To determine the absorbance corresponding to a percent transmittance of [tex]\( 56.0\% T \)[/tex], we follow these steps:
1. Understand Percent Transmittance:
Percent transmittance [tex]\( \%T \)[/tex] is a measure of how much light passes through a sample. It is given by:
[tex]\[
\%T = \frac{I}{I_0} \times 100
\][/tex]
where [tex]\( I \)[/tex] is the intensity of light passing through the sample, and [tex]\( I_0 \)[/tex] is the intensity of the incident light.
2. Convert Percent Transmittance to Fractional Transmittance:
To use transmittance in our calculations, we convert percent transmittance to fractional transmittance [tex]\( T \)[/tex] by dividing by 100:
[tex]\[
T = \frac{\%T}{100}
\][/tex]
For a percent transmittance of [tex]\( 56.0\% \)[/tex], we have:
[tex]\[
T = \frac{56.0}{100} = 0.56
\][/tex]
3. Calculate Absorbance:
Absorbance [tex]\( A \)[/tex] is related to the transmittance by the logarithmic formula:
[tex]\[
A = -\log_{10}(T)
\][/tex]
Substitute [tex]\( T = 0.56 \)[/tex] into the formula to get:
[tex]\[
A = -\log_{10}(0.56)
\][/tex]
4. Find the Absorbance Value:
Using a calculator or logarithm table, calculate:
[tex]\[
A \approx 0.2518
\][/tex]
Thus, the absorbance corresponding to a percent transmittance of [tex]\( 56.0\% T \)[/tex] is approximately [tex]\( 0.2518 \)[/tex].
