In UV-Vis spectrophotometry, absorbance is defined as $A=-{\log }_{10}\left(T\right)$, where transmittance $T$ is the fraction of light transmitted. Which expression correctly gives percent transmittance from absorbance $A$?

• A. $\%T=100\times {10}^A$
• B. $\%T=100\times {10}^{-A}$
• C. $\%T=100\times \frac{1}{A}$
• D. $\%T=100\times A$

Answer: (B)

Verified step by step guidance

1. Start with the given definition of absorbance in UV-Vis spectrophotometry: \(A = -\log_{10}(T)\), where \(T\) is the transmittance (fraction of light transmitted).
2. Rewrite the equation to express transmittance \(T\) in terms of absorbance \(A\). Since \(A = -\log_{10}(T)\), multiply both sides by -1 to get \(-A = \log_{10}(T)\).
3. Convert the logarithmic form to exponential form to isolate \(T\): \(T = 10^{-A}\).
4. Since percent transmittance (%T) is the transmittance expressed as a percentage, multiply \(T\) by 100: \(\%T = 100 \times T\).
5. Substitute \(T = 10^{-A}\) into the percent transmittance expression to get \(\%T = 100 \times 10^{-A}\), which is the correct formula for percent transmittance from absorbance.