The electron has got its own spin quantum
number; that means it can recess on its own
axis, so that the angular momentum is defined
by Planck's constant multiplied by spin quantum
number into spin quantum number plus 1 divided
by 2 pi.
The value of s is given 1 half or minus half
depending upon whether it is precessing along
the applied magnetic field or opposing the
magnetic field. For each value of m l, there
are two electrons differing in spin. Therefore,
what we can summarize is no two electrons
within any atom can have the same 4 quantum
numbers. This is known as Pauli exclusion
principle. Each electron differs from every
other electron in a given atom in its total
energy; that means either principle quantum
number or orbital moment quantum number or
magnetic quantum number or spin quantum number
-- all the four cannot be the same. At least
in one of them, the electron should differ
in every atom. So, this gives rise to a plan,
where we can keep on filling the electrons
and build up the elements.
For example, for K shell, we have principle
quantum number n would be 1; and, l should
be n minus 1, that is, 0; and, m l should
have 2 l plus 1; that corresponds to m l should
be 0. And hence, it is a single orbital. Only
two electrons are permitted in this orbital
with differing spins: one could be plus half
and another could be minus half. The orbital
is of S type; that means it is symmetrical
around the nucleus. Similarly, for L shell,
we have eight electrons according to Pauli
exclusive principle. For M, N, O shells, we
have 18, 32 and 50 electrons can be accommodated.
According to the principle of maximum multiplicity,
when an electron enters a level of fixed principle
quantum number n and l values, available orbitals
are occupied singly until each orbital is
occupied before any pairing occurs. This is
important for us, because among the 5 orbitals,
we have 3 orbitals in the p x, p y and p z
in three different directions. Even then,
one electron should go to p x, one electron
should go to p y, and another electron should
go to p z. Then only, another -- fourth electron
can enter the p x. Like that this gives us
a plan to fill the electrons and build up
the atoms.
The knowledge of the exact order in which
atomic orbitals are occupied is based on the
interpretation of atomic spectra in terms
of how spectral lines result from permitted
electronic transitions. Heavier atoms have
complicated atomic spectral patterns and overlaps
occurring in the similar systems.
You can take a look at this. This is the s
orbital that is round, spherical; p orbital
-- there could be three p orbitals: one along
p x; one along p y; and, one along p z. And
then, d orbital shapes are like this, where
the probability of electron being found around
the nucleus in this region of space is maximum.
And then, s orbitals -- we have shapes something
similar to this.
So, this is p x, p y and p z orbital.
Now, the energy level diagram also will tell
us that first the 1s orbital is filled in
which two electrons are permitted; and then,
the next electron will go to 2s; and then,
2p; then, 3s, 3p; and then finally, as the
electrons keep on increasing in number, the
orbital energy levels can get mixed up and
the electronic structure becomes complicated.
So, this gives rise to a filling order. We
can imagine like this -- first is 1s, and
then 2s, and then 3s, 2p, then 4s, 3p, 5s,
4p, 3d. Like that we can have electrons filled
for each element, where atomic number increases
by one unit and the electrons also increase
by one number.
So, if you go around looking at it and then
try to fit the electrons in different orbitals,
we will have hydrogen with one electron and
then helium with two electrons, then lithium,
beryllium, boron carbon, nitrogen, oxygen
and fluorine that go on adding one electron
each; and, one atomic number also keeps on
increasing if you are arrange all these in
a proper order. As described by Professor
Mandeleev, we have a periodic table and this
periodic table is a summation of all the elements
that we know on the earth. And, this is the
best way of representation.
For example, here you can see all these are
basically nonreactive elements, where electrons
like helium, neon, argon, krypton, xenon,
radon -- they are all called as noble gases.
And then, here is hydrogen, lithium, sodium,
potassium, cesium, rubidium, francium, where
one electron is there in the outer most orbital,
that is, s orbital. And then, beryllium, magnesium,
etcetera -- these are all basically divalent
metals. And then, we have transition metals
in which the electrons get filled up in the
inner orbital -- d orbitals. And, zinc, cadmium
and mercury are known as post transition metals.
And then, we have nonmetals in this region
IIIA, IVA, VA, V1A and VIIA groups.
And, here you can lanthanides as well as actinides.
And, here also inner filling of the d and
f orbitals take place -- f orbitals in lanthanides
and actinides and d orbitals in the transition
metals. And, you can see the portion marked
in the red corresponds to silicon, phosphorous,
sulphur, selenium, arsenic, tellurium, germanium,
a little bit of tin, etcetera. These are called
as semimetals or metalloids. And, fluorine,
chlorine, bromine, iodine, etcetera are all
called as halogens, which are nothing but
basically gases. But, they are all found in
the environment as salts when combined with
the metals represented in this area. Here
we stop for the atomic structure.
What I want to tell you at this stage is that
the elements found in this periodic table
are all in the nature available to us. And,
these elements are used in different combinations
in different substances. And, they enter into
the atmosphere, etcetera and then we have
the problem of determination of these elements
in trace and ultratrace elements. So, with
this structure in our mind, let us go and
take a look at how the electromagnetic radiation
interacts with these metals.
All the analytical methods available to us
for the characterization and determination
of the analyte can be broadly classified into
spectrophotometry -- spectrometric and non
spectrometric methods. This classification
is not exactly based on scientific principles,
but it emphasizes the importance of spectroscopic
techniques compared to other forms of chemical
analysis. In general, spectroscopy refers
to the interaction of various types of electromagnetic
radiation with matter, but can be logically
extended to include acoustic waves, ion beams
and electrons, etcetera. In one form or another,
all these techniques measure the change in
the intensity of the radiation or energy changes
when the matter is exposed to electromagnetic
radiation including X-rays, gamma rays, ultraviolet,
infrared, microwaves, and radio waves, etcetera.
So, let us look at the nature of the electromagnetic
radiation.
What is electromagnetic radiation? The characteristics
of electromagnetic radiations are best described
by a classical sinusoidal wave model. This
model fails to account for the absorption
and emission of the radiant energy. Phenomenon
associated with such processes can be explained
by considering the electromagnetic radiation
as a continuous stream of discrete particles
of energy called as photons. The wave particle
duality of the electromagnetic radiation is
basically complimentary to each other and
rationalized by wave mechanics. So, a plane-polarized
electromagnetic radiation of a particular
frequency follows a sinusoidal oscillation
along the direction in which the wave is propagating.
So, if the wave is going like this, the wave
will be going like this and it has got an
electronic component as well as a magnetic
component. That is why it is called electromagnetic
radiation.
Such a plane-polarized wave is represented
mathematically. So, mathematically, an electromagnetic
wave can be described as a sine wave something
like this -- A is equal to A 0 into sine theta;
where, A is the amplitude at any point; A
0 is the peak amplitude; and, theta is the
continuous variable.
Now, it can also be represented as A 0 into
sine omega t; where, omega t is equal to theta
and omega is the angular velocity in radians
per unit time. A complete cycle occurs when
w t changes from 0 to 360 degrees. This is
called one complete oscillation or one period.
Hence, the time over which one complete oscillation
occurs is given by t cycle is equal to omega
divided by 2 pi; or, nu -- frequency is equal
to 1 over t; that is, 2 pi by omega.
Now, for any wave moving at a constant velocity,
we can write v as a velocity is the multiple
of frequency and wavelength; where, v is the
frequency in milli seconds; nu is in hertz,
that is, cycles per second; and, lambda is
in meters. The frequency nu is the proportional
to the energy of the photon given by E is
equal to h nu; that is, Planck's constant
h defined as 6.62 into 10 raised to minus
27 ergs when E is expressed in ergs. And,
if you express it in joules, its value would
be 6.63 into 10 raised to minus 34 joules.
And sometimes, it is convenient to use wave
number denoted by nu bar to describe the radiation,
for example, in infrared spectrometry. Then,
the photon energy is expressed as E is equal
to h c into nu bar; where. c is the velocity
of light.
Now, we have talked of so many properties
of electromagnetic radiation. Let us take
a look at the units, because these are the
units we will be talking quiet frequently.
Now, you know here it is nanometer; its symbol
is Nm and unit is unit for wavelength; and,
this symbol nanometer is used in ultraviolet
visible and near-infrared regions. And, you
can also use angstroms and symbol is like
A zero; and, it is used in X-ray, UV-visible
spectrophotometry in older work. You can also
describe the same thing as milli microns;
and, this is used in visible range, that is,
in older work. Nowadays, most of these units
are used as nanometers.
And, wave number -- as I told you, the unit
is in centimeters inverse and frequency divided
by velocity of light; it is used in infrared
as well as in UV-visible. But, it is very
less common in UV-visible. You can also use
electronic volts (eV); and, unit for energy
used in X-ray and gamma ray. And, hertz is
of course, the unit for frequency and it is
used in radio frequency and microwave applications.
Cycles per second is also is the unit for
frequency and it is used in radio frequency,
but nowadays it is used very less in current
literature.
And, the same thing I can tell you that it
may be noted that regardless of the time of
the units of expression, any electromagnetic
radiation of frequency nu will have unique
wavelength and energy. The longer the wavelength,
lower is it is energy and frequency. Energy
is closely related to the temperature of any
object also. It can be expressed as E is proportional
to K B into T; where, K B is the Boltzmann's
constant and its value is 1.380 into 10 raised
minus 16 ergs and units are K inverse atom
inverse or 1.380 into 10 raised to minus 3
joules K inverse and atom inverse. If we consider
energy per mole of the material, then E can
be defined as being proportional to RT; where,
R is the gas constant and its value is 8.3145
into 10 raised to 7 ergs K inverse mole inverse
or 8.3145 joules K inverse mole inverse.
Now, the energy of the photons should not
be confused with the brightness or intensity
of the source. But, it relates to the colour
of the light. The power of a light source
is given by P is equal to number of photons
light it emits multiplied by the energy of
the photon. It is the energy of a beam of
radiation that reaches a given area per second.
Intensity of a source of radiation is the
power emanating per unit solid angle. This
is a very important concept that we will be
talking about later.
Now, you can see the electromagnetic spectrum
as consisting of a range of radiations. You
can define it in terms of frequency, that
is, here. You can define it in terms of angstroms,
micrometers and then millimeters, centimeters,
and meters, etcetera. And, you can define
them in terms of specific radiation, such
as gamma rays, X-rays, ultraviolet, visible
light, near-infrared, far-infrared. Then,
we have microwaves and then we have radio
waves. You can see that the visible light
is only a very small portion of the whole
electromagnetic range and it is composed of
seven colors, that is, violet, indigo, blue,
green, yellow, orange and red.
If you take a look at this electromagnetic
radiation, you can see that the range starts
from 10 raised to minus 6 nanometers up to
100 megameters, that is, kilometers. And,
the lowest would be gamma rays and the range
is from up to 1 angstrom unit. All the radiations
corresponding to this are called as gamma
rays. And, these rays can be used for the
determination of elements in techniques, such
as etcetera. And then, X-rays -- you know
that there are different kinds of X-rays:
soft X-rays and hard X-rays. Soft X-rays are
used in medical science for the image in the
bones and tissues, etcetera; and, hard X-rays
are used for the determination of metals.
And after the X-rays, comes the ultraviolet
rays. In the ultraviolet rays, we have far
ultraviolet, then ultraviolet, and then visible
region -- vacuum ultraviolet. These are the
three parts/regions of ultraviolet: one is
vacuum ultraviolet, another is far ultraviolet,
then we have normal ultraviolet. Up to 165
nanometers we have vacuum ultraviolet; and
then, between 165 to 180, it is all far ultraviolet;
and, 180 to 350 nanometers, we have ultraviolet;
from 350 to 800 nanometers, we have visible
range and that visible range is represented
by these areas -- different colours. And then,
after that, we have near-infrared followed
by infrared; and then, far infrared and then
followed by microwave and radio waves.
You can see that all these ranges of the electromagnetic
radiations are used in one form or the other
of a spectroscopic determination. So, it is
very important for us to know electromagnetic
radiations -- they are all used for the determination
of several metals and then organic substances
etcetera. And, all these things are used for
the UV-visible, infrared, vacuum ultraviolet;
and then, we have infrared, far-infrared,
microwave, ESR, such techniques -- they are
all useful.
Now, we would like to know how the radiation
is transmitted, because whenever we use electromagnetic
radiations in our instruments, there are two
types of interactions will occur: one is regarding
the interaction of matter with the instrument
components; and, another is interaction of
the electromagnetic radiation with the sample.
Now, this is how the transmission of radiation
takes place. Before that, let us understand
that the rate of propagation of electromagnetic
radiation through a transparent material,
such as atoms, ions, molecules and particles,
is less than that of vacuum. However, frequency
change will not be observed in the vacuum
or elsewhere, which means that permanent energy
transferred to the medium does not occur.
Therefore, the interaction involved must be
only temporary deformation of the electronic
clouds associated with the atoms and molecules
of the order of let us say about 10 raised
to minus 14 to minus 15 seconds. Since the
velocity of radiation in the media is wavelength
dependent, the refractive index of the media
also must change. The variation of refractive
index with wavelength is called dispersion.
So, essentially, what we are talking about
is interaction of electromagnetic radiation
with materials, not the samples or analyte
what we call it. Variation of refractive index
is called dispersion.
And, what is this dispersion? Dispersion is
basically a very complex phenomena. Dispersion
curves usually show two regions. One is normal
dispersion in which there is a gradual increase
in the refractive index with increasing frequency.
Sometimes anomalous dispersion occurs at frequencies
in which sharp changes occur coinciding with
the natural harmonic frequency of some part
of the molecule or a group of a molecule or
a functional group of a molecule or of that
of ion leading to the absorption of the beam.
So, in general, there are two types of dispersions:
one is normal, which shows the increase in
refractive index with increasing frequency;
another is sharp changes occur.
In spectroscopy, dispersion curves are important
for optical components such as lenses. So,
here the most suitable components for the
manufacture of lenses are those in which refractive
index should be very high and it should be
constant, it should not show anomalous dispersion
of the electromagnetic radiation. Now, why?
If it does not show all these things, this
results in reduced chromatic aberrations.
For the fabrication of prisms for example,
you have to pass the radiation through a prism
and it should not show any other aberrations
except changes in the frequency or changes
in the wavelength. So, for the fabrication
of prisms, refractive index should be as large
as possible, but also highly frequency dependent.
Similarly, diffraction.
Diffraction refers to the bending of a parallel
beam of electromagnetic radiation as it passes
through a sharp barrier or a narrow opening.
It is a consequence of interference, which
can be easily demonstrated in the laboratory.
When a parallel beam of light is allowed to
pass through a pinhole, two closely spaced
pinholes are seen on a screen placed across
it.
If the radiation is monochromatic, what you
would see is a series of dark and light images
appearing perpendicular to the plane of radiation
like this. So, here we have a radiation going
along and we have a small this thing -- a
pinhole; and, the radiation that are coming
out on this side, where we place a screen
on this side, you would see a sharp image
of black and white, black and white, black
and white. So, this phenomenon is diffraction.
Now, let us take a look at another phenomenon,
that is, reflection of radiation. So, what
is reflection of radiation? Mirrors -- you
would have seen the objects in the mirror
and mirrors basically reflect the radiation
falling on them without any loss of the incident
radiant power. Hence, they are used as optical
components of a spectrum. Concave mirrors
-- you would have seen in your cars and scooters
and motorcycles, etcetera; they reflect the
radiation as well as they concentrate the
reflected radiation at its focal point.
When radiation crosses an interface between
media differing in refractive index, reflection
always occurs, some amount of reflection.
For a beam entering an interface at right
angles, the fraction reflected is given by
I r upon I 0; that is, the refraction ratio
is n 2 minus n 1 whole square divided by n
2 plus n 1 whole square; where, we can define
I 0 as the intensity of the incident beam;
and, I r is the intensity of the reflected
beam; and, n 1 and n 2 are the refractive
indexes of the two media. So, this is a very
simple phenomenon. No matter what you do,
reflection always occurs and reflection is
not good in spectrophotometry or in any other
instruments unless the aim is to concentrate
the reflected light, such as a concave mirror
or something like that.
And then, what is refraction? Here I am showing
you the figure of refraction. There is a light
ray coming from one media entering another
media, such as glass and going out of the
glass again. Now, you can see that the light
ray even though it is parallel, even though
it is a single beam, it does not proceed along
the same way; instead, it bends and then proceeds
in another direction. So, you can see that
there are two interfaces: one is this area,
where it is air or vacuum; another area is
this glass or quartz or water or any other
medium in which light passes through; and,
from the medium, again it enters into another
medium. So, there are two interfaces: vacuum
or air.
Usually, vacuum -- we do not come across in
our day to day life, where light passes through
the vacuum. So, it is in general changed to
air. So, you can use a vacuum also, but there
is no problem. But, the normal situations
where we see are light rays entering from
air into one medium and then passing out through
again into the air medium after the medium
ends. So, we have a light ray that bends like
this and then goes out; and, this is perpendicular.
When the radiation passes at an angle through
the interface between two media having different
densities, an abrupt change in the direction
occurs; here abrupt change. This is called
as refraction owing to the changes in the
velocity of the radiation in the two media.
So, the velocity of the radiation changes
in the media. The extent of refraction is
given by Snells law; that is, sine theta 1
divided by sine theta 2 is equal to n 2 by
n 1. That is also the ratio of the velocity
of the radiation in the two medium; that is,
V 2 by V 1.
Now, all these things are college physics
and chemistry. So, I am not going into details
of all these things, but you can look at the
college physics text books, which will explain
these phenomenon in more detail. For example,
in vacuum, V 1 given is equal to 0 and n 1
is unity. So, you can write n 2 is equal to
sine theta 1 divided by sine theta 2. So,
refractive indices of materials can be measured
with air as one medium and available in databases.
Lot of substances, which are capable of refracting
a radiation falling on them are known and
these are available in the databases.
Now, let us take a look at another phenomena,
that is, scattering of radiation. Momentary
absorption of radiant energy by atoms, molecules
or ions followed by remission of the radiation
in all directions is known as scattering.
Particles having comparable dimensions to
that of the incident radiation removes most
the remitted radiation by destructive interference
except those travelling in the original direction;
that is, along the after passing through the
substance. A very small radiation... Particles
having comparable dimensions to that of the
incident radiation removes most of the remitted
radiation by destructive interference except
those travelling in the original direction.
A very small fraction of the radiation is
transmitted at all angles from the original
path and its intensity increases with the
particle size. This is one phenomena.
Another phenomena is scattering by molecules
or aggregates having smaller dimensions than
the incident radiation is known as Rayleigh
scattering. Larger molecules -- what do they
do? They scatter the radiations in different
quantities in different directions. This is
called as Mie scattering. When the scattered
radiation is quantized like those occurring
in vibrational energy level transitions in
molecules as a consequence of polarization
process, then it is known as Raman scattering.
This is another type of scattering, which
is quantized and used in the Raman's spectra.
What is polarization? This is another phenomenon
that is important for us to know what is polarization.
Basically, what you see when a light beam
is passing around, you would see that the
electronic vectors are there, magnetic vectors
are there. A beam of light passing through
a media -- if you view it from the receivers
end, that is, if the light is coming towards
the observer, you would see a number of beams,
a number of parts that is electrical and magnetic
part bundled together in not so systematic
manner. But, it is a big bundle coming towards
you in which the electronic and the magnetic
vectors are mixed up in a big bundle without
any sense of direction or something. Of course,
there is a sense of direction, but you would
see that they are not properly organized.
So, if you put a vertical polarizer in a vertical
plane, what you would see is all other things
are eliminated, except a vertically polarized
light wave; you would see like this. This
is known as polarization.
Ordinary radiation consists of a bundle of
electromagnetic waves in which vibrations
are equally distributed among huge number
of planes centered along the light path of
the beam. Viewed end on it looks like an infinite
set of electric vectors fluctuating from 0
to a maximum amplitude A. The vector in any
one plane say XY can be resolved into two
mutually perpendicular components; that we
have already seen when we started studying
the electromagnetic radiation. Removal of
the one of the two resolved planes of vibration
produces a plane polarized beam. It occupies
a single plane. And, radio waves emanating
from antennas and microwaves produced by Klystron
tube are plane polarized. These are the day
to day experiences. You would have heard lot
of radio, FM radio and other things; and,
you must be having a microwave oven also in
your house. And, the radio waves and microwaves
are plane polarized in our day to day life.
A polarized ultraviolet and visible radiation
is also required. It is produced by passing
the electromagnetic beam through a media that
selectively absorbs or reflects or refracts
that vibrates in only one plane. So, electromagnetic
radiations we need which are plane polarized.
Let us look at another phenomenon that is
diffraction of radiation. What is diffraction?
Basically, diffraction refers to the bending
of a parallel beam of electromagnetic radiation
as it passes through a sharp barrier or a
narrow opening. It is a consequence of interference,
which can be easily demonstrated in the laboratory.
You also would have experienced the diffraction
in your day to day life.
For example, if there is a source of light
that is passing through and a small opening
is made, you would see interference fringes
with light and dark, light and dark, light
and dark patches that are visible here. Even
in day to day life, such systems are very
readily if you have the patience to look at
them around you. For example, when a parallel
beam of light is allowed to pass through a
small pinhole, two closely spaced pinholes
are seen on a screen placed across it. Now,
if the radiation is monochromatic, a series
of dark and light images appear perpendicular
to the plane of radiation. This is the one
what I had showed you.
In the above figure, it can be shown that
vector CF is equal to vector BC into sine
theta. For two beams to be in phase at D,
it is necessary that vector CF should correspond
to the wavelength of the radiation. Therefore,
lambda is equal to vector CF; that should
be equal to BC into sine theta, where BC is
the vector. Since reinforcement can also occur
at 2 lambda, 3 lambda, etcetera, n lambda
should be a function of the vector BC multiplied
by sine theta; where, n is an integer called
as the order of the interference.
Now, this diffraction... When the phase differences
remain entirely constant with time, the system
is said to be coherent. Then only a regular
diffraction pattern is observed. The spacing
of the bands depends upon the distance between
the slits d and the following relation holds
good: n lambda is equal to d sine theta. This
is a very famous equation and you should not
be forgetting in your entire career if you
are undergoing this course. If two different
wavelengths of red and blue are used, the
two colors will be 
separated on the screen. If white light is
used, a number of small rainbows containing
all the colours will appear. By placing a
moving slit across the screen, any colour
or wavelength can be selected. This principle
is used in gratings. We will study more about
gratings and their uses in spectrophotometry,
which is very common nowadays in more detail
when we are studying the spectrophotometry
and UV visible, ultraviolet. and then in atomic
absorption, etcetera.
Now, prisms are the poor cousins of diffraction
units. For example, basically, what is a prism?
All of you would have seen prism. A prism
basically disperses the incident radiation
depending on its refractive index and its
variation with wavelength. A prism can be
used to disperse ultraviolet, visible and
infrared radiation. The material of construction
depends upon the wavelength region. For example,
for ultraviolet, what you would need is a
prism made of silica or quartz. For glass,
ordinary... For visible region, glass will
do. For infrared region, you need salts, for
example sodium chloride, potassium chloride,
potassium bromide; like that salts, which
can be crystallized into these kinds of prisms,
which will disperse the infrared radiation.
Here in this figure, you would see that when
we are passing the white light through the
prism, it separates into its components starting
from red, orange, yellow, green, blue, indigo
and violet. These are the rainbow colours
what you see normally in rainbows. Now, the
same thing essentially happens here and in
the nature also, where the rain drops acts
as the prisms when the sunlight passes through
the rain drops and they get reflected at a
particular angle; and, you would see the rainbow
colours into the sky, which is a beautiful
sight to behold.
Now, the same principle is used in these things
in spectrophotometry as well as in a atomic
absorption, infrared, etcetera. And, you can
see that I have shown you two prisms here.
One is 60 degree prism that is this angle
-- this is 60 degrees; and, they can be made
by the fusion. Suppose you draw a line here.
If you draw a line here, they are made by
the fusion of the right-handed and left-handed
prisms: one here and one here -- the right-handed
and left-handed prisms. And, by fusing together,
you can make a 60 degree prism. And, the other
one 
what I have shown here is a 30 degree prism;
and, this prism is made by -- on one side
it is coated with a mirror surface.
Here the light of the desired wavelength comes
through like this and then passes through
and then goes out of the prism on the opposite
direction. Now, here what is happening? The
light is coming inside and then changing,
going and hitting the mirrored surface, gets
reflected and comes back on the other side.
This type is known as Cornu mounting and the
30 degree prism is known as Littrow mounting.
A prism this is called Cornu. And, mirrored
black, etcetera -- this I have already referred
to you. Here the refraction takes place twice
on the same side with less material coupled
with the saving of space.
