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.
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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