Here I am showing you slightly improved figure.
You can see the different ridges here.
This is known as grating normal.
It cuts the grating vertically.
This line is grating normal.
This is the degree of 
the incident angle.
I have shown here the different wavelengths
300, 500, 700, 900, 1100 nm.
That means if I rotate this grating from vertical
position slowly first I can get 300 nanometers
and then 500 nanometers.
If I rotate it more I will get 700 then 900,
1100.
That means right from 300 to 1100 nanometers
I can get by rotating 
the grating.
When I get 300 nanometers I get certain amount
of radiation corresponding to 150 nanometers
that is half of the wavelength.
Then I can get still lower around 60 or something
like that, so this is known as first order,
second order, third order wavelengths.
First 
I 
get zero order.
The intensity of the second order 
would be much less than the first order, it
may be less than 50% or something like that.
Intensity of the third order also would be
much less.
I get both orders both 1 or 2 or 3 orders
with different intensities which may not be
significant.
But for very accurate work I cannot take at
the first order straight away.
Because there will be certain amount of radiation
associated with the second order that is half
of the wavelength.
So if I want to use a only a very accurate
work 
some people use 2 gratings.
With the first grating they get the first
order and then second order also.
And that radiation that comes out of that,
they will make it fall on the another grating
and again they get the first order.
so at that time the intensity of the second
order would be almost zero.
There are ways of getting rid of the second
order and third order.
But quite often it is not very important for
routine analytical purposes.
So one grating should be more than enough
for typical applications.
Sometimes people use a grating known as Echelle
grating.
Here I have to tell you that the number of
rulings is what makes quality of a grating.
Typical rulings vary from 1200 to 30,000 per
centimeter.
It is a great achievement.
It is an engineering marvel to draw 30,000
lines parallel per centimeter.
And the maximum typical numbers used in spectrophotometer
contain from 1200 to 1800 or something like
that.
That means in a single grating you will get
about 1200 to 1800 prisms.
The accuracy of the wavelength that comes
out would be much more of very high quality
compared to a prism.
Because in prisms there is only 1 prism.
Here I have 1200 prisms for the same radiation.
So a typical edge looks like this in this
figure I have shown here know 300 prism is
like this.
But there is special case I want you to understand
that I can use smaller number of gratings
containing about 70 to 80 lines per centimeter.
And then I can use the prism to separate the
remaining.
The second order, third order gratings are
automatically removed with minimum effort.
Instead of using 2 gratings I can use only
1 grating and a prism.
This type of arrangement where the number
of rulings are hardly 75 to 100, 130 etc.,
is known as Echelle grating.
Now-a-days 90% of 
the 
instruments in infrared spectrometer contain
Echelle gratings.
Now I want you to look at the top figure here.
I have a concave mirror and then all the radiation
that comes out is parallel.
That is the quality of the concave mirror.
That is why lot of concave mirrors are used
in most of the instruments.
And then I put a mechanical plate with a small
hole that allows me to take out only a small
portion of the incident radiation that is
coming out into the disperser.
This disperser could be either a prism or
a grating or Echelle grating with a prism
and all that.
So, from here I get all different wavelengths
and then I put 1 more slit here to choose
the radiation that is coming out.
If I move down I get shorter wavelengths if
I move up I get the longer wavelengths.
Now you can remove the photo.
There are different ways of doing this.
Instead of concave mirror.
I can use a plane mirror.
And then mechanical slit and then disperser
and I can have number of slits here instead
of a single hole like this on the top.
I can have number of holes which will permit
me to take out different wavelengths simultaneously.
If I put a detector on at each point I will
have what is known as multi channel detector
instrument.
A very simple arrangement.
But such instruments are also available including
the infrared spectrometers.
The monochromator slits play an important
role in determining its performance characteristics
and quality.
Usually two slits are employed one is entrance
slit which I shown you earlier after the concave
mirror and another one serves as the light
source which is exit slit on which the image
of the entrance slit is formed.
These are all very standard stuff described
in most of the reference books which I have
prescribed for this course also.
If the radiation source consists of discrete
wavelengths, a series of rectangular images
appears on the exit plane which appear as
bright lines corresponding to different wavelengths.
Movement of the monochromator setting in one
direction or the other produce a continuous
increase or decrease in the emitted intensity
when the entrance slit image has moved a distance
equal to that of its full width.
Illumination of the exit slit with the desired
wavelength is invariably associated with some
unwanted radiation.
This unwanted radiation normally is a radiation
having slightly differing wavelength than
what we have chosen.
Whenever we use particular wavelength from
a monochromator slit I do not get a single
monochromatic radiation but a band of radiation
containing mainly the one what we have chosen
and a little bit of this side and that side.
That is known as band width.
This is the pictorial representation of a
band width.
Here λ2 is my desired wavelength.
The maximum intensity of the radiant power
and this would be the intensity on the y-axis.
Maximum radiation is here but I also get radiation
corresponding to λ1 and λ3.
These are also nearby but maximum intensity
λ1 is almost nil here at this point this
is another slit from here.
At this point at the edge λ1 is nil, λ3
is nil only λ2 but somewhere around this.
I get both λ1, λ2 and λ3 and the λ2 intensity
would be very high.
So, since I get all the 3 wavelengths corresponding
to this radiation that is known as effective
bandwidth.
This is my exit slit, so much of radiation
keeps on coming but it will correspond to
a little bit of λ1 and λ2 and the effective
bandwidth.
This described by the size of the exit slit
also (watch the vedio).
That is what exactly I have written here.
When the monochromatic light falls on the
photocathode i.e a cathode coated with alkali
metals, electrons of varying kinetic energies
are emitted from its surface and fly over
to the anode in a phototube as long as the
voltage V applied between the anode and cathode
is positive.
It produces a small current.
Now we are talking about the interaction of
electromagnetic radiation with the detector.
Detector is nothing but a piece of metal on
which alkali metals are coated.
When the radiation impinges on this, electrons
of varying kinetic energy are emitted and
a small current flows in the circuit.
When the voltage across the phototube is adjusted
such that anode is negative the photoelectrons
are repelled by the anode and the photocurrent
decreases.
That means depending upon the voltage I get
different kinds of current corresponding to
the number of electrons that are released.
When I do not have the sample maximum current
is obtained.
When I have the sample part of it is absorbed.
So, the remaining part of the radiation that
falls on the detector that will produce less
current.
This current difference can be correlated
to the concentration of the pollutant, whatever
we are trying to determine.
The photoelectric current is measured as a
function of the applied voltage V0 at which
photoelectric current reaches 0, that is multiplied
by the electron charged by the coulombs 1.60×10-19.
That gives the kinetic energy of the electrons
in joules.
Maximum kinetic energy for various coatings
are plotted as a function of radiation frequency
and we get straight line.
A straight line response with the slope of
h with an intersect w which is known as work
function.
This is the theory of the detectors.
The plots can be described by the equation
KEm=hν - work , w is the work function, E
is KEm+w energy that is corresponds to hc/λ.
w is the characteristic of the surface material
and represents the minimum energy of binding
the electron to the metal atom.
So the moment, binding energy exceeds electron
will be released and current will flow.
It is also equal to the energy of the electromagnetic
radiation energy of the photon required to
eject the photoelectron from the irradiated
surface.
It can be concluded that no electron can be
ejected until the work function is exceeded.
Therefore energy is not uniformly distributed
over the beam front but concentrated in packets
or bundles of energy which is a thumping confirmation
of the quantum mechanical theory.
That is all about the detectors.
So the equation permits the calculation of
the energy of any electromagnetic radiation
of known frequency or wavelength that includes
infrared spectroscopy also.
Now I will just arrange to give you a small
demo regarding the energy of the electromagnetic
radiation and how we can use it in our day
today life.
I am going to present you one small example.
Here you can calculate the energy of the 5.5
A0 unit radiation that is an X-ray photon.
Here you can fill up the numbers E = hν or
hc / λ and you can put the h value.
Then c is 3×108 and then wave length.
So if you solve this you can calculate the
energy of the incident radiation corresponding
to this wavelength.
Now I can give any wavelength and ask you
to calculate what is the corresponding energy
of the electromagnetic beam.
That is the purpose of showing you this example.
Across the electromagnetic radiation if I
know the wavelength, I can calculate the energy
of the electromagnetic beam of that wavelength.
Here is one more example.
430 nanometers.
Earlier one was in X-ray region.
Now in the visible region 430 nanometer.
Again I use the same equation E = hc / λ.
The numerator will remain the same that is
6.63×10-34 joules seconds multiplied by the
velocity of the electron and divided by the
wavelength.
We will get 4.65×10-19.
The energy is usually we express in kilo joules
per mole.
I can write 4.6255, I had to multiply it by
number of the photons per mole into 10-3 to
convert it into kilo joules.
If I convert that I get the energy of the
430 nanometer photon corresponding to 278.4551
Kilo joules/mole this is only a demo example.
But maybe I will ask you in the exam also.
The quantum theory originally was proposed
for black body radiation.
Now I want to explain to you quickly other
aspects of instrumentation electromagnetic
radiation so that we can proceed on to the
infrared spectroscopy.
Part of it that is the main body of our course.
Now I want to tell you that the quantum theory
was originally proposed for black body radiation
that was extended to explain the emission
and absorption processes.
The essential postulates are like this.
The ions, atoms and molecules exist only in
certain discrete energy states.
When it changes its state it absorbs or emits
an amount of energy exactly equal to the energy
difference between the two states.
This is one postulate.
Another one is, during transition, energy
from one energy level to another energy level
the frequency or wavelength of the radiation
emitted or absorbed is equal to the energy
difference between the states.
I can write E1-E2 is equal to hν or hc/λ
and by E1 is the energy of the higher state
and it was the energy of the lower state.
Now I can also say for atoms and ions in the
elemental state the energy of the state rises
from the movement of the electrons around
the nucleus.
This we have already discussed a little bit
in the introduction part itself during atomic
structure.
Such energy levels are called electronic energy
levels.
Then I have vibrational energy levels and
rotational energy levels.
The lowest energy state of atom or a molecule
that exist at room temperature.
The energy populated at room temperature is
called as ground state, higher energy states
are termed as excited states.
Detectors used in infrared spectroscopy work
on the principle of photoelectric effect,
which I enumerated just now.
These include photomultiplier tubes and diode
array detector.
These are the technical terms for the detectors
used in infrared spectroscopy.
We can continue our discussion on the interaction
of radiation with matter.
A sample can be subjected to a chemical stimuli
in the form of heat, electrical energy or
light, bombardment or chemical reaction.
The stimulus causes the analyte species to
move from one energy state to another energy
state.
In the process energy is absorbed or scattered.
Information about the analyte can be obtained
by measuring the electromagnetic radiation.
In most of the atomic spectroscopy including
infrared, molecular spectra and other things
the measurement basically is of electromagnetic
radiation not of the sample.
But sample will have an effect on the energy
of the electromagnetic radiation that it is
going to interact with.
So most of the analytical instruments measure
the energy of the electromagnetic radiation.
We can get the information about the analyte
by obtaining electromagnetic radiation itself.
This is how normally we depict the emission
process here.
I have a sample and I will supply energy,
it goes from this state to higher energy state.
And then this is E1, E , E2 1 etc.
The energy difference between this and this
is when there is a interaction, when there
is no interaction like that at different wavelengths.
That is the emission.
Now absorption.
Part of the energy is absorbed and what comes
out would be the transmitted radiation and
its intensity would be lower than the incident
radiation P0.
I have similar energy levels 0, 1 and 2.
I have E1 = hν1 that is equal to hc / λ.
E2 is difference between these two.
The emission of radiation is another one,
but we are not going to consider much about
the emission.
Because, we are going to talk about infrared
absorption spectrum but just for the sake
of brevity let us spend little time for emission
also.
When excited atoms, ions or molecules return
to the ground state the excess energy is released
as heat or in the form of radiation that is
photons.
The excitation can be brought about by bombardment
with electrons or other elementary particles.
That gives rise to X-radiation.
Electric current as spark or heat source such
as dc arc or furnace etc., can be used as
energy sources.
This gives rise to ultraviolet, visible light,
infrared radiation etc.
Beam of electromagnetic radiation this produces
fluorescence, sometimes.
Exothermic chemical reaction produces chemiluminiscence.
But we are not going to consider any of these.
But these are the different things you should
know about.
There are different types of spectra.
The typical spectra have three components
i.e lines, bands and continuum.
Lines spectra are a series of well defined
peaks.
Band spectrum consists of a several groups
of closely spaced but not well resolved peaks.
Continuum part has no boundaries.
It is sort of illuminated area that contains
your spectra.
Sometimes the line spectra and band spectra
are super imposed on one another.
That is also seen especially in solar spectrum.
But that is not important as far as our course
on infrared is concerned.
Line spectrum of atomic particles are preferably
obtained in the gas phase.
Because the matrix effects are very less in
the gas phase.
Typical widths of the peaks are about 10-5
nanometers or
10-4 A0 units.
X-ray line spectra are produced by transitions
of the electrons when they fall from higher
energy level to the lower energy level.
From higher shell to lower shell they emit
certain radiation of lower energy that is
x-rays.
And band spectra produced by radicals, small
molecules and bigger molecules also but the
peaks are associated with the vibrational
energy levels.
The life time of vibrational energy state
is approximately 10-15 seconds compared with
that of the electronic state excitation that
is about 10-8 sec, almost double the electronic
state.
So the transition always occurs from the lowest
vibrational energy level of the excited state
to any of the vibrational energy level of
the ground state.
The loss of energy from vibrational levels
to that of ground state, lowest energy level
occurs through the collision with other molecules.
I hope you are able to understand what I am
trying to tell you.
Now first I take certain amount of material
excited to higher energy state.
From there it falls slowly couple of steps
until it reaches the ground level of the vibrational
excited state.
It comes to zero of the excited states and
then it falls to the zero of the ground state.
That is what we are talking about.
Black body when heated to incandescence produces
continuum spectrum.
I think everybody is familiar with this.
Early mornings sunlight containing red, blue,
yellow etc., are all sort of continuum spectrum.
The energy peaks shift to shorter wavelengths
with increasing temperature.
Heated solids are important sources of UV,
visible as well as infrared radiation.
That means the IR source lamps which we use
should be of heated solids only.
The sources of the radiation for electromagnetic
radiation 
are usually bulbs, Thomas Alva Edison’s
bulbs, tungsten lamps etc., now-a-days there
are LED lamps, fluoresce, hydrogen lamps etc.
All of them contain a heated surface.
Most of the radiation sources are basically
heated surface even though they are called
as bulbs technically.
We will continue our discussion in the next
class.
Thank you very much.
