1.05 times 10^6 s^-1, respectively. A pump-probe experiment monitoring the decay of S_2* gives an exponential decay with a time constant of 5 ns. Determine the rate constant for internal conversion. Starting with the rate equation, derive an expression for the population of S_2*, [S_2*], as a function of time. Note: You will have to take a simple integral to do this. What is the quantum yield of fluorescence?

Explanation / Answer

c)

The quantum yield or quantum efficiency is used to measure the probability that a molecule will fluoresce or phosphoresce. For fluorescence and phosphorescence is the ratio of the number of molecules that luminescent to the total number of excited molecules. For highly fluoresce molecules, the quantum efficiency approaches to one.Molecules that do not fluoresce have quantum efficiencies that approach to zero.

Fluorescence quantum yield () for a compound is determined by the relative rate constants (k) of various deactivation processes by which the lowest excited singlet state is deactivated to the ground state. The deactivation processes including fluorescence (kf), intersystem crossing (ki), internal conversion (kic), predissociation (kpd), dissociation (kd), and external conversion (kec) allows one to qualitatively interpret the structural and environmental factors that influence the intensity of the fluorescence. They are related by the quantum yield equation given below:

kfkf+ki+kec+kic+kpd+kdkfkf+ki+kec+kic+kpd+kd

Using this equation as an example to explain fluorescence, a high fluorescence rate (kf) value and low values of the all the other relative rate constant terms (kf +ki+kec+kic+kpd+kd) will give a large , which suggest that fluorescence is enhanced. The magnitude of kf , kd, and kpd depend on the chemical structure, while the rest of the constants ki, kec, and kic are strongly influenced by the environment.

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