WEBVTT
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greetings to you in the last two classes
we have had some sort of introduction to the
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environmental pollution monitoring and then
atom inductively coupled plasma atomic
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emission spectroscopy and then as part of
it go we have decided to look at the structure
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of the atom and what we have covered in the
previous class is the discovery of the fundamental
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particles of the atomic structure and the
nuclear arrangement
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the nuclear arrangement basically consists
of protons and neutrons held together by colonic
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forces and van der waals forces etcetera
and we have also discussed the stability
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of the nucleus depending upon the structure
of the protons and neutrons we also discussed
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about the isotopes now subsequently we have
this we have moved to the outer arrangement
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of the electrons and we have said that
bohrs theory daltons theory and rutherfords
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theory etcetera all these things refer to
the arrangement of electrons around the nucleus
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and the size of this electronic arrangement
the space around which the electrons orbit
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around the nucleus is approximately ten thousand
times larger than the size of the nucleus
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so we have also said that the movement
of the electrons from one orbit to another
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orbit is the reason for the transition
of the elements transition of the electrons
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two different orbitals and these transitions
are governed by quantum mechanical rules and
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the quantum mechanical rules according
to bohrs theory can be interpreted
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and each line spectra for hydrogen atom has
been ascribed to five different series and
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the we have discussed that it is the exact
quantity of energy corresponding to the difference
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in each orbit that that corresponds to
the movement of the electron
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so if all the electrons fall to the principal
quantum number shell that is n is equal to
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one we have what is known as lyman series
and so we this here it is the n is equal
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to one here it is two three four like that
these are the different orbitals and this
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falls in u v and vacuum ultraviolet region
followed by if the electrons fall on to the
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second shell then we have what is known as
balmer series and balmer series is occurs
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in the visible range similarly paschen series
where the electrons fall to the third shell
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around the nucleus that is paschen series
thats in near near i r and i r and then followed
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by bracket series and front series
so n is equal to four five six seven etcetera
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we have different kinds of transitions occurring
around hm the electron which can be
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interpreted like this we also said that the
electrons process around themselves also and
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for each electron we need to describe a position
which is denoted by four different quantum
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numbers that is n l m and s so the sommerfeld
theory modified bohrs theory to include some
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elliptical orbits so he just said unlike
bohrs theory all the electrons are revolving
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around the nucleus in circular orbits but
he modified it to elliptical orbits
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and the elliptical orbit is a special case
of a circular orbit is a special case of
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electrical hm elliptical orbit because
any elliptical orbit is defined by two parameters
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a and b and when a is equal to b then we have
circular orbit so you can look up your basic
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mathematics structure studies to
find out the nature of elliptical orbits and
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circular orbit suffice it to say that circular
orbit is only a special case and that happens
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only in the case of hydrogen and the velocity
of the electron moving in an orbit will be
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greatest as as it approaches closest to the
nucleus
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and least when it is farther this is another
concept of the sommerfeld theory what
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he says is as the electron moves nearer the
nucleus the speed of the electron increases
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as it moves away it is it decreases this is
somewhat similar situation regarding the planets
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the planet arrangement of around the
sun also follow elliptical orbits and whenever
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the any planet comes very near very near the
sun this speed of the planet increases
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and it tends to move further and further away
faster towards further distances
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as it comes as it moves further away the
speed decreases so essentially similar arrangement
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he has proposed sommerfeld and this introduces
variability the in the orbit also which as
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a whole will process around a nucleus so this
precessional movement will result in small
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energy changes and it will be reflected in
the fine structure of the spectrum also so
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the sommerfeld theories contribution to the
spectroscopy is that there will be small energy
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changes which are reflected in the spectroscopic
um fingerprint of all the elements
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so this permitted the subdivision of the bohrs
stationary states of slightly different energy
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levels corresponding to the differences in
orbit shapes so right now as of now this is
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the basis of modern concept of electronic
configurations that means whenever we want
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to build the electrons around the nucleus
that is if you remember your high school chemistry
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periodic table is there all the elements are
arranged according to their atomic weight
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and atomic number
and if you want to know how the electrons
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are hydrogen has one lithium has two hydro
helium is two lithium is three like that beryllium
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boron carbon nitrogen oxygen sulfur all
those things have have one electron each extra
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added to each element and the basis of
modern concept of electronic how the electrons
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are arranged around the nucleus is based on
summerfelds theory
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so it projected the possibility of penetrating
objects also that means the orbit is basically
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a space around the nucleus so two orbits can
interact they can intersect each other depending
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upon the their shapes that means the different
electrons can occupy this common orbitals
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at different times so we what we are saying
essentially is over a period of time there
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will be time waited energy density around
their nucleus in a specific area in a around
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the nucleus in a specific volume
so that is what whenever two shapes are inter
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mixing each other the possibility of two electrons
or more electrons around that area space is
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much more so that is when we call the orbits
are penetrating each other so we hm we have
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some sort of a qualitative picture of the
more complicated atoms also so this is the
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summerfelds model of an atom and you can see
that the when n is equal to one the orbit
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is exactly circular spherical actually the
orbit is circular but the space around the
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nucleus is spherical that means you will be
able to find the electron in this space all
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all over the space but not above beyond this
space ok where i have written a circular
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circle defined a circle
now when the n is equal to two we need to
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have two orbits and you can see that the circular
part remains the same and there is a two p
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and two s also so this two s orbital is a
one s is circular as ours spherical and two
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s is elliptical and you keep on compressing
elliptical nearer towards this side you
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will end up with a circulars in a space so
the actual orbit is two s and two p also there
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is another possibility ok now in three
s we have when n is equal to three so we have
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three s three p and three d orbitals
similarly if it is n is equal to four we have
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four s four p four d and four s like that
the you can see that there is certain amount
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of overlapping for example if you look
at this area the overlapping of n is equal
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to one and n is equal to two there is certain
area in which the spaces overlap that means
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the probability of finding an electron to
finding both electrons in this area exists
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similarly there is more overlapping and as
the electron as the we keep on adding electrons
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along the periodic table the things become
very complicated
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and then it is um the electron can be moving
in any of these areas in any direction
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also and this is known as rosette path
of an electron now this is basically a sommerfeld
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model that is this is the nucleus this
is the electron electron is revolving around
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the nucleus and it is in the electrical orbital
the orbit is an elliptical orbit
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so the distribution of electrons in the atoms
is somewhat slightly more involved i think
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all of this you would have studied at your
p u c level ok so what we are going to do
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now is basically to define the rules not go
into more theoretical aspects so that we have
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a clear understanding of the atomic structure
so first thing we have to know is about the
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rule of eight that is the inert gas atoms
with the exception of helium contain eight
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electrons in their outermost arrangement minimum
maximum eight
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for example helium has got only two all the
electrons which are having less than eight
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the rule doesnt apply of course and neon argon
krypton xenon etcetera all they radon these
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elements if you which you find in the periodic
table to the extreme right they all have two
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electrons and then ten electrons eighteen
thirty six and fifty four ok and eighty six
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electrons also are there in radon so they
represent the end of a reserve various horizontal
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series of periodic classification
so this rule of eight whenever there are eight
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electrons in the outermost orbit it represents
a complete structure of the electrons and
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the element is is a neutral element for example
this helium neon argon krypton xenon and
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radon they are all neutral elements they do
not carry any charge and they are very
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stable in inner they are also known as inert
gas elements ok so they are they do not
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undergo many chemical reactions and all this
because the electronic arrangement is is
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in such a way that there is no exchange of
electrons or energy between the inert elements
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and other other elements
so you know c r bury this is the name of another
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scientist he postulated that maximum number
of electrons in the various shells are two
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eight eighteen and thirty two he also stated
at that time xenon and radon [laughter] etcetera
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they were not discovered that is why he
said thirty two is the last this thing
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he also stated that no shell can contain more
than eight electrons unless another shell
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further removed from the nucleus is being
formed
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so this concept permitted logical explanation
for the configuration of transition and inner
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transition elements we will study about
the arrangement of the electrons in the periodic
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table further what a what actually this means
but i am i suspect that most of you already
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know about these things so we are not going
to elaborate but we will touch upon this
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later
so the um transition and inner transition
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elements are part of the periodic table
we are filling up of inner electronic levels
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um takes place while the outermost orbit
contain the same number of electrons ok so
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how do we look at the electronic arrangement
of these inert elements here i have written
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the symbol helium neon argon krypton xenon
and radon this is the atomic number so number
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of protons or electrons are there so if
there are two electrons there it will have
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only one orbit and that is k k shell one
shell then it can contain maximum two electrons
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then comes the rule of eight so you move the
move to neon it has got ten electrons the
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first will contain two next will contain eight
and go to argon that is the third inert element
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that we know and it contains eighteen electrons
the electronic arrangement will be two eight
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and eight there is ten plus eight is eighteen
similarly go for krypton that is two eight
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eighteen and eight so that you can always
see that the last orbit last shell will have
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only eight electrons whatever is the number
of electrons in the inner shells same thing
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is true with the xenon and same thing is true
with radon
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so the rule of eight is followed very rigorously
in the periodic table while filling the electrons
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so the bohr sommerfeld concept of electrons
revolving around the atomic nuclei is definitely
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you know related to well defined shapes
and it is essentially a rough practical pictorial
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presentation obviously the hm we cannot
define a space around their nucleus in which
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the electron keeps on moving in what exactly
it cannot be traced as a as if you are
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tracing if a ball is moving around you you
tie a string to the ball and then move it
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around your eye can pinpoint wherever it is
there
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but with electrons it doesnt happen so so
it is what it describes is a sort of shape
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and it is essentially a rough pictorial presentation
even if you play with a string string with
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a ball attached and you rotate it very fast
you will also see only a blur defining a particular
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shape look at the fan turning around you above
your head and you can see you will not be
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able to see the shape of the fan blade
but it will show you some sort of a blurred
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picture of the total space in which the fan
blades are moving
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so essentially same thing happens here only
thing is electrons are much smaller and the
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shapes are different so modern concepts are
basically based on the wave mechanics that
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depict the density the relative density of
the electronic charge in any given space around
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the nucleus so at any given point within the
atom the the electron density is based on
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the theory of probability rather than actual
happening
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so this means that electrons will tend
to group themselves in a series of positions
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relative to the nucleus so they may be considered
as energy level because if the electron is
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concentrated in one particular area that area
will be having more negative charge if it
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is less a density it will have relatively
less negative charge so basically it is
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sort of energy level in which we described
that the electron is a is placed at such and
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such energy level around the nucleus the third
electron is in the s orbital p orbital d orbital
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something like that and then the transitions
are permitted only between these energy
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levels from one electron density to another
electron density area this gives rise to the
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spectrum
because there will be number of energy levels
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and where the electron density is more so
from one energy level density electron will
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be moving to higher energy levels when you
excite atom and or they fall to the lower
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different lower different energy by emitting
the radiation emitting the energy two different
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movements different lower level energy
so these energy levels any transition of
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electron gives rise to the spectrum there
so every electron in an element is described
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in terms of its principal quantum number n
and then orbital quantum number l and then
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magnetic quantum number m and spin quantum
number s it is better for you if you
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remember that every electron is a distinct
electron in a given element so the um all
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the four quantum numbers that is n l m and
s are never same for two electro any two electrons
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in a given element ok so that is how if n
m n may be same l may be same magnetic quantum
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number m maybe same if all the three are same
the two electrons that will distinguish them
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only would be through the spin a like one
is will be rotating around the positive axis
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another is rotated will be rotating around
the negative axis
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so each electron around the nucleus is defined
by four quantum numbers which are which do
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not repeat for another electron in the same
element so it is as if it has got a postal
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address wherein it is very distinct so the
energy levels corresponding to the principal
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quantum number n is given by this equation
that is w is the energy of equation minus
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two pi square z square e to the power of four
and then you know the electronic mass multiplier
25:31.880 --> 25:40.840
divided by planks constant multiplied by one
over n square that is if n is equal to one
25:40.840 --> 25:47.510
we have w would be exactly equal to two minus
two pi square z square e to the power of four
25:47.510 --> 25:54.340
and then mass divided by planks constant
so in this equation it is better for us
25:54.340 --> 26:06.970
to remember that w is the energy of the electron
and hm the z is the total number of electrons
26:06.970 --> 26:17.919
or atomic number e is the electronic
charge we know what is the number and mu
26:17.919 --> 26:30.400
is the electronic mass and h is planks constant
so what this equation mean actually crudely
26:30.400 --> 26:40.160
this energy w what we represent it crudely
amounts to the mean distance of the electron
26:40.160 --> 26:48.000
where if the probability of finding it is
maximum and that distance is measured from
26:48.000 --> 26:53.799
the nucleus so that is the main distance at
which an electron may be found
26:53.799 --> 27:03.960
the principal quantum number in that equation
is denoted by n now so the value of value
27:03.960 --> 27:15.870
of n can vary from one to infinity so n may
be one n maybe two n is three like that so
27:15.870 --> 27:22.690
n square becomes less and less and when you
divide it when you divide one by n square
27:22.690 --> 27:32.260
the distance becomes more and more so
as the electron as a quantum principal
27:32.260 --> 27:40.510
quantum number n increases the electron will
be located further and further away from the
27:40.510 --> 27:44.780
nucleus
so you keep on removing the electron further
27:44.780 --> 27:52.100
and further away at some point it will go
out of the orbit of the electron at that
27:52.100 --> 28:01.210
time we call it it is ionized and electron
is no more available around the nucleus
28:01.210 --> 28:06.440
and the nucleus is having excess positive
charge there because the negative charge has
28:06.440 --> 28:11.790
been removed but the new proton or neutron
will not go away only the electron as gone
28:11.790 --> 28:23.180
away so the net charge will be positive so
ion is um hm it is called s ion so principal
28:23.180 --> 28:33.100
quantum number varies these are and they
may be designated as k shell l shell m shell
28:33.100 --> 28:42.299
etcetera ok
so hm as we have seen k shell will have two
28:42.299 --> 28:49.750
electrons l shell will have ten electrons
like that there will be the different arrangement
28:49.750 --> 28:57.870
of electrons now we move on to the second
identity of an electron that is denoted by
28:57.870 --> 29:06.690
orbital quantum number l now what is this
orbital quantum number i want you to understand
29:06.690 --> 29:14.590
that the shell that is n is equal to one n
is equal to two etcetera they represent circular
29:14.590 --> 29:21.750
area around the nucleus and that circular
area keeps on increasing l is equal to k is
29:21.750 --> 29:28.610
equal to n is equal to one n is equal to two
would be bigger n is equal to three would
29:28.610 --> 29:34.730
be bigger circle like that the principal quantum
number and it keeps on increasing
29:34.730 --> 29:43.940
now this orbital quantum number refers
to the movement of the electron in that shell
29:43.940 --> 29:56.789
so because it is moving around the nucleus
the electron will be having orbital angular
29:56.789 --> 30:07.669
momentum so that is defined by this vector
quantity h that is planks constant multiplied
30:07.669 --> 30:17.620
by square root of l into l plus one divided
by two pi so the value of l varies from zero
30:17.620 --> 30:29.870
to n minus one so if n is equal to one n minus
one would be zero so the value of l is zero
30:29.870 --> 30:37.960
if n is equal to two the value of l would
be zero and one
30:37.960 --> 30:43.730
because n is equal to two means n is equal
to one also is there and second one also is
30:43.730 --> 30:49.250
there for n is equal to one it is already
zero n is equal to two it will be n minus
30:49.250 --> 30:54.940
one would be one so n is equal to two will
have two orbitals corresponding to l is equal
30:54.940 --> 31:03.000
to zero that is one orbital and another orbital
corresponding to l is equal to one similarly
31:03.000 --> 31:13.480
if n is equal to three l will have two n plus
one hm it will have zero one and two
31:13.480 --> 31:20.020
similarly n is equal to four would be having
zero one two three it will have four sub shells
31:20.020 --> 31:37.720
ok and customarily these levels are named
after these spectral terms s p d and f so
31:37.720 --> 31:49.850
l is equal to zero these hm referred as
a s orbital l is equal to one is referred
31:49.850 --> 31:59.000
as p orbital and l is equal to three is
referred as d orbital and f would be four
31:59.000 --> 32:06.210
so the electrons present in these orbitals
are referred as s p d f electrons only
32:06.210 --> 32:13.880
now you should remember that this s orbital
is circular this p orbital where l is equal
32:13.880 --> 32:21.900
to one is like a dumbbell and d orbital
also would be dumbbell but with at different
32:21.900 --> 32:30.380
axis same is true with f orbitals also that
is different dumbbell shapes oriented in
32:30.380 --> 32:38.110
space around the nucleus so if you remember
the dumbbell space it will be like this one
32:38.110 --> 32:44.730
space above one space below in between the
dumbbells there is a very thin line that is
32:44.730 --> 32:53.340
connecting the two spaces
so when you draw a dumbbell shape it can be
32:53.340 --> 33:01.100
ascribed a mathematical equation just like
a graph so the wave function is associated
33:01.100 --> 33:07.740
with the orbital motion of the electrons that
wave function is called as orbital thus we
33:07.740 --> 33:28.080
have s p d f orbitals also so we define s
is equal to one s orbital s electrons and
33:28.080 --> 33:36.960
it is also described by a mathematical equation
which is given by s p d f etcetera orbitals
33:36.960 --> 33:48.309
now this is how the electron n is equal
to one n is equal to two n is equal to three
33:48.309 --> 33:56.780
are shown here and this is for hydrogen
atom the electronic orbitals for magnetic
33:56.780 --> 34:03.620
quantum number m is equal to zero so when
n is one you can see that there is a small
34:03.620 --> 34:11.309
red dot here it is a circular this is the
arrangement of electron ok so the electron
34:11.309 --> 34:19.419
would be around here then at the center of
this dot there is nucleus so when the n is
34:19.419 --> 34:28.809
equal to two we have l is equal to zero and
l is equal to one here zero is circular l
34:28.809 --> 34:34.749
is equal to one would be sort of dumbbell
shape you can see more clearly the same thing
34:34.749 --> 34:43.279
when n is equal to three we have a bigger
one representing the size of the atom and
34:43.279 --> 34:49.569
then this is circular again this is like a
dumbbell shape and d m n is equal to l is
34:49.569 --> 34:57.950
equal to two would have is also like a dumbbell
shape but oriented differently in space
34:57.950 --> 35:06.990
so n is equal to four same thing is true slightly
clearer pictures but more complicated because
35:06.990 --> 35:14.329
you have to remember that this is representing
a space around the nucleus where the probability
35:14.329 --> 35:22.460
of finding the electron is more in these areas
rather than in between somewhere here in between
35:22.460 --> 35:28.269
the dumbbell shape the chances of finding
the electrons as is very less same thing is
35:28.269 --> 35:34.099
true at n is equal to five n is equal to so
we have n is equal to five means l should
35:34.099 --> 35:39.910
be equal to four you can see that the shape
is more diffused l is equal to one we have
35:39.910 --> 35:47.239
two dumbbell shape and then n is equal to
two l is equal to two we have four dumbbells
35:47.239 --> 35:54.029
like that the number of dumbbells will keep
on increasing in the space around the nucleus
35:54.029 --> 36:05.289
so we will define the magnetic quantum number
and spin quantum number in our next session