, MODULE II
SPECTROSCOPIC TECHNIQUES AND APPLICATIONS
The study of interaction of electromagnetic radiation with matter is called spectroscopy.
Absorption laws
The absorption of light by molecules is governed by certain laws. They are collectively
known as absorption laws. They are
1. Beer’s law
2. Lambert’s law
3. Beer – Lambert’s law
Beer’s law
When a monochromatic light is incident on a homogeneous medium, then the intensity of
transmitted light decreases with increase in concentration of absorbing solution.
Log α c
Log = kc
Lambert’s law
When a monochromatic light is incident on a homogeneous medium, then the intensity of
transmitted light decreases with increase in thickness of the medium.
log α t
log = kt
Beer – Lambert’s law
When a monochromatic light is incident on a homogeneous medium, then the intensity of
transmitted light decreases with increase in concentration of absorbing solution as well as
thickness of the medium.
log α ct
log = εct
Where I0 is intensity of incident radiation, It that of transmitted radiation, ε is the molar
extinction (absorption) coefficient, c is the concentration and t is the thickness of the medium.
Absorbance (A)
It is the logarithm of ratio of intensity of incident radiation to that of transmitted radiation.
A = log
Transmittance (T)
It is the ratio of intensity of transmitted radiation to that of incident radiation.
T=
log = εct
-log T = εct
Derivation of Beer – Lambert’s law
When a mono-chromatic light is passed through the homogeneous medium of
concentration (C), the rate of decrease in intensity of radiation (-dI) with thickness of the
medium (dt) is proportional to the intensity of incident radiation (I) and also the concentration
(C).
∞IC
= KCdt, where K is the proportionality constant.
SREE BUDDHA COLLEGE OF ENGINEERING, PATTOOR Page 1
, Let I0 be the intensity of incident radiation and It that of transmitted radiation passing through
any finite thickness (t) of the medium, then
∫ = KC∫
= KCt
𝐼
= KCt
𝐼𝑡
This is the integrated form of Beer-Lambert’s law.
= KCt = Ct
𝐼
A= = εCt
𝐼𝑡
Where ε is the molar extinction (absorption) coefficient. It depends on the nature of medium and
also the extent of absorption.
The absorbance of a 0.01M dye solution in ethanol is 0.62 in a 2cm cell for light of wave
length 5000 A0. If the path length of light through the sample is doubled and the
concentration is made half, what will be the value of absorbance?
A = εct
= = = 1, absorbance remains same
A dye solution of concentration 0.04M shows absorbance of 0.045 at 530nm; while a test
solution of same dye shows absorbance 0.022 under same conditions. Find the
concentration of test solution.
A = εCt, Here ε and t are constants
=
=
C2 = 0.0195M
The percentage transmittance of a 0.01m dye solution in ethanol is 20% in a 2cm cell for
light of wave length 5000A0. Find the absorbance and molar absorption coefficient.
A = log = εCt
A = log = 0.6989
ε= = = 34.945 M-1cm-1
SREE BUDDHA COLLEGE OF ENGINEERING, PATTOOR Page 2
SPECTROSCOPIC TECHNIQUES AND APPLICATIONS
The study of interaction of electromagnetic radiation with matter is called spectroscopy.
Absorption laws
The absorption of light by molecules is governed by certain laws. They are collectively
known as absorption laws. They are
1. Beer’s law
2. Lambert’s law
3. Beer – Lambert’s law
Beer’s law
When a monochromatic light is incident on a homogeneous medium, then the intensity of
transmitted light decreases with increase in concentration of absorbing solution.
Log α c
Log = kc
Lambert’s law
When a monochromatic light is incident on a homogeneous medium, then the intensity of
transmitted light decreases with increase in thickness of the medium.
log α t
log = kt
Beer – Lambert’s law
When a monochromatic light is incident on a homogeneous medium, then the intensity of
transmitted light decreases with increase in concentration of absorbing solution as well as
thickness of the medium.
log α ct
log = εct
Where I0 is intensity of incident radiation, It that of transmitted radiation, ε is the molar
extinction (absorption) coefficient, c is the concentration and t is the thickness of the medium.
Absorbance (A)
It is the logarithm of ratio of intensity of incident radiation to that of transmitted radiation.
A = log
Transmittance (T)
It is the ratio of intensity of transmitted radiation to that of incident radiation.
T=
log = εct
-log T = εct
Derivation of Beer – Lambert’s law
When a mono-chromatic light is passed through the homogeneous medium of
concentration (C), the rate of decrease in intensity of radiation (-dI) with thickness of the
medium (dt) is proportional to the intensity of incident radiation (I) and also the concentration
(C).
∞IC
= KCdt, where K is the proportionality constant.
SREE BUDDHA COLLEGE OF ENGINEERING, PATTOOR Page 1
, Let I0 be the intensity of incident radiation and It that of transmitted radiation passing through
any finite thickness (t) of the medium, then
∫ = KC∫
= KCt
𝐼
= KCt
𝐼𝑡
This is the integrated form of Beer-Lambert’s law.
= KCt = Ct
𝐼
A= = εCt
𝐼𝑡
Where ε is the molar extinction (absorption) coefficient. It depends on the nature of medium and
also the extent of absorption.
The absorbance of a 0.01M dye solution in ethanol is 0.62 in a 2cm cell for light of wave
length 5000 A0. If the path length of light through the sample is doubled and the
concentration is made half, what will be the value of absorbance?
A = εct
= = = 1, absorbance remains same
A dye solution of concentration 0.04M shows absorbance of 0.045 at 530nm; while a test
solution of same dye shows absorbance 0.022 under same conditions. Find the
concentration of test solution.
A = εCt, Here ε and t are constants
=
=
C2 = 0.0195M
The percentage transmittance of a 0.01m dye solution in ethanol is 20% in a 2cm cell for
light of wave length 5000A0. Find the absorbance and molar absorption coefficient.
A = log = εCt
A = log = 0.6989
ε= = = 34.945 M-1cm-1
SREE BUDDHA COLLEGE OF ENGINEERING, PATTOOR Page 2
