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welcome to the lectures on molecular spectroscopy
in this week which is the first week we have
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a few introductory concepts and the first
lecture is on basic properties the we should
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know of the electromagnetic radiation now
spectroscopy is the introduction of electromagnetic
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radiation with matter and the properties of
electromagnetic radiation such as the electric
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field the magnetic field their variation in
time and how the wave lengths and the wave
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frequencies of this radiation are connected
to the energies of so one is the focus of
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this lecture
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so let me first introduce you to the oscillating
electric and magnetic fields as waves so what
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we see here is ah an axis system x y z rectilinear
in which the time dependent oscillations of
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the electric and magnetic fields are shown
as waves in mutually perpendicular directions
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you can see that the blue ah oscillation is
marked as magnetic field and its in the y
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z plane the red oscillation are marked as
the electric field and thats plane in a perpendicular
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to the y z namely the x is at x is at plane
and both of this waves ah the oscillations
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both of this oscillations red and blue oscillations
are perpendicular to the direction of propagation
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which is the propagation marked as direction
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so electric field and magnetic fields of an
electromagnetic radiation oscillate in time
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with a same frequency so this is the ah purpose
of showing this animation and you can see
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that and you want to play this again you can
see how the waves are shown as oscillating
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in time
this is a classical picture albert einstein
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of course came up with the theory that light
is it consists of what are called the packets
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and the packets have specific energy which
are proportional to the frequency of the oscillation
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so lets now ah introduce some of those terms
the oscillation of the electric field in time
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and in space is typically given by a simple
harmonic ah oscillation namely the electric
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field which is a vector is given in the terms
of magnitude of the amplitude of the wave
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e naught and a cosine k where k is called
the wave vector for the wave and is given
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by the wave length of the wave we will see
in that in a minute lambda is the wave length
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so e is e naught of cosine k z minus omega
t and omega is known as the angular frequency
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of the wave it as to be k as to be inverse
ah dimension of z which is length and omega
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as to be inverse dimension of t and you can
see that the omega angular frequency is given
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by this formula two pie times mue where mue
is the frequency of oscillation the magnetic
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field b is given in a similar passion with
an amplitude b naught by c and a cosine oscillation
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also given by k z minus omega t in both cases
i have put in factor called a phi which is
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usually a phase shift or a face difference
for the waves shift thats the starting point
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of the wave we can determine
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now there are two or three properties that
i have introduced the wave length angular
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frequency and also introduced a unit called
wave number lets see the frequency of the
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wave mue is basically the number of the waves
the passing point given in a unit time lets
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see that in the oscillation here you can see
that the frequency is number of waves for
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example passing through this point the blue
dot that you see here in a unit time so its
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number per unit time the number of full waves
is pass a given point in one second here the
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time is in in seconds and the number per second
is called the frequency the other definition
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that you have to keep in mind is the wave
length wave length is denoted by the symbol
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lambda and being a length as the unit of length
and usually in terms of meter or sub units
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of meter like ah millimeter or micrometer
or nanometer
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so on but the wave length is the is the length
of one oscillation the wave number is the
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number of such waves in a unit length so lets
see that the wave length is the length of
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a wave a full wave and you can see that a
full wave obviously marked by points of repeated
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occurrence successive occurrence for example
between the two cress or between the two turfs
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or between the starting point of the wave
or some time amplitude being zero or some
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amplitude and going through one full cycle
whatever is the distance that length is called
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the wave length so this is the lambda is the
same whether it is between this times or whether
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it is between this points or its between this
points
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so its successive ah occurrence for its length
of one full wave what about wave number suppose
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we have a unit length marked by a distance
here lets see if this is a unit length then
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in that length the number of waves so you
can see immediately wave length and the wave
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number or inverse of each other because one
is the length of the wave the other waves
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how many such waves are there in unit length
so this are elementary ideas but never this
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are important so we have three units namely
the frequency three quantities namely the
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frequency the wave length and the wave length
which usually written as mue bar and wave
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length is ah with the dimension numbers per
unit length or with the unit meter inverse
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and this are connected to each other through
the speed of light in vacuum in which of course
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as a value c as a value two point nine nine
seven nine two four five eight times ten to
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the eight meters per second thats the speed
of light in vacuum and the relation between
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the frequency and the energy of a photon which
in einsteins formulation the electromagnetic
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wave is treated as a collection of packets
and the energy of individual packets are the
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photon is given by the frequency and h is
of course plancks constant and frequency and
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the wave length are related to each other
by the speed of light c is equal to mue lambda
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and if you substitute for that you see that
energy is h c by lambda or its h c times one
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by lambda therefore you can see that the energy
is proportional to to the wave number the
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energy is proportional to frequency but the
energy is inverse the proportional to the
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wave length
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so this are fundamental relations in treating
the electromagnetic radiation as a wave for
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the course on spectroscopy we shall use electromagnetic
radiation with a classical property that we
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have familiar with that it is a wave the reason
being that such an approximate ah formulation
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is sufficient to understand at fairly detail
level what happens to the transitions what
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happens to the intensities of this spectra
lines and so on of course an exact or more
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accurate even description of the electromagnetic
radiation if it is done in the form of photons
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will require creations of photons of photons
and so on and thats taking more into mechanics
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therefore the spectroscopy that would do is
a combination of two ideas namely the energy
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levels of the molecules being treated quantum
mechanically and the electromagnetic radiations
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treated as a classically so it is a semi classical
model that we will have spectroscopy our approach
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to spectroscopy is that of a semi classical
model semi classical obviously implies that
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its both classical and not classical what
is not classical
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we treat the molecules as a quantum mechanical
system as quantum mechanical system and therefore
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we study the molecular energy level by solving
the quantum mechanical equation namely the
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showing equation and
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therefore molecular energy levels are treated
using quantum mechanics
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the semi classical part the classical part
of the semi classical is that of the treatment
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of electromagnetic radiation as consisting
of waves of oscillating electric field and
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oscillating magnetic field and not necessary
as photons and then invoking the quantum electro
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dynamical theory of the electromagnetic radiation
we dont do that thats for much more advanced
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work and for the current spectroscopy model
and this for probably couple of other courses
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in chemistry the semi classical model is sufficiently
accused please remember molecules by quantum
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mechanics radiation by classical mechanics