Eo = Et + Ef + H is the correct expression.

We know  the number of photons in each energy term (the total is given, and the # transmitted and fluoresced have been solved for in a) and b)) and we also know all of the of the wavelengths of these photons, so we now can solve for the heat left in the sample
 

Therefore the heat left in the sample is 0.09 J.

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