Instrumental Methods of Analysis

Basics of spectroscopy, Jablonski diagram, Instrumentation of UV-Visible
Spectrometer,
Beer-Lambert’s law and its deviation
Shweta Mishra, M. Pharm (Pharmaceutical Chemistry)
shweta.mishra@saip.ac.in
Sri Aurobindo Institute of Pharmacy, Indore-Ujjain State Highway,
Indore, Madhya Pradesh 453555
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ADVANTAGES OF INSTRUMENTAL METHODS OVER CHEMICAL ONES
• Speed (can be automated, sample throughput is high)
• Sensitivity (trace or ultra-trace analysis is possible)
• Selectivity (accurate in the presence of many other components)
• Reproducibility (reliable, objective)
• Sample requirement is small (ml or mg or less can be handled)
DISADVANTAGES
• Cost
• Complexity
• Maintenance
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Introduction to the electronic structure of the atoms
• In 1904 Sir JJ Thomson proposed the theory of matter. He pictured the positive charge of an atom
distributed uniformly throughout a sphere of protons and neutrons and the negative charge was
surrounding it in a jelly like fashion.
• Rutherford modified this theory that electrons revolves around the nucleus in such a way that
the centrifugal force exactly balances the inward attractive force much like our planets to around the sun.
Hence regardless of their speed, they enter the nucleus. Moreover the electron losing energy would
omit continuous radiation without any sharp breaks.
• In 1903, Bohr proposed a radically different view of the atomic a structure based on the optical
spectrum of hydrogen. He included the postulates of quantum theory proposed by Max Planck.
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Introduction to the electronic structure of the atoms
• Bohr proposed that the electron in a hydrogen atom always described a fixed circular path around the
nucleus. Search orbits named ‘stationary states' maybe thought of various circles differing in radius.
• The angular momentum of each
stationary state was an integral multiple of
N.H/2П which amounts to angular momentum.
• The angular momentum mvr is given by the
formula:
mvr = N (H/2П)
where N is an integer called a quantum
number
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• He also postulated that as long as the electron remained in a given
orbit it neither radiates nor absorbs energy. When the electron moves
from one orbit to another it was considered to involve the absorption
or emission of definite quantity of energy depending upon whether
the electron moved from lower state to higher one or vice versa. This
energy manifests as radiation and the frequency of such radiation is
manifests as a spectral line which could be related to the energies of
electron in the two states E1 and E2:
• E2 - E1 = hυ
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• Line spectra appear in two forms, absorption spectra,
showing dark lines on a bright background, and
emission spectra with bright lines on a dark or black
background.
• These two types are in fact related and arise
due to quantum mechanical interactions between
electrons orbiting atoms and photons of light.
• Photons of light each have a specific frequency.
• The energy of a photon is a function of its frequency
and is determined by:
E = hf
where f is the frequency of the photon, E is the energy
and h is Planck's constant (= 6.626 x 10-34J.s)
Production of Line Spectra
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• An electron orbits around a nucleus in a stable
energy level. If a photon of a specific frequency
interacts with the electron, it can gain sufficient
energy to "jump up" one or more levels. The
photon is absorbed by the electron so cannot
continue on to be detected by an observer. The
electron then "de-excites" and jumps back down
to a lower energy orbit, emitting a photon of
specific frequency. This photon, however, could
be emitted in any direction, not just in the same
direction as the original incident photon.
• The Balmer series of visible lines for atomic
hydrogen are caused by transitions from the n =
2 orbit to and from higher orbits. This is shown
schematically in the diagram for the Bohr model
of the atom. The Lyman Series involves transitions
down to the n = 1 orbit and involve higher
frequency photons in the UV region whilst the
Paschen Series (to n = 3) produces IR spectral
lines. 7
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Spectroscopy
• It is the branch of science dealing
with the interaction of
electromagnetic radiations with
matter in quantized that is
specific energy levels. It refers to
the study of how radiated energy
and matter interacts e.g. UV-
Visible spectroscopy, IR and NMR
spectroscopy etc.
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Spectroscopy? Spectrogram?
Spectrometry? Spectrograph?
The measurement of a
specific spectrum
The machine for recording spectra
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SPECTROSCOPY
Atomic Spectroscopy Molecular Spectroscopy
Absorption Emission Absorption Emission
AAS Flame emission/
Flame
photometry
UV, IR, NMR, Electron
spin resonance spectra,
Raman spectra
Flourimetry,
Phosphorimetry
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The absorption and emission spectrum concept
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The origin of UV band
• If energy is supplied to the sample, for example, by passing
electromagnetic radiation through it, the sample atoms or molecules
may absorb energy and be promoted into the higher energy level.
• For an atom that absorbs in the UV, the absorption spectrum
sometimes consist of very sharp lines as would be expected for a
quantized process occurring between two discrete energy levels.
• For molecules, however, the UV absorption usually occurs over a wide
range of wavelengths, because molecules (as opposed to atoms)
normally have many excited modes of vibration and rotation at room
temperature. In fact, the vibration of molecules has many states of
vibrational and rotational excitation.
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The energy levels for these states are quite closely spaced,
corresponding to energy differences considerably smaller
than those of electronic levels. The rotational and
vibrational levels are thus superimposed on the electronic
levels. A molecule can therefore undergo electronic and
vibrational rotational excitation simultaneously. Because
there are so many possible transitions, each differing from
the others by only a slight amount, each transition consists
of a vast number of lines spaced so closely that the
spectrophotometer cannot resolve them and usually
consider them as a broad band of absorption centered near
the wavelength of the major transition in UV spectrum.
• Deactivation of the thermally excited atoms to lower
energy states occurs very rapidly and photons of light are
emitted which have energy (δE) equal to the difference
between the upper and lower energy states.
• δE = Eh - El = (Eelectronic - Evibrational - Erotational)h - (Eelectronic -
Evibrational - Erotational)l
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When a sample containing metallic atoms is
heated above 2000ᵒC, it undergoes partial or
complete partial or complete dissociation into
free atoms and then volatilizes to free
gaseous atoms. The electrons of the gaseous
atoms exist in discrete quantized energy
levels, i.e. they are in the orbitals which have
specific energy levels that are characteristic of
the element. The electrons in the outer
orbitals of the atom may absorb thermal
energy and be promoted to one or higher
energy states. The gain in energy of each
electron during a transition is a specific
quantity corresponding to the difference
between the energy levels after and before
excitation. 14
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• δE = E2 - E1 = hυ = hc/λ = hcΰ
• E α 1/ λ
• Consequently, a very large number of wavelengths are
absorbed, each corresponding to a particular δE value,
which are so close together that they appear as a
continuous band spectrum. The transition δE4, given
by the highest proportion of molecules, corresponds
with the wavelength of maximum absorption (λmax).
Light at longer and shorter wavelengths is absorbed
less strongly because fewer molecules give related
transitions. Longer wavelengths have insufficient
energy to induce electronic transitions but they are
sufficiently energetic sufficiently energetic to increase
the vibrational energy levels, and the associated
rotational levels, of many molecular bonds.
https://d396qusza40orc.cloudfront.net/physicalchemistry/Spectroscopy_Course/spectroscopy-graphs/visible-
spectrum-phenolphthalein.html
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Transition Time scale Radiative process
Internal Conversion 10-14 - 10-11 s No
Vibrational Relaxation 10-14 - 10-11 s No
Absorption 10-15 s Yes
Phosphorescence 10-4 - 10-1 s Yes
Intersystem Crossing 10-8 - 10-3 s No
Fluorescence 10-9 - 10-7 s Yes
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Order of energy:
Energy for absorption > Energy for Fluorescence > Energy for phosphorescence
Order of wavelength:
Wavelength for absorption < Wavelength for Fluorescence < Wavelength for phosphorescence
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Instrumentation of spectrometers:
The essential components of
spectrometers:
A source of EMR
A monochromator
A sample compartment
A detector and associated
electronics
A recorder or display
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Light source
• Ideal requirements of light source:
It should generate a beam with sufficient power for ready detection
and measurement.
It should emit continuous radiation in the region being studied.
It should be stable.
It should emit a measurable signal throughout the region.
The distribution of energy through a spectrum is mainly a function of
temperature; higher the temperature of the light source the shorter
the wavelength of the peak emission.
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• Common energy sources for the various regions are indicated below:
IR Radiation:
Globar and nerst glowers are the common sources of IR radiation.
The globar is an electrically heated rod of silicon carbide, and the
Nernst glower is a small rod of refractory oxides which, when heated
to 1200-1500 degrees, will conduct electricity and thus maintain itself
in incandescence.
Both these sources operate without a glass envelope, which would
absorb IR radiation of wavelength greater than 2μm.
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 Visible radiation:
Tungsten filament lamp is used for the region 350 nm- 2000 nm.
Tungsten filament is contained in a glass envelope.
IR Radiations which may cause stray light effects can be removed by using
suitable filters.
The life of the lamp is limited by the evaporation of tungsten, which darkens the
inside of the envelope and reduces the energy of the incident light.
Tungsten-halogen lamps, are used in more expensive instruments and halogen
gas is filled inside a quartz envelope.
The halogen prevents evaporation of the tungsten and increases the life of the
tungsten.
The higher operating temperatures extends the lower wavelength limit to 310 nm
and gives greater light intensity.
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 UV Radiations:
 The most convenient light source for measurement in the UV region is a
deuterium discharge lamp.
It consists of 2 electrodes contained in a deuterium- filled silica envelope.
The passage of high voltage from a special power supply across the
electrodes causes emission of deuterium lines which, at low pressure
inside the lamp, broaden to give a continuous spectrum in the range 185-
380 nm.
Above 380 nm, the emission is not continuous, and the sharp lines at 486
nm and 656.1 nm may be used to calibrate the wavelength scale in this
region.
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 Below 185 nm the output is reduced by absorption in the silica
envelope.
Deuterium lamps give approx. five times greater light intensity than
hydrogen lamps when operated at same voltage.
UV-Visible spectrophotometers normally have both a deuterium
lamp and a tungsten (or tungsten-halogen) lamp, and selection of the
appropriate lamp is made by moving either the lamp mountings or a
mirror to cause the light to fall on the entrance slit of the
manochromator.
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Monochromators
• Light gives radiation from 400-800nm
• This is called polychromatic light which is of several wavelength
• Hence a filter or monochromator is used to convert polychromatic
light into monochromatic lights used
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Monochromators
Ideal requirements of the monochromator:
oIt should be able to isolate a particular wavelength or range of
wavelengths.
oIt should adhere to the beer-lambert’s law.
oIt should emit a measurable signal throughout the region.
Commonly used monochromators are:
• Filters
• Prisms
• Gratings
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Absorption Filters
Glass filters are pieces of coloured glass which transmit limited
wavelength ranges of the spectrum.
The color is produced by incorporating oxides of such metals as
vanadium, chromium, manganese, iron, nickel, and copper in glass.
The color absorbed is the complement of the color of the filter. For
example, a filter absorbing yellow light will appear blue.
The range of wavelengths transmitted (bandwidth) is very high and
may exceed 150 nm.
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Wavelength (nm) Color Complement color
400-450 Violet Yellow-green
450-480 Blue Yellow
480-490 Green-blue Orange
490-500 Blue-green Red
500-560 Green Purple
560-575 Yellow-green Violet
575-590 Yellow Blue
590-625 Orange Green-blue
625-750 Red Blue-green
Below 400 nm the color gradually becomes invisible as
it passes into UV; above 750 nm it passes into IR.
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 Gelatin filters consisting of a mixture of dyes incorporated in gelatin
and sandwitched between glass plates are more selective, with
bandwidths about 25 nm.
Merits:
• Simple, cheaper
Demerits:
• Less acurate, bandpass is more (+/- 30 nm), intensity is less
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Interferometeric filters
• They have an even more narrower bandwidth (about 15 nm) and
consists of 2 parallel glass plates, silvered internally and separated by
a thin film of cryolite or other dielectric material.
• Such filters make use of interference of light waves rather than
absorption to eliminate the undesired radiation, and serve as
relatively inexpensive monochromators for a specific purpose.
• Eg. Isolation of calcium radiation at 626 nm and sodium at 589.3 nm
in flame photometer
• Ordinary filters are incapable for this and cause large errors in
measurement of calcium content.
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• Also known as fabry-perot filter
• It has dielectric spacer made up of
CaF2, MgF2, or SiO.
• Thickness of dielectric spacer film can
be ½ ʎ (1st order),
2/2 ʎ (2nd order) , 3/2 ʎ (3rd order).
• Mechanism is constructive interference
followed by this equation.
• ʎ=2ηb/m
ʎ=wavelength of light
η= dielectric constant of material
B= layer thickness
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Prisms
• When a beam of monochromatic light
passes through a prism, it is bent or
refracted.
• The amount of deviation depends upon
the wavelength, eg. Blue light being
refracted more than red.
• If white polychromatic light is substituted
for monochromatic light, a separation of
different wavelengths lead to the
formation of a spectrum from which a
required wavelength can be selected.
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• Prisms are made up of quartz for use in UV region, since glass absorbs
wavelengths shorter than about 330 nm.
• Glass prisms are preferable for the visible region of the spectrum, as
the dispersion is much greater than that obtained with quartz.
• For the IR region, the transparent substances usually used are NaCl
(2– 15 μm), KBr (12-25μm), LiF (0.2-0.6μm), and CsBr (15-38μm).
• Prisms produce a non-linear dispersion, with long wavelengths being
less efficient separated than short wavelengths.
• The older spectrophotometers show larger divisions btw each nm in
the UV region than in the Visible region.
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Gratings
• The dispersing element in the monochromator of
most modern UV, Vis, IR spectrophotometers is the
diffraction grating.
• It consists of a very large number of equispaced
lines (200-2000 per mm) ruled on a glass blank
coated with a thin film of aluminium.
• Parallel lines or grooves are chemically joined on a
thin layer of photoresist coated glass which
produces interference of light beams.
• They can be used as transmission gratings or when
aluminized can be used as reflection gratings.
• Rotation of grating permits appropriate
wavelengths of the spectrum to emerge from the
exit slit of the monochromator.
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• The ruling of a grating can be shaped to
concentrate the light in certain orders
to give greater efficiency which is
especially imp in IR.
• A grating can be plane or concave.
• Concave gratings are capable of
focusing on its own spectra without the
use of lenses or mirrors.
• For convenience plane gratings are
used which can be made to cover all
spectral regions from 180 nm- 15 μm.
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Sample Compartment
Ideal requirements:
• It should hold the sample and
should be made of substance which
are transparent in the region being
studied.
• It should be reproducible in path
length.
For example. Quartz cells in UV can
hold 3 ml sample with 1 cm
pathlength.
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• Samples presented for the spectrometric analysis may be in the solid,
liquid or gaseous state.
• For the analysis of liquids and gases in the UV-Visible region above
323 nm, cells (or cuvettes) constructed with optically flat fused glass
may be used.
• Measurements below 325 nm (the UV cut off value of glass), requires
the use of more expensive fused silica cells, which are transparent to
below 180 nm.
• The standard path-length of cells for the measurements of molecular
absorption or fluorescence in the UV-visible region is 10 mm.
• The most common sample-containing materials in IR spectroscopy are
NaCl (2.5 – 17 μm) and KBr ( 2.5 – 30 μm).
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Detector
Ideal requirement of the detectors:
• Respond to the radiant energy over a broad wavelength range.
• It should be sensitive to low levels of radiant power.
• It should respond rapidly to the radiation.
• It should produce an electrical signal that can rapidly be amplified and
the signal produced is directly proportional to the power of the
striking area.
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Detectors
Commonly used detectors are:
• Barrier-layer cells
• Phototubes
• Photomultiplier tubes
• Photodiodes
• Thermocouples
• Bolometers
• Thermistors
• Golay detectors
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Barrier-layer cell:
• One of the simplest detector.
• Advtg.
Requires no power supply but gives a current
which, under suitable conditions, is directly
proportional to the light intensity.
• Instrumentation:
It consists of a metallic plate, usually copper or
iron, upon which is deposited a layer of selenium
or sometimes copper oxide.
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• An extremely thin layer of a good conducting metal, eg, silver, platinum
or copper, is formed over the selenium to act as one electrode, the
metallic plate acting as the other.
• Ordinarily, selenium and metallic oxides and sulphides have extremely
small electrical conductivities, the electrons being in energy levels at
stationary state that is they are not mobile.
• Light of suitable frequency, imparts sufficient energy to the electrons so
that they leave the selenium and enter the transparent metal layer.
• If 2 electrodes are now connected to the galvanometer, a current will
flow shown by the needle of galvanometer.
• If the resistance is small, the current produced is directly proportional to
the intensity of the light.
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• The current output also depends upon the wavelength of the incident
light.
• With higher resistance, there would be loss of linearity.
• The useful working range of selenium photocells is 380- 780 nm.
• Demerits: lack of sensitivity
• Merits: Requires no power supply but gives a current which, under
suitable conditions, is directly proportional to the light intensity.
Cheapest and still used in colorimeters and flame photometers. 46
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Phototubes:
oElectrons are liberated when light falls on a metal surface, and if this
is enclosed in an evacuated envelope and kept at a negative voltage, a
current which is proportional to the incident light can be drawn from
it.
oThe essential feature for a sensitive surface in these cells is that the
electrons should be liberated easily from the metal.
oElements of high atomic volume, eg. K or Cs, are commonly used and,
in order to increase the sensitivity, composite coatings such as Cs/
CsO2/ AgO2 have proved of more value than the metal alone.
oThe sensitive surface is enclosed in a high vacuum and forms the
cathode of the cell.
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oApplication of a sufficiently high potential
between cathode and anode ensures that all the
electrons liberated by the action of light reach
the anode.
oA saturation photocurrent which exhibits a linear
relationship with the intensity of illumination is
then obtained.
oBy using different metals, the cells can be made
to respond to different regions of the spectrum.
oIn spectrophotometers 2 cells are usually used,
one being responsive to the UV and visible
radiation of wavelengths upto about 620 nm,
and the other to radiation of wavelengths 620-
1000nm.
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oA modification of the above type of cell involves the inclusion of an
inert gas at a low pressure to give gas-filled cells.
oThe underlying principle is that the liberated electrons cause
ionization of the gas with consequent increase in the photocurrent
but, owing to the lack of linear response, the cells cannot be used in
instruments designed for accurate intensity measurement.
PHOTOMULTIPLIER tubes (PMTs)
In order to obtain greater sensitivity to very weak light intensities,
multiplication of the initial photoelectrons by secondary emission is
employed.
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Several anodes at a gradually increasing potential are contained in 1
bulb.
Electrons from the photocathode are attracted to anode 1 and
liberate more electrons which travel to anode 2 because of its higher
potential relative to anode 1.
This process then continues to the last anode, and the result is a final
photocurrent 106-108 times greater than the primary current, which
still shows a linear response with increase in the intensity of
illumination.
PMT are ideal for measuring weak light intensities such as occur in
fluorescence and in the determination of trace elements by their
emission spectra.
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The current from phototubes and PMTs never falls to zero.
A small residual current called dark current is produced, due to
spontaneous discharge at the high voltage of the dynodes or to the
thermal emission from the cathode.
PHOTODIODES
In essence, the diode is charged to a pre-set potential by a
continuously scanning electron beam.
If radiation impinges on the diode, the charge is depleted in
proportion to the intensity of the radiation.
When the electron beam scans again, a current in proportion to the
light intensity flows to recharge the diode to the preset voltage.
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Photodiodes, like vacuum phototubes and PMTs, are single-channel
detectors, i.e. they monitor the total intensity of light and cannot
distinguish between different wavelengths.
A spectrum is obtained with single-channel detectors by varying the
monochromatic light passing through the sample.
When used in combination with a dispersing system each diode can
monitor the light intensity at a different wavelength, and the array
provides an almost instantaneous spectrum.
The multi-channel detector based upon linear diode arrays is of
particular advantage in monitoring fast reaction kinetics and eluate
(combination of mp and ana.) in HPLC.
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Thermocouples
A thermocouple consists of elements of 2
different metals joined together at one end, the
other end being attached to a sensitive
galvanometer.
When radiant energy impinges on the junction
of the metals, a thermoelectromotive force is set
up which causes a current to flow.
 Thermocouples are used in the IR region, and to
assist in the complete absorption of the available
energy the ‘’hot’’ junction or receiver is usually
blackened.
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Bolometers
These make use of the increase in
resistance of a metal with increase in
temperature.
Like thermocouples they are used in IR
region.
If 2 platinum foils are suitably incorporated
into a wheatstone bridge, and radiation is
allowed to fall on 1 foil, a change in
resistance is produced, which results in
current which is proportional to the
incident radiation.
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Thermistors
• Its made of metal oxides.
• It functions by changing resistance
when heated.
• It consists of 2 closely placed
thermistor flakes, one of the 10 µm is
an active detector, while the other acts
the compensating/ reference detector.
• It is made of semi-conducting material
which has a high negative coefficient of
resistivity, i.e. the resistance decreases
with increase in temp. and this gives
the intensity of the IR radiation.
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Golay detector
In this detector, the absorption of IR
radiation causes expansion of an
inert gas in a cell chamber.
One wall of the chamber consists of
a flexible mirror and the resulting
distortion varies the intensity of
illumination falling on a photocell
from a reflected beam of light.
The current from the photocell is
proportional to the incident
radiation.
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Display system
• The signal from the detector is normally proportional to the intensity
of the light incident on the detector and after amplification may be
displayed as % transmittance or absorbance.
• There are 3 common systems for displaying the %T or absorbance, i.e.
a) Moving coil meter
b) Digital display
c) Strip chart recorder
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Single beam spectrophotometers
• https://www.youtube.com/watch?v=XAp-5r3LxQo
• https://www.youtube.com/watch?v=pxC6F7bK8CU
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Double beam spectrophotometer
• http://mas-iiith.vlabs.ac.in/exp1/expt1/instrument_animation.html
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Principle of UV-Visible spectroscopy:
BEER-LAMBERT’S LAW:
When a beam of light is passed through a
transparent cell containing a solution of an
absorbing substance, reduction of the intensity of
the light may occur.
This is due to:
a) Reflections at the inner and outer surfaces of the
cell
b) Scatter by particles in the solution
c) Absorption of light by molecules in the solution.
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• The reflections at the cell surfaces can be compensated by a
reference cell containing the solvent only, and scattering may be
eliminated by filtration of the solution.
• The intensity of the light absorbed is then given by:
I absorbed = I0 - IT
Where I0 is the original intensity on the cell
IT is the reduced intensity transmitted from the cell.
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• The transmittance (T) is the ratio IT / I0 and the % transmittance (%T)
is given by:
%T = 100 IT / I0
• In 1760, lambert investigated the relationship between I0 and IT for
various thickness of substance and found that the rate of decrease in
the intensity of light with the thickness, b, of the medium is
proportional to the intensity of incident light.
• Expressed mathematically,
- db / dI α I
or – dI/ db = k’ I
where k’ is a proportionality constant
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-db / dI = 1 / k’ I
Integrating, -b = 1/k’ lnIT + C
Where IT is the intensity transmitted at thickness b.
When b = 0,
C = - 1/k’ ln I0
Therefore, -b = 1/ k’ ln IT – 1/k’ ln I0
LnI0 / IT = k’b
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On conversion to a common logarithm, the expression becomes
Log I0 / IT = k’b/ 2.303
The quantity log I0 / IT is called absorbance (A) and is equal to the reciprocal
of the common logarithm of transmittance.
A = Log 10 I0 / IT = log 10 (1/T) = -log T = 2 – log (%T)
Older terms for absorbance such as extinction, optical density, and
absorbancy are now obsolete.
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• Lambert’s law is defined as:
The intensity of a beam of parallel monochromatic radiation decreases exponentially
as it passes through a medium of homogenous thickness.
More simply it is stated that the absorbance is proportional to the thickness
(pathlength) of the solution.
• Beer showed in 1852 that a similar relationship exists between the absorbance and
the concentration.
Log I0 / IT = k’’c/ 2.303
where k’’ is a proportionality constant and c is the concentration.
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• Beer’s law is defined as follows:
The intensity of a beam of parallel monochromatic radiation decreases
exponentially with the number of absorbing molecules.
More simply stated that the absorbance is proportional to the
concentration.
A combination of the two laws yields the Beer-Lambert Law:
A = Log I0 / IT = abc
In which the proportionality constants k’/2.303 and k’’/2.303 are
combined as a single constant called absorptivity (a).
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Molar absorptivity
• When c is in moles per liter, the constant is called molar absorptivity
(formerly called as molar extinction coefficient) and has the symbol ϵ.
• The equation therefore becomes,
A = ϵbc
The molar absorptivity at a specified wavelength of a substance in
solution is the absorbance at that wavelength of a mol/l solution in a 1
cm cell.
The units of ϵ are therefore 1 l/mol/cm
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Specific absorbance
Another form of the beer-lambert proportionality constant is the
specific absorbance, which is the absorbance of a specified
concentration in a cell of specified pathlength.
The most common form is A (1%, 1cm), which is the absorbance of a
1 g/ 100 ml (1% w/v) solution in a 1 cm cell.
The beer-lambert equation therefore takes the form,
A = A 1cm bc
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1%
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oOne factor that influences the absorbance of a sample is the concentration
(c).
oThe expectation would be that, as the concentration goes up, more
radiation is absorbed and the absorbance goes up.
oTherefore, the absorbance is directly proportional to the concentration.
oA second factor is the path length (b).
oThe longer the path length, the more molecules there are in the path of the
beam of radiation, therefore the absorbance goes up.
oTherefore, the path length is directly proportional to the concentration
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Concentration and pathlength
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oFundamental requirement under BL-Law is:
Every photon of light striking the detector must have equal chances of
absorption.
oSuppose we want to measure some high concentrations, above the
usual linear range of calibration curve, without diluting the samples
and without shorter path-length cells
What will be the result?
The absorbance would be non-linear which means the maximum
absorbance value will shift from 1 to 2 because of stray light effects.
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oIn order to reduce that if the wavelength is set to higher values the
linearity would be improved that’s bcz the stray light is lessened by
the reduced absorbance at the higher wavelength.
oThe intensity of light transmitted from an absorbing solution (IT) will
show small random fluctuations owing to small variations in the light
source intensity, detector and amplifier noise etc.
oConsequently, every absorbance value will have a small random error
associated with it.
oThe % relative error is the difference between the true conc. And that
calculated from the measured absorbance (δc) expressed as a % of
the true conc. (c):
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% relative error = 100 δc/ c
oThe % relative error is dependent on the magnitude of the measured
absorbance and the type of detector used to measure the intensities
of light.
oFor modern instruments with a phototube detector, it may be shown
that the relative error is at minimum when abs is 0.869.
oThe optimum accuracy and precision are therefore obtained when
the absorbance is around 0.9.
oIn general practice, the abs values in range 0.3-1.5 are sufficiently
reliable, and the combination of cell path-length and conc. of analyte
should be adjusted to give an absorbance within this range.
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Instrumental parameters
Slit width
It is the width (usually in mm) of the entrance and exit slits of the
monochromator.
The slits are rectangular apertures through which light enters inside
and exists from the monochromator.
Their purpose is to control the spectral resolution of the
monochromator, that is, it has the ability to separate close
wavelengths.
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Light is focused onto the entrance slit B, is focused by concave mirror
C onto the grating D, which disperses the light according to
wavelength.
Concave mirror E then focuses the light on the exist slit F, forming a
spectrum across the exit slit.
Only the particular wavelength that falls directly on the exit slit
passes through it and is detected.
Adjusting the rotating angle of the grating changes the wavelength
that passes through the exist slit.
In a standard monochromator design, the entrance slits and exist slits
have equal width.
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The wider the slit widths, the larger the range of wavelengths that
passes through the monochromator.
Most research-grade instruments have user-controllable slit widths.
In general, smaller (narrower) slit widths yield greater spectral
resolution but cut down the amount of light that is transmitted
through the monochromator.
In an Absorption spectrophotometer, a monochromator is used to
limit the wavelength range of light passed through the sample to that
which can be absorbed by the sample.
In the most common arrangement, the light source is focused onto
the entrance slit and the absorbing sample is placed immediately
after the exist slit, with the photodetector exactly behind it to detect
the intensity of transmitted light.
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What is the optimum slit width for
absorption spectroscopy?
The answer to this question depends on the purpose of the
measurement.
If the purpose is to record an accurate absorption spectrum, for
example, for use as a reference spectrum for future measurements or
for identification, then a sufficiently small slit width must be used to
avoid the polychromaticity deviation from the BL-law.
The requirement is that the spectral bandpass be small compared to
the spectral width of the absorber.
The monochromaticity or spectral purity of the light incident on the
sample cell is defined by the spectral bandwidth, which is the width
of the triangle (in nm) at one half of the peak intensity.
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Difference between spectral bandwidth,
spectral bandpass and slit width
• The spectral bandwidth is defined as the width of the band of light at
one-half the peak maximum (or full width at half maximum [FWHM])
• Spectral bandpass is the FWHM of the wavelength distribution
passed by the exit slit. Resolution is related to bandpass but
determines whether the separation of two peaks can be
distinguished.
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In a dispersive instrument, the spectral bandpass is given by the
product of the slitwidth (sw) and the linear dispersion (LD).
The slit-width is user-variable in many instruments, whereas the LD is
fixed by the design of the monochromator. So, the SW is adjustable,
setting it to the smallest slit width will insure the smallest spectral
bandpass and result in the minimum polychromaticity error.
However, the signal-to-noise ratio decreases as the slit width is
reduced, so it is not always practical to use the smallest slit width
possible.
A smallest slit width, even if it is possible on that spectrometer, will
not be useful if the random signal-to-noise error exceeds the error
caused by non-linearity.
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The effect that increasing slitwidth has on measured absorbance value
depends on the width of the absorption band and on whether the
wavelength of measurement corresponds with a maximum or minimum
absorbance.
The width of the absorption band is defined as natural bandwidth, which is
the width of the absorption band at one half the A max.
Furthermore, as the absorbance increases due to higher conc. Or longer
pathlengths, the % error increases, resulting in a negative deviation from
the BL-Law.
If the slit width is too narrow, the resultant reduction of the incident
energy lowers the signal to noise ratio and decreases the precision of the
measurement.
The optimum slitwidth is therefore the widest setting that provides
spectral fidelity.
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Scanning speed
• If the scan speed selected for the automatic recording of the
spectrum is too fast, electronic and mechanical damping of the
spectrophotometer’s signal to the recorder may prevent the recorder
pen responding quickly enough to the rapid changes of absorbance.
• The effects observed in progressively faster replicate scans of an
absorption spectrum are that the apparent lambda max is displaced
in the direction of the scan, Amax are decreased, Amin are increased
and the resolution btw adjacent bands is reduced.
• The optimum scan speed is normally the fastest speed that maintains
the pen fidelity.
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Stray light
Any radiation reaching the photodetector other than
the narrow range of wavelengths normally transmitted
by the monochromator.
It arises from scattering and refraction inside the
monochromator, due to mainly imperfections on the
optical surface.
If stray light comprises wavelengths which the sample
does not absorb, it will fall on the photocell during the
measurement of the intensity of both the incident
light (Io) and unabsorbed light (IT). Thus, the observed
absorbances is given by:
Aobs = log [Io+ SL/ IT + SL]
88
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89
 The effect of stray light is
particularly evident at high
absorbances, i.e. when IT is
low, where deviation from the
BL-Law may be observed.
 This figure shows the effect of
increasing levels of stray light
on a Beer’s law plot.
©

It should be noted that the
spectrophotometer cannot measure
absorbances greater than that corresponding
with the level of stray light.
For example, if the unabsorbed stray light is
equivalent to 1% of the intensity of light at a
particular wavelength, the limiting value of
Aobs is 2 (approximately). 90
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The effect of stray light may also be seen at wavelengths near the
extremes of the usual wavelength range of light sources, where the
available energy is low.
For example, the intensity of light from a Deuterium lamp below 220
nm decreases rapidly with decreasing wavelength.
Unabsorbed stray light of higher wavelengths may reduced the
absorbance sufficiently for a spurious maximum which are common
below 220 nm and may be detected by marked deviations in Beer’s
law when solutions of different conc. are examined.
Alternatively, stray light at a particular wavelength can be detected by
placing the solution of a substance that is known to absorb
completely at that wavelength.
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Observed absorbances other than infinite absorbance (%T = 0)
confirms the presence of stray light.
Chemical effects
Deviations from BL-Law may occur if the substance undergoes
chemical changes (e.g. dissociation, association, polymerization,
complex formation) as a result of the variation of conc.
For example, a solution of benzoic acid high conc. In a simple
unbuffered aqueous solution has a low pH and contains a higher
proportion of the unionized form than a solution of low conc.
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• The ionized and unionized forms of benzoic acid have different
absorption characteristics:
λmax = 273 nm λmax = 268 nm
ε273 = 970 ε268 = 560
Therefore, increasing the conc. of benzoic acid produces higher
absorpitivity values at 273 nm with positive deviation from BL, and
lower absorpitivity values at 268 nm with negative deviation from
beer’s law.
93
C6H5COOHC6H5COOH
©

References
• Beckett and Stenlake, 5th Ed., CBS publishers
• YR Sharma, Introduction to spectroscopy
• Pavia, Introduction to spectroscopy
• https://commons.wikimedia.org/wiki/File:Bohr_atom_animation.gif
• https://www.priyamstudycentre.com/2019/02/hydrogen-
spectrum.html
• https://www.edinst.com/blog/jablonski-diagram/
94
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Instrumental Methods of Analysis

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