In UV-Vis spectrophotometry, how are percent transmittance (%T) and absorbance (A) related algebraically?

• A. $A=\frac{\%T}{100}$
• B. $A=-{\log }_{10}\left(\frac{\%T}{100}\right)$
• C. $A=2-{\log }_{10}(\%T)$
• D. $A={\log }_{10}\left(\frac{\%T}{100}\right)$

Answer: (B)

Verified step by step guidance

1. Understand that in UV-Vis spectrophotometry, absorbance (A) and percent transmittance (%T) are related through a logarithmic relationship because absorbance measures how much light is absorbed, while transmittance measures how much light passes through the sample.
2. Recall the definition of transmittance (T) as the ratio of transmitted light intensity (I) to the incident light intensity (I_0), expressed as a decimal: \(T = \frac{I}{I_0}\).
3. Percent transmittance (%T) is simply transmittance multiplied by 100: \(\%T = T \times 100\).
4. The fundamental relationship between absorbance and transmittance is given by the equation: \(A = -\log_{10}(T)\).
5. Substitute \(T = \frac{\%T}{100}\) into the absorbance equation to get the algebraic relationship: \(A = -\log_{10}\left(\frac{\%T}{100}\right)\).