In UV-Vis spectrophotometry, absorbance is defined as $A=-{\log }_{10}\left(\frac{I}{I_0}\right)$. What are the units of absorbance?

• A. Absorbance is dimensionless (no units).
• B. Absorbance has units of $\frac{1}{\mathrm{cm}}$.
• C. Absorbance has units of $\mathrm{mol}\cdot L^2$.
• D. Absorbance has units of $m^2$.

Answer: (A)

Verified step by step guidance

1. Recall the definition of absorbance in UV-Vis spectrophotometry: \(A = -\log_{10}\left(\frac{I}{I_0}\right)\), where \(I_0\) is the intensity of the incident light and \(I\) is the intensity of the transmitted light.
2. Understand that absorbance is calculated as the logarithm of a ratio of two intensities, \(I\) and \(I_0\), which have the same units (usually watts per square meter or similar).
3. Since absorbance is the logarithm of a ratio of two quantities with identical units, the units cancel out, making the ratio dimensionless.
4. The logarithm function operates on a dimensionless number, so the result, absorbance \(A\), is also dimensionless and has no units.
5. Therefore, absorbance is a pure number without any physical units, which is why it is often described as unitless or dimensionless.