In UV-Vis spectrophotometry, how is the absorbance value displayed on a spectrophotometer defined in terms of incident light intensity $I_0$ and transmitted light intensity $I$?

• A. $A=\frac{I}{I_0}$
• B. $A=-{\log }_{10}\left(\frac{I}{I_0}\right)$
• C. $A={\log }_{10}\left(\frac{I}{I_0}\right)$
• D. $A=-{\log }_{10}\left(\frac{I_0}{I}\right)$

Answer: (B)

Verified step by step guidance

1. Understand that in UV-Vis spectrophotometry, absorbance (A) quantifies how much light is absorbed by a sample as light passes through it.
2. Identify the two key intensities involved: the incident light intensity \(I_0\), which is the light entering the sample, and the transmitted light intensity \(I\), which is the light exiting the sample after passing through.
3. Recall that absorbance is related to the ratio of transmitted to incident light intensities, specifically through a logarithmic relationship to express the attenuation of light.
4. Write the absorbance formula as \(A = -\log_{10}\left( \frac{I}{I_0} \right)\), where the negative sign ensures that absorbance is positive when transmitted light is less than incident light.
5. Interpret this formula: a higher absorbance means less transmitted light relative to incident light, indicating more absorption by the sample.