If the percent transmittance for a sample is 50 at 350 nm what is the value of a

Absorbance (A) and transmittance are opposites; when transmittance is large, absorbance is small, and vice versa. They're related by the following equation:

A = log (1/T)

In this case, T = 0, so 1/T approaches infinity. The log of a number approaching infinity will also approach infinity, so A is approaching infinity as well.

This result makes sense; if the percent transmittance is 0, that means all of the incoming light is being absorbed by the sample. In other words, the absorbance is as large as it possibly could be because transmittance is as small as it possibly could be.