This document provides an introduction to spectrometric methods and the Beer-Lambert law. It defines key terms like absorbance, transmittance, molar absorptivity, and wavelength. The Beer-Lambert law states that absorbance is directly proportional to concentration, path length, and molar absorptivity. It also explains that absorbance follows a linear relationship with concentration at a given path length and wavelength for a single analyte. Deviations from Beer's law can occur under certain circumstances.

1. An Introduction
to
Spectrometric Methods
1
Bivek Timalsina
bivektim@gmail.com

2. Quantum Mechanical Properties of
Electromagnetic Radiation (EMR)
 The amount of energy involved in transitions from its ground state to
exited state (following absorption of energy) and from excited to ground
state (by emission of radiation) is given by the following equation;
ΔE = E1 – E2 = hV
where, ΔE = change in energy state of the electron or the energy of
electromagnetic radiation absorbed or emitted by an atom or molecule.
E1 = energy of electron in original state,
E2 = energy of electron in the final state,
h = the Plank’s constant
V= frequency of the electromagnetic radiation in hertz (C/ λ),
where, C= speed of electromagnetic radiation (3x108 m/s)
λ = wavelength of electromagnetic radiation
(= 6.63 x 10-34 JS)The greater the energy, the higher the frequency and
wavenumber and the shorter the wavelength
2

3. Energy level and transition in atom and
molecule
E0
E1
E2
E3
E4
Atomic energy level Molecular energy level
3

4. Emission of Radiation
4

5. Absorption of Radiation
5

6. The Beer-Lambert Law
I0
Sample
I
Detector
Source
Cuvette
6
 Transmittance, T, is simply defined as “the fraction of light that reaches a
detector after passing through a sample”
T = I/I0 …………… (i)
Where, I0 = intensity of Incident radiation
I= intensity of transmitted radiation
 Percentage Transmission (%T) = % T = I/I0 x 100
0 < %T < 100

7. The Beer-Lambert Law
 Absorbance (A):
A = -log T = log (1/T) = log (I o / I)
Absorbance is also called as Optical Density (O.D.)
range from 0 (= 100% T) to infinity (=0%T).
 The Beer-Lambert law states
Absorbance is directly proportional to:
1. concentration, c, of absorbing species in the sample (A c)
2. path length of light, L, through the sample (A L)
A = € C L ……………… (iii)
Where, € = Molar absorbance coefficient of the absorber
C = Concentration of absorbing solution, and
b = Path length through the solution (or thickness) 7

8. The Beer-Lambert Law
 Absorbance (A):
A = € C L ……………… (iii)
 Concentration of the analyte is given in unit mol/L (M)
 The path length, L, in cm
 , is called the molar absorptivity or molar absorption
coefficient
“Absorbance of 1 M solution measured in a cell of 1 cm
pathlength”
 , is characteristic for each substance at a particular
wavelength, .
11111 
 cmMcmmolL
cm
L
molcl
A

8

9. Concentration
Absorbance,A
0
0.5
1
Concentration
Transmittance,T
A=cL
certain 
constant L
One analyte
T=10-A =10- bc
Beer’s law is a relation between absorbance
and concentration which is a straight line
passes by origin at constant pathlength, b,
and at certain wavelength, .
Transmittance decreases
exponentially as concentration
increases
Beer’s law is obeyed for
monochromatic light
Slope = L
The Beer-Lambert Law
9

10. Beer’s Law and Multicomponent samples
 For sample containing several absorbing components (say X and
Y) given that there are no interactions between the components, the
total absorbance is,
Atotal = Ax+ By = €x Cx L + €y Cy L
10

11. The Beer-Lambert Law
Blank
Detector
Source
I0
Use of Blank
I0
Sample
I
Detector
Source
Cuvette
11

12. The Beer-Lambert Law
A = € C L
Use of Curve
12

13. This relationship is a linear for the most part. However, under certain
circumstances the Beer relationship gives a non-linear relationship.
These deviations from the Beer Lambert law can be classified into three
categories:
Real Deviations - These are fundamental deviations due to the limitations
of the law itself.
Chemical Deviations- These are deviations observed due to specific
chemical species of the sample which is being analyzed.
Instrument Deviations - These are deviations which occur due to how the
absorbance measurements are made.
Derivation of Beer Lambert Law
13

14. Readout
Absorbance
0.00
Source
Detector
The Beer-Lambert Law
A = € C L
14
Path Length Dependence, L

15. Path Length Dependence, L
Readout
Absorbance
0.22
Source
Detector
b
Sample
The Beer-Lambert Law
A = € C L
15

16. Path Length Dependence, L
Readout
Absorbance
0.44
Source
Detector Samples
Of course, we are not introducing two cells in the
light pathway, but let us assume that we doubled
the path length of light through the absorbing
medium
The Beer-Lambert Law
A = € C L
16

17. Readout
Absorbance
0.66
Source
Detector Samples
The Beer-Lambert Law
A = € C L
17
Path Length Dependence, L

18. Concentration Dependence, c
Readout
Absorbance
0.00
Source
Detector
The Beer-Lambert Law
A = € C L
18

19. Concentration Dependence, c
Readout
Absorbance
0.42
Source
Detector
b
Sample
The Beer-Lambert Law
A = € C L
19

20. Concentration Dependence, c
Readout
Absorbance
0.63
Source
Detector
b
Sample
The Beer-Lambert Law
A = € C L
20

21. Wavelength Dependence, 
Readout
Absorbance
0.30
Source
Detector
b
The blue solution do absorb the red radiation
The Beer-Lambert Law
A = € C L
21

22. Wavelength Dependence, 
Readout
Absorbance
0.00
Source
Detector
b
The red solution can not absorb the red
radiation but it can absorb radiation that
is complimentary to red.
The Beer-Lambert Law
A = € C L
22

23. 23