Chapter 15, Problem 15.1P

Interpretation Introduction

Interpretation:

The percent transmittance and absorbance for the given sample are to be calculated from the given data.

Concept introduction:

UV–vis spectroscopy uses light from the UV and visible regions of the spectrum. These wavelengths range from $200-800$ nm.

At each wavelength, the intensity of light that reaches the detector (${\text{I}}_{\text{detected}}$) is measured and compared with the initial intensity of light radiation from the source (${\text{I}}_{\text{source}}$). At certain wavelengths, the sample (analyte) might interact with the light. The fraction of light may be transmitted, absorbed, and scattered through the sample. The fraction of transmitted light is detected by the detector in which case ${\text{I}}_{\text{detected}}$ would be smaller than ${\text{I}}_{\text{source}}$. The percent transmittance ($\text{\%T}$) is calculated according to the equation: ${\text{\%T = (I}}_{\text{detected}}{\text{/I}}_{\text{source}}\text{) × 100}$.

The percent transmittance is converted to the corresponding absorbance by using the following equation:

${\text{A = - log(I}}_{\text{detected}}{\text{/I}}_{\text{source}}\text{) = 2 - log(\%T)}$.

Answer to Problem 15.1P

The calculated percent transmittance for the given sample is $\text{25\%}$.

The calculated absorbance for the given sample is $\text{0}\text{.60}$.

Explanation of Solution

It is given that the intensity of the radiation from the source (${\text{I}}_{\text{source}}$) is $\text{1}{\text{.0 × 10}}^{\text{-4}}\text{ W}$ and the intensity of radiation exiting the sample (${\text{I}}_{\text{detected}}$) is $\text{2}{\text{.5 × 10}}^{\text{-5}}\text{ W}$.

The percent transmittance ($\text{\%T}$) is calculated according to the equation: ${\text{\%T = (I}}_{\text{detected}}{\text{/I}}_{\text{source}}\text{) × 100}$.

Thus, by putting all given values we get

$\begin{array}{l}{\text{\%T = (I}}_{\text{detected}}{\text{/I}}_{\text{source}}\text{) × 100}\\ \text{ = (2}{\text{.5×10}}^{\text{-5}}\text{/1}{\text{.0×10}}^{\text{-4}}\text{) × 100 \%}\\ \text{ = 25 \%}\end{array}$

Thus, the calculated percent transmittance for the given sample is $\text{25\%}$.

The percent transmittance is converted to the corresponding absorbance by using the following equation:

$\begin{array}{l}{\text{A = - log(I}}_{\text{detected}}{\text{/I}}_{\text{source}}\text{) }\\ \text{ = 2 - log(\%T)}\\ \text{ = 2 - log(25)}\\ \text{ = 2 - 1}\text{.39794}\\ \text{ = 0}\text{.60}\end{array}$

Thus, the calculated absorbance for the given sample is $\text{0}\text{.60}$.

Conclusion

The percent transmittance and absorbance for the given sample are calculated from the given data by using corresponding equations.