 # Beer-Lambert Law

## What is Beer-Lambert Law?

Beer-Lambert law has a modern definition which is a combination of two different laws and stated as for a given material sample path length and concentration of the sample are directly proportional to the absorbance of the light.

### What is Beer’s Law?

Beer law states that concentration and absorbance are directly proportional to each other and it was stated by August Beer.

### What is Lambert Law?

Lambert law states that absorbance and path length are directly proportional and it was stated by Johann Heinrich Lambert.

## Beer-Lambert Law Equation

Beer-Lambert law equation is as follows:

$\large I=I_{0}e^{-\mu (x)}$

Where,

I: intensity

I0: initial intensity

μ: coefficient of absorption

x: depth in metre

### 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: aerosols

g: mixed gases

RS: Raman scattering effects

NO2: Nitrogen dioxide

w: water vapour absorption

O3: Ozone

r: 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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