Final answer:
The % transmittance is 50%, and the calculated absorbance (using the formula A = -log(T)) is approximately 0.30, as 50% transmittance corresponds to a transmittance of 0.50. However, none of the provided options match the calculated value, indicating an error in the options given.
Step-by-step explanation:
If a solution absorbs 50% of a specific wavelength of light, it means that 50% of the light is transmitted through the solution. Transmittance (T) is the fraction of light that passes through a sample, while absorbance (A) is a measure of the light absorbed by the sample. Transmittance is often expressed as a percentage (%T). The relationship between transmittance and absorbance can be represented by the formula A = -log(T) or A = -log(%T/100). In this case, if the % transmittance is 50%, then T is 0.50 (or 50/100), which gives us:
A = -log(0.50)
Calculating this, we find that A is approximately 0.301. Therefore, the answer to the question is % transmittance = 50%, and absorbance is roughly 0.30 (which is closest to option a).
However, none of the given options match this calculated value exactly. If these are the only options provided for the question, you would typically select the one that most closely resembles the calculated value. Still, since there is an option error, it would be appropriate to seek clarification or to note the discrepancy.