# 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

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.