Spectroscopy studies how light interacts with matter, revealing information about a substance’s identity and quantity. When light encounters a sample, it can be reflected, scattered, absorbed, or transmitted. Transmittance is the measure of how much light successfully passes through a substance without being absorbed or scattered. This fundamental measurement allows researchers to analyze chemical solutions and material properties.
Defining Transmittance and the Calculation
Transmittance, symbolized by \(T\), is the ratio of the light intensity exiting the sample (\(I\)) to the intensity of the light entering it (\(I_0\)). This ratio quantifies the fraction of light transmitted through the material. The formal calculation is expressed by the formula \(T = I/I_0\).
A transmittance value of \(1\) (or \(100\%\)) means all light passed through without reduction, such as when measuring a transparent solvent blank. Conversely, a transmittance of \(0\) (or \(0\%\)) means none of the light passed through, indicating complete blockage or absorption.
The measurement is often reported as percent transmittance \((\%T)\), calculated by multiplying \(T\) by \(100\). This percentage scale provides an intuitive sense of a sample’s optical clarity. Although transmittance is the direct instrument measurement, scientists frequently convert this value for practical chemical analysis.
The Essential Link to Absorbance
Instruments measure transmittance, but scientists convert this ratio into absorbance (\(A\)) for quantitative analysis. Absorbance is the amount of light absorbed by a substance, preventing its transmission. This value is inversely related to transmittance: as \(T\) increases, \(A\) decreases.
The conversion involves a logarithmic relationship, expressed as \(A = -\log_{10}(T)\). The negative logarithm transforms the exponential relationship between light intensity and concentration into a linear one. The formula can also be written as \(A = \log_{10}(I_0/I)\).
This logarithmic scale means that small changes in transmittance at low values correspond to larger changes in absorbance. For example, \(10\%\) transmittance corresponds to an absorbance of \(1.0\), while \(1\%\) transmittance corresponds to \(2.0\). This linearity makes absorbance the preferred value for determining the concentration of a compound in a solution.
How a Spectrophotometer Measures Light
The physical measurement relies on a spectrophotometer, which isolates specific wavelengths and measures their intensity before and after passing through a sample.
Components of a Spectrophotometer
- Light source
- Mechanism to select a specific wavelength (monochromator)
- Sample compartment (cuvette)
- Detector
The process begins by shining light through a monochromator, which separates the light into individual wavelengths. A narrow band of light is directed toward the sample, held in a cuvette. Before the sample is measured, the instrument first measures the incident light intensity (\(I_0\)) using a reference blank (usually the solvent).
The reference blank is then replaced with the sample solution, and the instrument measures the transmitted light intensity (\(I\)). A detector counts the photons that reach it. The spectrophotometer internally calculates the transmittance ratio (\(I/I_0\)) or converts it into the absorbance value.
Applying Transmittance to Determine Concentration
The goal of measuring transmittance and converting it to absorbance is to determine the concentration of a compound in a solution. This application is based on the principle that the amount of light absorbed is directly proportional to the number of light-absorbing molecules present.
The resulting absorbance value is directly proportional to the concentration of the absorbing species, provided the light path length remains constant. Scientists use this linear relationship to create a calibration curve by measuring the absorbance of solutions with known concentrations. The concentration of an unknown sample is then determined by measuring its absorbance and finding the corresponding point on this established curve.