Derivation of Beer Lambert Law

INTRODUCTION:

Beer Lambert Law derivation helps us to define the relationship of the intensity of visible UV radiation with the exact quantity of substance present. The Derivation of Beer Lambert Law has many applications in modern day science. Used in modern day labs for testing of medicines, organic chemistry and to test with quantification. These are some of the fields that this law finds its uses in.

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Schematic Diagram of Beer Lambert Law

Absorption of energy causes the absorption of light as well usually by electrons. Different forms of light such as visible light and ultraviolet light gets absorbed in this process. Therefore, change in intensity of light due to absorption, interference and scattering leads to:

ΔI = I0IT

The following equations are necessary for us to obtain our ultimate derivative equation. Transmittance is measured as the ratio of light passing through a substance. It can be calculated as IT/I0. To calculate the of transmittance percentage we can do so by:

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Percent Transmittance

Another key metric is absorbance that is defined as the amount of light absorbed. This is usually calculated as the negative of transmittance and is given by:

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Absorbance (A)

The rate of decrease in the intensity of light with the thickness of the material the light is directly proportional to the intensity of the incident light. Mathematically, it can be expressed as:

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As k’= Proportionality constant

Taking in the reciprocal of the equation we get,

Beer Lambert Law images

Integrating the above equation we also get,

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In the above equation b and C is the constant of integration and IT is the intensity being transmitted at the thickness

In order to solve the above equation with the constant of integration we then get,

Beer Lambert Law images

While solving for C in the equation will give us,

Beer Lambert Law images

Converting to log10 we get,

Beer Lambert Law images

Rearranging the equation we get,

Beer Lambert Law images

Lambert Derivation

Thus, Lambert’s law was formed and it states that the monochromatic radiation changes exponentially and decreases when it passes through a medium of uniform thickness.

Beer Lambert Law images

Beer Derivation

Thus, this concludes the derivation of Beer Lambert law. This goes to show you that in order to derive a particular law, there are a lot of different equations that need to be found out first, to achieve the ultimate result. If you like Physics related articles, you might want to check out another topic like Electric Potential.


Practise This Question

In which of the following frequency distributions, the class intervals overlap?