# Ultraviolet-Visible (UV-Vis) Spectroscopy / Derivation of Beer-Lambert Law - Instrumental Methods of Analysis B. Pharma 7th Semester

Ultraviolet-Visible (UV-Vis) Spectroscopy – Derivation of Beer-Lambert Law

Objectives

At the end of the session students will be able to

State Lambert and Beer’s laws

Derive the fundamental equation of quantitative spectroscopy

Explain the terms absorbance and transmittance

Distinguish between absorption coefficient, specific absorption coefficient and molar absorption coefficient

Lambert’s Law

Lambert’s law states that when monochromatic light passes through a transparent medium of uniform thickness, the rate of decrease in the intensity of light is directly proportional to the intensity of light

The candela (abbreviation, cd) is the standard unit of luminous intensity in the International System of Units (SI).

It is formally defined as the magnitude of an electromagnetic field, in a specified direction, that has a power level of 1/683 watt (1.46 x 10 -3 W) per steradian at a frequency of 540 terahertz (540 THz or 5.40 x 10 14 Hz).

. A frequency of 540 THz corresponds to a wavelength of about 556 nanometers (nm), which is in the middle of the visible-light spectrum.

A steradian is the standard unit solid angle in three dimensions; a sphere encloses 4 pi (approximately 12.57) steradians.

-dI/db∝ I

Where

Ø  I is the intensity of radiation

Ø  b is pathlength (length of the medium through which light travelled)

Ø  dI and db are the differences in intensity and pathlength respectively

Beer’s Law

August Beer

Beer’s law states that when monochromatic light is passed through a solution of uniform concentration, the rate of decrease in intensity of light is proportional to the intensity of light

Beer- lambert’s Law

Combining both the equations,

A=  log⁡〖I0/It=abc〗 Where a is specific absorption coefficient, the value of which is dependent on the way concentration is expressed and on the unit of path length.

This is the fundamental equation of spectroscopy

Terms used in spectrophotometry

Transmittance is the ratio of intensity of transmitted light to that of incident light

Absorbance: logarithmic ratio of intensity of incident light to that of transmitted light

Synonyms: Optical density, Extinction

Absorption coefficient: Absorbance per unit path length

Classical definition: the reciprocal  of path length in cm that is required to reduce the intensity of incident light to 1/10th of its value

Synonyms: Absorptivity, extinction coefficient

Specific absorption coefficient : Absorbance per unit concentration per unit path length

a=A/bc

A1%1cm :  A specific absorption coefficient when  concentration is expressed as % solution and path length in cm

Molar absorption Coefficient (ɛ): Specific absorption coefficient when concentration is expressed as moles per liter solution and path length in cm

Molar absorption coefficient and Molecular weight

Molecular weight in g = 1 Mole

Assume Concentration of the solution is c % solution

c g is c/M.wt moles

Concentration of the solution is 10c/M.wt moles/litre

ε=A/bc    ( M.wt)/10

Summary

Lambert’s law explains the  effect of path length on the intensity of light

Beer’s law explains the effect of concentration of the solution on the intensity of light

Both laws assume monochromatic light

Absorbance is logarithmic ratio of intensity of incident light to that of transmitted light

Transmittance is the ratio of intensity of transmitted light to that of incident light

The combined law gives the fundamental equation of quantitative spectroscopy

The fundamental equation of spectroscopy is

A=  log⁡〖I0/It=abc〗 Where a is specific absorption coefficient, the value of which is dependent on the way concentration is expressed and on the unit of path length.

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