Absorbance is a quantitative measurement used to understand how matter interacts with light. It functions as a precise measure of the amount of light that a sample prevents from passing through it. When light strikes a substance, some of the light energy is taken up by the molecules, causing a reduction in the light’s intensity as it travels through the material. For instance, measuring the absorbance of a DNA sample at a specific wavelength can be used to calculate its concentration in a laboratory setting.
Defining Absorbance Through Ratios
The value of absorbance, symbolized by \(A\), is calculated based on the intensity of light before and after it passes through the sample. Absorbance is derived from a ratio comparing the initial light intensity (\(I_0\)) to the final light intensity (\(I\)). This calculation requires measuring the incident light (\(I_0\)) entering the sample and the transmitted light (\(I\)) exiting the sample. The mathematical relationship involves the logarithm of the ratio of these two intensities.
The formula used to define absorbance is \(A = \log_{10}(I_0/I)\). This logarithmic relationship is used because light intensity decreases exponentially as it travels through an absorbing medium. Taking the logarithm converts this exponential relationship into a linear one, which simplifies calculations. This framework is fundamental for quantitative analysis in spectroscopy.
The Unitless Nature of Absorbance
Absorbance is a dimensionless quantity because it is defined as the logarithm of a ratio of two identical physical quantities. Light intensity, whether incident (\(I_0\)) or transmitted (\(I\)), is measured in the same physical units, such as watts per square meter (\(W/m^2\)).
When \(I_0\) is divided by \(I\), the units cancel out, leaving a unitless ratio. Since absorbance is the logarithm of this unitless ratio, the final absorbance value must also be unitless. For example, a value of \(A=1.0\) indicates that 90% of the light was absorbed by the sample.
Despite being mathematically unitless, absorbance measurements are frequently reported using the designation “Absorbance Units” (AU). This practice distinguishes the measurement in scientific literature and laboratory reporting. Sometimes, the term “Optical Density” (OD) is also used interchangeably with absorbance.
Units Associated with Molar Absorptivity
While absorbance has no units, its relationship with a sample’s properties is described by the Beer-Lambert law. This law states that absorbance (\(A\)) is directly proportional to the concentration (\(c\)) of the absorbing species and the path length (\(l\)). The proportionality constant is known as molar absorptivity, symbolized by epsilon (\(\epsilon\)).
The mathematical expression of this relationship is \(A = \epsilon l c\). Since \(A\) is unitless, the product of \(\epsilon\), \(l\), and \(c\) must also result in a unitless value. Path length (\(l\)) is typically measured in centimeters (\(cm\)), and concentration (\(c\)) is usually expressed in molarity (\(mol/L\)).
Therefore, molar absorptivity (\(\epsilon\)) must possess the necessary units to cancel out the units of both path length and concentration. This requires the units for molar absorptivity to be \(L \cdot mol^{-1} \cdot cm^{-1}\). These units ensure that the final calculation yields a dimensionless value for absorbance.