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Misaiel Dominguez

Calculating rate constant of intersystem crossing from Jablonski diagram

I am to calculate the rate constant for $T_1 \to S_0$ intersystem crossing, with reference to the Jablonski diagram attached below. I know this should not be difficult, but for some reason I cannot put the number together to get the correct result.

I have that

$$\Phi_\text{ISC} = \frac{k_\text{ISC}}{\sum_i k_i}$$

where the denominator represents a sum of all decay pathways for the $T_1$ state. However, how can this sum be calculated if we do not know the rate constants to begin with?

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