Beer-Lambert Law

What is the Beer-Lambert Law?

The Beer-Lambert law, known by various names such as the Lambert-Beer law, Beer-Lambert–Bouguer law or the Beer’s law states the following:

For a given material, the sample path length and concentration of the sample are directly proportional to the absorbance of the light.

Various Names for Beer-Lambert Law

The Beer-Lambert law is known by so many names because more than one law is involved.

• In 1729, Pierre Bouguer discovered the law.
• Later, in 1760, Johann Heinrich Lambert quoted Bouger’s discovery saying that the absorbance of a sample is directly proportional to the path length of light. Although Lambert dint claim the discovery, he was often credited with it.
• In 1852, August Beer discovered a related law which stated that the absorbance is proportional to the concentration of the sample.

Beer-Lambert Law Equation

The Beer-Lambert law equation is as follows:

Where,

I is the intensity

I₀ is the initial intensity

μ is the coefficient of absorption

x is the depth in meter

Learn how to derive the Beer-Lambert Law equation by visiting the page below:

• Beer-Lambert Law Derivation

Beer-Lambert Law Applications

This law finds applications in various fields such as:

• Analytical chemistry: This analysis mainly concentrates on the separation, quantification, and identification of matter by spectrophotometry. There is no involvement of extensive pre-processing of the sample to get the results. For example, bilirubin count in a blood sample can be determined by using a spectrophotometer.
• In atmosphere: Solar or stellar radiation in the atmosphere can be described using this law. The law in atmospheric applications has a modified equation: \(\large T=e^{-m(T_{a}+T_{g}+T_{RS}+T_{NO2}+T_{w}+T_{O3}+T_{r}+..)}\)

  Where,

  a is the aerosols

  g is the mixed gases

  RS is the Raman scattering effects

  NO₂ is Nitrogen dioxide

  w is the water vapour absorption

  O₃ is Ozone

  r is Rayleigh scattering

Beer-Lambert Law Limitations

Using this law it becomes easy to study the absorptivity coefficient of the sample when the concentration is low ie; <10mM but as the concentration becomes high ie; >10mM there is a deviation as the electrostatic interactions become more.

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