In UV-Vis spectrophotometry, absorbance is defined as $A=-\log {10}_{}T$, where $T$ is transmittance (unitless). Which expression correctly gives transmittance in terms of absorbance?

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

Answer: (C)

Verified step by step guidance

1. Start with the given definition of absorbance in UV-Vis spectrophotometry: \(A = -\log_{10} T\), where \(A\) is absorbance and \(T\) is transmittance.
2. Recall that the logarithm function can be inverted by exponentiation. To express \(T\) in terms of \(A\), rewrite the equation as \(-\log_{10} T = A\).
3. Multiply both sides of the equation by -1 to isolate the logarithm: \(\log_{10} T = -A\).
4. Use the definition of logarithm to rewrite the equation in exponential form: \(T = 10^{-A}\).
5. This expression shows that transmittance is equal to 10 raised to the power of negative absorbance, which matches the correct answer.