So, we were talking of the peak in scattering
cross section in a scattering when you have
angles much greater than 90 degrees around
say 180 degrees. So, back ward peak and the
kind of energy is that were used in this in
that experiment will suggest that the scattering
or the deflection of the particle should be
hardly few degrees. So, forward peak is or
close to 0 degree peak is well expected but,
a peak of around 180 degrees total back a
scattering that is difficult to understand.
And as we discussed the explanation is much
easier and elegant.
If we are shown that the particles inter change
their nature. So, if centre of mass frame
this is neutron and this is proton and the
because of scattering it goes in this direction
and because of scattering it goes in this
direction. So, only a small deflection in
the path but, then if this b during the inter
action if this becomes n neutron. So, you
get neutron this side and this neutron during
the interaction if this becomes proton than
you see proton this side. And it will appear
to the experimentalist as if the scattering
is through well large angles around 180 degrees.
If protons are going this way protons are
coming this way if neutrons are going this
way neutrons are going returning this way.
Now, this kind of exchange of neutron and
proton, the character of the particle is possible,
if you take the exchange particle charged
exchange particle in to the consideration.
So, from here one can talk of the basic nature
of 4 says interactions which is in contemn
theory mediate by contused particles and from
there one can reach or one can understand
this kind of conversions. The most familiar
case that you have is electromagnetic interactions
and you remember in the school days we say
that.
If there is a charge q 1 and if there is a
charge q 2 than q 1 exerts a force  on q 2. 
So, this is our say first introduction
or first level description. Then, we say that
q 1 exerts an force on q 2, q 2 exerts a force
on q 1 and the force the magnitude of before
is q 1 q 2 by 4 pi epsilon naught r square
and so on. But, then has our understanding
of nature increases our tools are more sharpened.
We say that no this action at the distance
picture is not good it is not consistent with
any of the theories.
And the things so that, second level thing
comes were we introduce field, classical field.
So, that is our next level right second level.
Next level description classical fields we
say that q 1 creates a field  and field exerts force on q 2. 
So, q 1 creates a field so you make
it a 2 stay process q 1 creates a field and
then q 2 is placed in that field that is why
it takes variances force.
So, the interaction is through this field
it is not a direct interaction, interaction
is through this field. So, that is the next
level of understanding and here this classical
field is continuous in all those things. And
then even further when you go next level.
So, these are like 2 dynamics when you talk
in terms of fields classical fields that is
classical electro dynamics. And next level
when you bring in contemn nature into picture
and you talk of quantum electro dynamics;
then you say that this field is not continuous,
it has to be quantised the field has to be
quantised. Any energy transfer has to be in
units of certain minimum package.
So, that contestation field is talked in terms
of quantised units and there comes photons.
The field is described in terms of this quantised
photons and interaction between q 1 and q
1 is through is exchange of, what we call
virtual photons. 
So, the interaction 
is in terms of exchange of photon. It is photons
are the mediator of this electromagnetic interactions
you say that q 1 emits photons and those photons
are absorbed by q 2, q 2 emits photons those
photons are absorbed by q 1. And these photons
which are used in this interaction they are
called virtual photons in the sense that they
are not experimentally observable.
We do not observe those photons as we observed
the photons coming from this tube light. The
light is coming from this bulb and we can
observe that light we can measure the intensity;
we can calculate the number of photons and
all those things. These photons exist for
very short time and we do not observe them,
they only take part in these interactions.
Now, if we do the same thing to our nucleon
interactions.
So, we have a nucleon call it N 1. I have
a nucleon call it N 2 just like a q 1 and
q 2. So, we have 2 nucleons here and the if
the field if the interaction is mediated by
such virtual particles then this N 1 should
emit some particle that exchange particle
and this N 2 should absorbed that exchange
particle. So, n 2 absorbs that particle. So,
that is how the interaction will go. Now,
what kind of particle? Is this photon was
no charge and no rest mass and so on. This
particle can have charge can have mass. Can
have charge if I remember our experiment if
neutron is to be converted into proton and
proton is to be converted in to neutron. That
can happen only if this exchange particle
has got charged right. So, it can also have
mass because the mass is related to range
of interaction because if you consider this
type model this type of mechanism for interaction.
Then crucially Energy uncertainty comes in
to picture. If a non zero rest mass particle
is emitted from a proton. And this protons
still remains proton or becomes neutrons,
mass wise is the same. So, if a particle exchange
particle is virtual exchange particle is emitted
and this nucleons still remains a nucleon.
So, that means that extra energy has created
which is the mass energy of the exchange particle
and similarly, if this particle gets absorbed
into another nuclear and even after that nucleon
remains nucleon 938 M e V remains 938 M e
V so that, means the energy of that virtual
part which is absorbed it appears nowhere.
So, apparently energy conservation is violated.
First you have created a particle a without
talking energy from nucleon, nucleon is still
nucleon proton and neutron is still 938 M
e V and then you have created a particle.
And then that energy that m c square that
exchange particle rest mass energy that got
absorbed in to another nucleon and still its
energy did not increase. So, it appears there
energy and certainty and that is of this type
mass of let me put this pi here.
You know why I am putting pi here? This is
the kind of uncertainty but, than the uncertainty
principal is allows this. You can have this
kind of situations, where energy appears to
been created out of nothing or energy have
appears to get lost in nothing. So, those
kind of are allowed by the theory by the central
theme of the theory. The quantum theory is
one of the very central idea of quantum theory
is uncertain the principal but, then this
is allowed provided this violation this energy
in certainty last for a very short time delta
t which is related to this delta e to that
famous relation delta e delta t is h cross
or h. So, in that case this delta t should
be h cross divided by e, h cross divided by
m pi e square. So, these particles can be
created or absorbed and they should exist
to mediate the interaction between this 2
nucleon, only for a time which is given by
a relation of this type.
And therefore, the range that means this 2
particles are this much far away and if the
part if this exchange part has to go from
here to here should get emitted here and should
get absorbed here or should get emitted and
should get absorbed here. The particle has
to travel this length and even if the speed
of the particle is close to c. This range
of interaction can be, should be less than
or of the order of c times delta t. Cannot
exceed this if this particles are too far
away, then the virtual particles emitted here
will only be absorbed by the same particle
those virtual particles not reach there. But,
they can exist only for this much of time,
because they are when they are created they
are getting absorbed there is an uncertainty
of this order in the energy. And therefore,
they can exist for this much time and so if
this distance between this 2 nucleons is more
than c times delta t. This exchange mechanism
will not give any force interaction between
these two. So, the range is related to the
mass.
So, this is equal to h cross c divided by
m pi c square. From here you can find what
should be the rest mass? Because the range
more or less in it is around 1, 2 femtometers
as the range. So, if you 2 femtometers for
examples, then m pi c square is h cross c
divided by 2 femtometers. And how much is
the h cross c? h cross c is something like
200 mega electron volt, h cross c f m, h c
you must be remembering 1,2,4,0 1240 12 40
e v nm or e v fm. We call it electron volt
nanometer or call it mega electron volt femtometer.
The same 1240 comes divided by 2 pi, 2 pi
is around 6.28 also, it would be 200 M e V
femtometer 2 femtometer so 100 M e V.
So, this exchange particle should have mass
something of this type about 100 M e V per
c square divided by M e V by c square is the
mass unit. So, it should be around 100 M e
V by c square. Compare it to nucleon mass
energy 938 M e V. that. So, proton or neutron
the rest mass energy is around 938 939 M e
V. So, this is a massive part this exchange
part is a massive part is not small compared
to nucleon, which is emitting it or which
is absorbing it around 100 M e V. Now this
virtual part are virtual in the sense that
they exists for very short time and we are
not absorbed them in real world. Otherwise
they are not imaginary at such if a particle
or certain properties is used here is created
here and absorbed here.
Such an particles those properties must exist
all with all conservation law and everything
with the same properties. Like photons that
we can absorb the photons, photons do exist
they have some properties the virtual photons
we do not observe but, the property of the
virtual photon has the same property of this
photon. If this photon does not have charge
that photon also does not have charge. So,
everything angular momentum everything. If
photon exists than only you can have virtual
photons there. So, do we have this type of
particles and it terms that yes we do have
and those particles are pions.
And there are 3 varieties of them pi plus
pi minus and pi 0 neutral. The three verities
of a pions, these are the particles which
are absorbed in laboratories real particles
real pions, which are created in atmosphere
by those cosmic rays which also created in
laboratory using unclear accelerator and nuclear
reactions. So, this particle do exist and
therefore, if they can exist with all quark
quark and the quark in the structure and all
laws of physics followed by these particles
.Then you can have corresponding virtual pions.
So, all these things are very well studied.
And this have mass around 139.6 mega electron
volt rest mass energy or mass is this divided
by c square. This has slightly smaller 1 mass
135 M e V. So, they are the right kind of
particles which can meditate forces between
the nucleons. You I must have told earlier,
this force between nucleons is some kind of
residual color force. Is the strong force
we have strong force, weak force, electromagnetic
force and gravitational force. The strong
force is a where are quarks are interacting
with the exchange of gluance and that is when
that is because of the color charged carried
by the quarks, just like electrical charge
carried by the particles; the result in electromagnetic
interaction in term in electromagnetic forces.
Similarly, the color charges existing on these
quarks that results in this strong forces.
And each nucleon is color neutral nucleon
is made with those colors quarks and the total
color is 0.
So, just like 2 atoms with 0 charge each atom
with 0 charge can combine to form molecule
or can interact. Similarly, these nucleons,
which have 0 color here, 0 color here but,
still if they are close enough. So, that the
distribution becomes important than you have
some forces. Al right so this is about a pion
exchange.
Now then you can have n p scat n p interaction
can have the all kinds of varieties. This
can emit. What can it emit? This can emit
a neutral pions, n can emit neutral virtual
pion and still remain neutral and this proton
can absorb that and can still remain proton
and similarly, this proton can emit this can
this proton can emit neutral pion and still
remain proton. And this neutron can absorb
that pion and can still remain neutron. These
are within that virtual processes so do not
worry too much about the energy and certainty
moment able certainty and all those things
because they are for that flitting time. The
time also you can estimate, if you estimate
time from here if time you can estimate from
this range itself.
Time we say that it is range divide by c.
That is how we to get and the range is something
like 2 femtometres and c is 3 into 10 to the
power of 8 meter per second.
So, this is in seconds. So, this is 10 to
the power minus 23 seconds. So, the processor
are very small time so do not worry about
how this reactions are energetically balanced
and anything is like that. So, that is 1.
Yet another process is that, n can emit what
negative pion the charge conservation should
be should be there. So, n can emit a negative
pion and convert itself into proton. The energy
valuation is similar to neutron and proton
has similar masses and this pion is has an
extra mass. So, this is possible and then
we can other this is n this is p, this p can
absorb this pi minus to become neutron right.
So, this proton becomes neutron this neutron
becomes proton if there is a pi minus exchange.
And then proton can do a similar thing, proton
can convert itself to neutron by emitting
pi plus and this neutron can absorb that pi
plus and become proton. So, there are three
varieties of a possibilities you can have
this n p interaction can be mediated by all
3 kinds of pions. It can be mediated by neutral
pion it can mediated by negative pion, it
can be mediated by a positive pion.
If you considered p p interaction, interaction
between proton and a proton, what kind of
exchange particle can mediate this? Out of
the 3 pi 0 pi plus and pi minus. I am looking
at interaction between 2 protons. So, what
of this 3? Which pions can mediate this interaction
between 1 proton and another proton like m
p 1 side neutron other side proton. It was
possible for the first particle to emit a
neutral pion or a positive pion or a negative
pion all 3 could go there and get absorbed
right, these 3 equations, these 3 varieties.
So, this m p interaction can be mediated by
positive pion by negative pion and can be
mediated by neutral pion. In that same spirit
if I have 2 proton sitting at some separation
and say that this can this emits a particular
pion and that pion get absorbed there. Fine
1 proton emits a particular pion and other
proton absorbs it. What kind of pion that
can be? pions yes neutral pion it has to be
neutral pion nothing else ok.
P plus neutral pion p emits a neutral pion
and still remain p and the other p absorbs
that pion and still remain p. This the only
possibility, if this p emits positive pion
that is possible it can emit a positive pion
and convert itself to n but, then this cannot
be absorb by the second fine. So, this cannot
be absorbed we do not have the particle of
this nature 2 units of charges so on. You
do not have any clue on like that. So, this
is not possible similarly, pi minus is not
possible so p p scattering of p p interaction
can only be mediated by this neutral pion.
Whereas n p interaction can be mediated by
all 3 of them there were small difference
in the when you analysis scattering data n
p data n p p data n p scattering data and
p p scattering data with same energy similar
energy and so on. Remove all that interaction
effects so that, you are only looking at the
nuclear interactions between proton and neutron
proton. If you compare these 2; what is the
strength of interaction? What is the strength
with which it is scattering? Those parameters
are there to compare scattering link and other
things. So, if you compare how strong they
are in interacting you find that when it comes
to you compare this p p and this n p there
is a slight difference, slight difference
very close to each other but, there is a slight
difference.
And if you analysis this n n n p p they are
same the strength of this and this are same.
Whereas that of n p slightly different. People
give credit for that difference or responsibility
for that difference to this difference in
mass, slight difference in mass of neutral
pion charged pions. These interactions can
only go through neutral pions whereas these
interactions can go through the neutral as
well as the all three contribute.
So, slight difference comes from there. With
this mechanism the potential are created the
2 approaches first which we described for
quite some time was we have the experimental
later and from those data and with some arguments
you keep on constructing potentials with variable
parameters so many parameters can adjust the
value of the parameters. So, that you match
with the data start with potential. What is
the bases of starting with potential? Why
not harmonic potential? Why not some other
kind of potential? But, since the square potential
square potential hard parameters like depth
and width; we could play with those numbers
and could adjust the numbers so that, the
netron binding energy resulted from that.
That does not mean that, the interaction is
described by square well potential. So, this
type of approach where we just collect some
potential with so many parameters which we
can play with which we can vary. And then
we fix the values of those parameters according
to the data available so that, the numbers
coming from here match with the experiment
that is known as phenomenal logical approach.
The potential is constructed that way are
called phenomenal logical potentials. Whereas
if you start with a mechanism that the interaction
is generated in this particular way and from
that mechanism you come out with a potential
that can also have certain exist able parameters
but, this shape of the potential is not arbitrary,
the shape of the potential coming from the
mechanism that more basic mechanism that you
are contemplating. Now here is that kind of
case where the interaction mechanism first
laid down and from here theory is developed
modules are developed to get to the potentials.
So, you come in the year of 1934’s 1935’s
and then came out with potentials with you
called a potentials in or we call it.
One exchange 1 pion exchange potentials, OPEP
1 pion exchange potentials. So, and the dominant
part is e to the power mu r over r and many
more things but, these are the dependence
dominated by this. You have spin part, you
have non central part those things are put
but, the r dependent part comes out to be
this exponentials. So, there is justification
of the shape its coming because of this 1
pion exchange. You have a different branches
or different germs of nuclear interactions
here with this kind of energy of pions around
135 140 mega electron. We will have certain
range which will come out around how much
2 femtometer we took than it was 100.
So, little less than that so that, so in this
range which you can say for nuclear range
this is almost near the end this virtual but,
if you are looking at interaction at the separation
of a 0.5 femtometers 0.4 femtometers like
that much smaller separations. So, other may
exist or other exchange particles exist with
much higher energy that those can come in
to picture. Pions are not only the exchange
particles you have omega many other type of
particles with higher energies. Since, they
have higher energy that energy violation is
larger and therefore, the range c delta t
that they can cover smaller.
So, they will not take part into interaction,
if the separation it say 1.5 femtometers or
1.7 femtometers because there life time or
their existence time those higher mass particles
their existence time is so small, they can
let say they can travel only a distance of
0.4 femtometer. So, these mesons will not
contribute in the interaction if the 2 nucleons
are the separation of 1 femtometer or 2 femtometer.
However 1.5 femtometers but, if nucleons are
pushed at that small separation 0.4 femtometer
0.5 femtometer 0.3 femtometers than those
mesons will also start interacting.
So, that the repulsive force for example,
we talked of repulsive core and all those
things that will not come from 1 pion exchange
that will come from those higher order particles.
So, one can have 2 pion exchange one can have
omega mix on exchange and varieties of those
things. So, this is one approach where 1 starts
with more basic mechanism and comes out with
potential. Yes the nuclear potentials between
2 nucleons that is all about that ok. So,
this is about a force or interaction between
2 nucleon yes we talked about bound system
of 2 nucleons that gave some information about
the interaction. And we also talked about
scattering between these 2 nucleons p p scattering
or n p scattering n m scattering but, essentially
it was 2 nucleons interacting with each other.
Now if I look at a nucleolus apart from this
deuteron all nuclei will have more than 2
nucleons helium 4 nucleons right similarly,
iron 56 nucleons all packed in that nuclear
radius nuclear volume.
So, if we try to look at the interactions
between all those nucleons which are there
in the nuclear that could be a very formal
able task. With two nucleons we had so much
of discussions and so much to understand and
so many experiments so many theory and big
expressions and non central part and central
part and spin dependence and exchange and
this and that just with 2 nucleons. Now if
there are 10 nucleons 20 nucleons or 30 nucleons
or 56 nucleons or 80 nucleons and if we try
to look at the net interaction and the total
energy and all those properties the magnetic
moment or regular movement term in this. And
then from the very basic nucleonic interactions
it could be very difficult task and yet another
complication is that in a nucleolus you have
so called many body forces.
Coming into picture that means many body forces
means suppose we have 3 nucleons 1 here 1
here 1 here this is named a this is named
b this is named c and you say that force on
a you do not talk in terms of 4. We talk in
some potential but, anyway I am not going
to do any mathematics qualitative only. So,
force on a is because of b and because of
c normally this is how we think on a if a
and b are there alone b exacts force on a
a exacts force on b if a and c are alone existing
alone then c will exert force on a and a will
exerts force on c. If both of them are here
then net force on this is force from b plus
force from c that is how we think but, in
nuclear apart from there we have yet another
term which is some extra something extra.
If we have 3 nucleons together than there
is something extra you can if you wish you
can write b c. This is 3 body force. This
is 2 body force.
So, how it is out of calculation lot of theory
developed is multi body forces. It is not
that since there are too many particles also
I have 2 many pairs to consider for interaction
if even more than that those pair wise interactions
will come under 2 body forces but, you have
3 body forces may be 4 body forces. After
relative importance will decrease most dominant
will be 2 body forces and than 3 body and
4 body so that, means even if I am if I know
this nucleon interaction potential very well.
I will not be able to write the for the entire
interaction inside the nucleolus because those
3 body 4 body will also be present so that,
is yet another complication even this 2 body
interactions. If you try to write for all
pairs in the nucleolus and all that do you
understand how big it will be? Similar is
the situation in atomic physics of course,
that three body things are not relevant not
much significant there.
The simplest was hydrogen or hydrogen like
where you only had 1 electron and 1 particle
here z e and then the its simultaneous easy
you write this just as h cross minus square
by 2 m delta square and this potential energy
between this and this correct. So, it is minus
z e square over 4 pi epsilon r but, if you
have multiple electron system than the hemultonion
will have for each electron you will write
kinetic energy term. For each electron you
will write potential energy with the nucleolus.
And on top of that we will also write the
interaction between the electrons among the
electrons them self submission over and submission
over j and i naught equal to j, than it will
be e square four pi epsilon naught mode of
r i minus r i. So, the whole thing becomes
very difficult to handle.
So, how does atomic physicist deal with the
situation. They say that this entire atom
is producing some kind of effective central
potential for 1 electron to come. In the atom
if you have z electrons 20 electrons or 16
electrons. So, that nucleus plus all these
remaining electrons the all though the potential
if you write the potential it will be weird
thing but, one assumes that all this is equivalent
to a central single central potential and
you do not have to considered the coordinates
of this electrons, coordinates of that electrons,
coordinates of that electrons. And what kind
of potential they are producing for the 1
electron? I have in mind all these things
are replaced by 1 single potential origin
and some kind of v as a function of r finish
this v as a function of a r is not with this
expression will be equivalent of all these
things but, once you have that central potential.
Then you solve just 1 equation not this.
Equation like this, you consider 1 electron
in this potential. This is that equivalent
potential coming from electron and nucleus
and everything. So, that what formula or expression
is to be written that there is a separate
story. But at the end of it is 1 single potential
with 1 single co-ordinate coming in and this
electron 1 electron I have in mind this is
called single particle potential so that,
1 particle 1 electron I have in mind that
will be at this position r and with this it
will stop spreading the equations to get the
energy possible energy of that electron and
that is valid for all the electrons of the
atom. All the 16 electrons of the atom for
each 1 of them this same potential and same
energy levels are available. So, when you
do that what happens if it is a central potential
and not columbic potential?
You will have energy pending on two parameters
energy depending on n and energy depending
on l. Orbital angular momentum quantum number,
principal quantum number. And then you will
have energies like 1 s that is n equal to
0 and l is equal to n equal to 1 and l is
equal to 0 so that, this is 1 s than you will
have 2 s. We will have 2 p right l is equal
to 0 l equal to 2 p, then you will have 3
s you will have 3 p then the 4 s is somewhere
here in general 3 d is slightly ever and then
you have 4 p and then you have 5 s and so
on. So, energy is different energy levels
are appear for different n and l and it so
happens that there are gaps in energy bigger
gaps. Here also there is gap but, this is
smaller gap here is a bigger gap here is a
bigger gap.
So, these are called shells major shells.
Now this is 1 shell this is another shell
this is another shell this is another shell
and so on. And these are energy levels they
are non degenerate they are degenerate energy
level 1 degeneracy comes from spin because
the central potential that we solve that does
not have spin in it. So, spin up spin down
those energy will be same as long as this
hamiltonious concerned. They may depend on
the same energy they really depend on spin
but, then you have to bring in extra terms
l dot s or something.
So, the basic hamiltonion allows spin degeneracy
and on top of that it will allow that l degeneracy
because with any given l m l can be plus l
l minus 1 l minus 2 up to minus l. So, that
degeneracy is also there energy does not depend
on m l it depends on l energy depends on l
s and p their energies are different. So,
it depends on l but, it does not depend on
ml therefore, the same energy l is equal to
1 then m l equal to plus 1 ml equal to 0.
They will appear at the same energy and then
spin up and spin down. So, the total number
of contemn state will be 2 here, will be 2
here, will be 6 here, will be 2 here, will
be 6 here, will be 2 here, will be 10 here,
will be 6 here and so on right. And then if
you look at those gaps and call them as shells
than this shell is at 2 and this shell is
at 10. And cumulative this shell itself contains
eight quantum levels quantum states at this
2 also.
So, you have ten and this is 1 shell this
makes it 18 this is 1 shell and this makes
it 36 and so on. Next will be 54 and so on.
And these different shells with different
energy with larger gaps in between that reflects
in the periodicity of many of the properties
in of atoms much before all these was there
developed the periodic table concept was there
because baa people has seen that periodicity
in properties. So, and atomic weights not
atomic numbers atomic weights with they have
determine with the different elements and
therefore, in terms in increasing order of
atomics weights they had tried before this
atomic number came into picture. So, some
kind of periodic table was involving and finally,
now we know that it is all if it is arranged
with this atomic number very nice property
has come in the groups in periods and so on.
So, that shall structure is now is very well
established. Now look at your screen on the
screen you should see the picture.
So, on this graph they have shown is a atomic
number on this x axis and you can see 0,4,8,12
at this interval it is written this is scale
on the y axis it radius atomic radius in Pico
meters and this graph has been created in
excel, very simple and this is vertical lines
are added you can see it. Now see here, what
happens? The atomic radius keeps decreasing
it is here. This is 3 this is lithium this
is z is equal to 3 lithium and then it decreases
this is z is equal to 4, 5, 6 and so on. This
is 8 next cell starts here and then all of
sudden you see that data come from this radius
and then again it decreases and when the next
measure shell starts it increases again it
decreases and then it goes and here it increases
again right. The shell closes at different
places and there it really gets up. Here this
is 37 shell closes 36 and 37th. Once you go
to 37 you can see it has gone up similarly,
here you can see it is 19. So, shell closes
at eighteen and as you go for 19th all of
sudden atomic radius increases. This sudden
change in atomic radius is one indication
that somewhere you are having those different
shells. I will show 1 more thing.
This is ionization energy, ionization energy
is the energy that is needed to remove 1 electron
is first ionization energy 1 electron from
the atom so that, is an ionization energy
and here also you will see here the ionization
energy is very high. That means it is now
difficult to remove that electron from the
atom but, one more electron next element here
all of a sudden here ionization energy drops.
So, a new shell has started with this addition
of 1 electron and therefore, it is so easy
to take it out. So, ionization energy is much
less so it is loosely bound its very small
energy you can take it out. So but, then it
goes up it reaches here this is 18 is a shell
closer you can look at your board. 18 is a
shell closer at 18; so, 18. If you have 18
electrons than the ionization energy is quite
high but, if you have 19 electrons the ionization
will all of sudden drops. So, that shows the
shell structure if inside the shell if you
look at inside the shell that means from here
to here it is slowly increasing. And when
you change the shell you are going from one
shell to the other shell 18 to 19 than it
suddenly it goes down than after 18. Then
next shell closer is at 36 on the on the board
we have seen that 36.
So, look at from 18 to 36 the ionization slowly
increasing or decreasing or slowly changing
but, as you go from 36 to 37 all of sudden
the energy ionization energy goes down right.
So, this kind of discreet changes this kind
of sudden jumps in various properties they
indicate that there is some kind of a shell
structure where 1 shell closes than next shell
starts and than that next shell keeps filling
and once that shell is close then again next
shell starts. And that change from the starting
of a new shell that is marked by sudden change
in properties right.
So, come to the board again this is a helium
z is equal to 2 is helium very tight atom
removing electron is not that easy but, once
you go from helium to lead here that third
electron can just come out easily. And similarly,
next will be there at 10 in the periodic table
10, then 18 and then 36. These kind of different
shells are there. And how do you make it?
Just by saying that two electrons will come
here 1 with spin 1 with spin down and any
third electron must go here in that different
shell. Why this third electron cannot be accommodated
here? This is because they are foramens electrons
are foramens no 2 foramens can occupy the
same quantum state. That is why they have
to go up. Now similar structure exists in
nuclei also in nuclei also or what we can
do? We can have and every kind of potential
1 particle potential single particle potential.
There are so many nucleons in the nucleus.
Think that this whole nucleus is presenting
to any 1 single nucleon the whole nucleon
to any 1 single nucleon this whole reaming
nucleus is presenting this potential same
thing for all nucleon. So, this potential
gets the energy levels and then fills the
energy those quantum states from below and
remembering that protons and neutrons are
also foramens. So, quantum state can accommodate
only 1 particle. So, all that polices and
principles and then you come up with a similar
cell structure. The first thing is if there
are this kind of interaction that shell structure
should be visible in experiments for example,
nuclear radii you have seen on your screen
you have seen atomic radii. How atomic radii
change?
As number of electrons increases and goes
from one shell to the next shell similarly,
nuclear radii if there is a cell structure
inside the nucleus than this nuclear radii
should also have this kind of jumps sudden
jumps or corresponding to ionization energy.
Here you will have neutron separation energy
or proton separation energy that should have
this kind of sudden jumps at certain fixed
numbers.
So, next lecture will look at the experimental
some of the experimental data and see this
if those data also just a cell type of structure
inside the nucleus so that, similar atomic
models. The method of atomic models can be
implied there also and you will see that they
do exist. And based on that they do that one
developed to what we call nuclear shell model.
