Kinetics (light) Question

Question

For naphthalene in a glassy matrix at 77 K excited to the S1 state, the quantum yield of fluorescence is

0.20, the quantum yield of triplet formation is 0.80, and the quantum yield of phosphorescence is 0.018.

a) Using the measured lifetime of fluorescence of 96 ns, determine the rate constant for

intersystem crossing from S1 to T1.

b) From the measured phosphorescence lifetime of 2.6 s, determine the rate constant for

intersystem crossing from T1 to S0.

Any help I'm glad of from a puzzled MSc. student.

Answer 1

You have a two competing processes from S1, and two-competing processes from T1:

From S1

S1 --> T1 ISC, quantum yield = 0.80

S1 --> S0 fluorescene, lifetime = 96 ns, quantum yield  = 0.20

From T1

T1 --> S0 ISC, quantum yield = 0.80 - 0.018 = 0.782

T1 --> S0 phophorescence, lifetime = 2.6 s, quantum yield = 0.018.

Use the quantum yields as a measure of relative rates for the competing processes, and recognize that the lifetime is just the inverse of the rate constant for each process, since each is first-order.

Start with rate constant for S1 --> T1 ISC.  Relative rate of this ISC process vs. S1 --> S0 fluorescence is 0.80/0.20 = 4.0.  Rate constant for ISC is therefore 4.0x the rate constant of fluorescence, which is 1/96 ns = 1.04 x 10^7 s^-1.  So rate constant for ISC is 4.2 x 10^7 s^-1.

Next, find rate constant for T1 --> S0 ISC.  Relative rate of this ISC process vs. T1 --> S0 phosphoresce is 0.782/0.018 = 43.4.  Rate constant for ISC is therefore 43.4x the rate constant of phosphoresce, which is 1/2.6 = 0.385 s^-1.  So rate constant for ISC is 17 s^-1.