stabilize knickers that means the
neutron to proton ratio it becomes
greater than one the shaded region in
the figure is called the belt of
stability this is what it is the belt of
stability
it shows what nuclides would be stable
right and these are the stable nuclei x'
now let's go to the next one to find out
if you're given any quads and find out
whether that nuclei will be stable or
not stable what you have to do is you
have to find out the number of neutrons
and the number of protons and you find
out the place of that nuclides on this
diagram here let's say if it is
somewhere over here that means on the
left side of this zone stability zone on
the left side what is that means that
means that nuclides has too much
neutrons so it will be K to decrease the
number of neutrons and increase the
number of protons right and how that
would be possible it would be possible
by beta emission that means any nuclei
that will have proton Neutron numbers in
this region here there they will simply
give beta radiation that means given
electron and convert a neutron to a
proton and this way decrease the neutron
to proton ratio and comes to this belt
over here to the stable zone here like
this now if it is on this side of this
stable zone then what will happen in
that case that means they have too much
proton compared to Neutron so the decay
will be type of decay that will decrease
the number of proton and increase the
number of neutron and that will be
positron emission decay or it will be
electron capture both the positron
emission and the electron capture will
decrease the number of protons by one
and increase the number of neutrons that
means any on this side here
positron capture simply or it may be
positron emission any over here will be
the beta emission to reach to the
stability but if it is too high over
here actually
then big particles need to come out from
those nuclearized unstable nucleus such
as alpha particles as a matter of fact
and to reach to more stable state nor
stable nucleus as a matter of fact then
so the nuclei below the belt have too
many protons so they tend to become more
stable by positron emission or electron
capture and here alpha beta particles
actually like this yes question beta
particle comes out in the orbital don't
now that that we know we can't really
say alright I see what you mean what
you're saying is this right now you're
saying that if a neutron actually if a
nucleus gives a electron and we
visualize it as a proton is converted to
Neutron is converted to the proton so
that means that the product nucleoid
will have one more proton so that atom
should have one more electron now we
don't know we can't really tell whether
the electron there is the one which
comes out from the nucleus
new single there is no single Neutron at
the menu or single Neutron yes by given
that yeah that will be a proton a proton
is actually hydrogen yeah that that you
can look it that way but if you consider
the mini proton many electron atom
nucleus right when an electron beta
emission is given that electron comes
out from that atom it doesn't stay there
because you see the emission beta
emission effect of beta emission
remember we gave the penetration
penetrating power off of the particles
and for the electron we said 100 for the
alpha particle was just one anyhow or 10
what any other so what what that simply
means the beta particles that comes out
from the nucleus does not stay in the
outside of the nucleus and then becomes
the electron of an atom no you can you
can say that okay let's continue now
alpha emission again there are no stable
nuclei with an atomic number greater
than 83 this is another things like all
the atoms naturally occurring atoms in
fact up to 83 now after 83 all the atoms
are not simply stable they are all
radioactive greater than 83 and nuclei
with such large atomic numbers tend to
decay by alpha emission they are not
very stable actually most of those are
made in the labs by nuclear reactions
nuclear reactions and they are not
stable
they have half-lives we will talk about
that certain time but they are not very
stable so what happens if they are not
stable they decay
how by giving really large particles
like beta particles as a matter of fact
alpha particles excuse me alpha
particles because the helium is large
particles and they became by giving
alpha emission actually alpha emission
now sometimes the decay process or the
emission processes are not one step that
means that an unstable radioactive
nuclei cannot reach to a stable nuclide
state by only one step so they may be
more than one step radiations and
nuclear reactions as a matter of fact as
we see here for example uranium-235
uranium-238 I guess maybe in uranium 238
goes in alpha emissions and not only
alpha emissions in fact in the same time
it may give a beta emission gamma
emissions in all others just the energy
carries out and goes down from 238
atomic mass number 238 atomic number 92
and then decays in series each of these
corresponds to a decay step and decay
reaction and finally ends up to lead
which is 208 or 206 mass number 207 and
the atomic number of lead I guess is 82
as it's 82 there because that is the
stable nuclei in fact stable nuclide so
you see again some radioactive nucleus
radioisotopes undergoes a chain nuclear
reactions to reach to the most stable
nuclei in that series again so let's see
what it says here some radioactive
nuclei cannot stabilize by undergoing
only one nuclear transfer
transformations they undergo a series of
decays until they form a stable nuclei
often a nucleoid of lad
in this case you know the ladder is very
stable as a matter of fact now the
question here is why some nucleons are
more stable than the others what is the
reason now there are different ways of
explaining that first of all they simply
say that if a nuclei has even number of
protons and even number of neutrons it
is always more stable than the odd
number of neat neutrons an odd number of
protons as a matter of fact so that's
again important now in addition to that
they simply say that if a nuclei has 2 8
20 28 50 82 protons and it has like 2 8
20 28 50 82 and 126 neutrons they are
more stable why they are simply called
magic numbers actually you can probably
visualize this or associated with the in
a chronic structure of the atoms
remember when the atom electrons
structure is the same as the noble gas
electron structure which means closed
shell electrons structure they are more
stable right all of the noble gases in
fact very inert they are not reacting
very stable and in this case the nuclei
that have these number of protons and
neutrons are more stable and they simply
call these numbers called magic numbers
again nuclei with an even number of
protons and neutrons tend to be more
stable than those with odd numbers as I
said and here we look at the number of
stable isotopes of one isotopes with
even and even 157 isotopes are stable
and all of those 157 isotopes has even
number of proton even number of neutrons
now there are 53 stable isotopes with
even number of protons and odd number of
neutrons and there are only five ice
Taub's which is which are stable and
they have actually odd number of protons
and odd number of neutrons again you see
the oddness of the number of protons and
the number of neutrons becomes a very
important factor in determining the
stability of the nuclei is actually the
nucleus as a matter of fact now these
simply gives you the elements with the
number of stable isotopes and again all
of the elements which have even number
of protons always has more stable
isotopes with the one with odd number of
protons again these are odd number this
is even odd even odd and that gives you
the number of stable nuclei stable
nucleus again try to show you that
somehow even number of protons and even
number of neutrons yields a more stable
nucleus again no more stable nuclides
now so far we have simply talked about
the decay of n decline right that means
like a unimolecular reaction it
decomposes it emits particles or you
know and goes to a lower energy more
stable state but it is also possible
that when you simply strike a nuclei
with another smaller light nucleons you
may have a nuclear reactions nuclear
reactions now as a result of this new
nuclear these type of nuclear reactions
always an element identity is changed
that mean is not the same elements that
we have at the beginning and that's why
these type of nuclear reactions are
called nuclear transmutations that means
the chemical identity identity of the
atom changes as a matter of fact so
let's look at how we describe nuclear
transportations can be in
Jews by accelerating particle two
collided with the nuclide you simply
have an accelerate and very accelerating
particle miss simply means high energy
particle has kinetic energy very large
kinetic energy so remember again usually
these particles are charged particles to
be able to accelerate a particle it has
to be charged and usually positively
charged particles like a proton or like
an alpha particles now the nucleus the
nucleus is also a positively charged so
to have two particles with both
positively charged which they repel each
other they should have a very large
amount of energy that they will strike
each other right so therefore usually
the smaller particle charged particle is
accelerated now the speed of that
increased increase actually it is
increased almost nine ninety seven
percent of the speed of light
can you imagine very very high speed you
can increase the speed of a proton by
the accelerators as we will show you
very close to or let's not say close to
if you consider that 97 percent of the
speed of light is close to the speed of
light so they increase the energies of
that and then when it strikes another
nuclides then this transmutation
reaction is taking place
transportation reaction is taking place
so the particle accelerators they are
called atoms smashers that means we
accelerate the particle accelerator
accelerate accelerate then hit it to a
nucleus right now think about this is a
nucleus not the atom but the nucleus
they have to hit to the nucleus in fact
and we have the enormous seven circular
tracks with radii that are miles along
the particle accelerators to increase
that we use actually these accelerators
are used I guess this one is I can't
remember but about 10 kilometers
somewhere about seven kilometers
circumference and here we have a
magnetic view
electric field and charged particle
enter to this and they go up here in the
electrical field that merrily increases
the kinetic energy increase in the
kinetic energy kinetic energy and
finally we get it out and hit it to
another nucleus right this is how the
transmutation reactions are simply
taking place and there is an accelerator
in New York and there is an accelerator
in Chicago and in the states and there
is also one
accelerator in Geneva CERN and that is
used by all the European country
scientists in fact there not much of
those are very expensive actually and
they built them up underground
everything is underground again right
and you carry out the reactions you
smash the high-energy particles small
particles and then you watch and follow
what products will come on what kind of
reactions and these are actually all
chemical reactions remember the boson
experiment was also carried out in CERN
in Geneva right there now other nuclear
transmutation nuclear generation use of
neutrons again now those that are
accelerated are charged particles you
can't really accelerate the neutrons
there right because it doesn't have a
charge but you can use it neutrons from
nuclear reactions actually that comes
out from the atom and use that Neutron
and carry out the transportation
reactions and here again says most
synthetic isotopes used in medicine are
prepared by bombarding neutrons at a
particle which won't repel the neutron
particles actually in nuclear reactors
actually if you have a nuclear reactors
and if you have a proton given nuclear
radioactive reactions the nuclear
reactions you can take those protons and
then collided with other atoms
since the neutron it says has neutral
charge it doesn't need to
large energy to hit the positively
charged nucleus actually right nuclei
and for example cobalt-60 which is used
in in hospitals in in in nikiro of
cancers and radio therapies are prepared
by bombarding the iron 57 by the
neutrons in fact and in two or three
steps you get cobalt 50 which is a
radioactive cobalt 60 which is a
radioactive that's how its prepared now
transuranium elements when we say
transuranium elements these are the
elements that have greater atomic number
than uranium which is 92 remember all of
those are not stable and all of those
are prepared in the lab elements
immediately after the uranium were
discovered by bombarding isotopes with
neutrons you see we just bombard them
with neutrons large elements atomic
number higher than hundred and ten were
made by colliding large atoms with
nuclei of white elements with high
energy this is again from those
accelerators lots such as alpha
particles you accelerate those and hit
it to another nucleons now right in the
nuclear equations for nuclear
transmutations again these nuclear
transmutations is a nuclear reactions
though they will have a nuclear reaction
equations just like this for example you
have a nitrogen-14 and then you bombard
it with helium and this is an alpha
particle actually charged particle alpha
particle and you get oxygen in fact 17
and then the hydrogen this is proton
this is actually a proton and then or
you can simply you write it like this or
you can write it like this you see again
the helium is alpha particle that means
that there is a two plus charge on that
that means it is the nucleus of the
helium not the helium atom not the
helium atom and again this
year-11 it is not the hydrogen atom that
means one proton and one electron it is
only the proton and you can write that
reaction equation like this instead of
this again so nitrogen-14 bombarded with
alpha particles and we end up with
oxygen 17 and a proton now short way of
writing this is this way like this you
see again here this is called the target
nucleus the nucleus of the nitrogen like
this and this is called the product
nucleus again that comes out and the
first one here is the bombarding
particles and the second one is the
ejected particles you see again there is
simply logic to this instead of writing
it like this actually and this
corresponds to a nuclear reaction
equation and describes the
transmutations actually of nitrogen to
the oxygen 17 by bombarding with alpha
particles now I should probably say here
again in all these nuclear reaction
equations they have to be balanced right
we should make sure that we check that
balance means that some of the mass
numbers here 14 18 and here is 17 118
balances and atomic number here is 72 9
and here is 8 + 1 9 again so we should
always have that checked and balanced
for the nuclear equations actually now
let's look at the kinetics of
radioactive decay
now all radioactive decays now decays
not the transportation reactions
actually but only the decays are first
order processes first order processes
and simply the kinetics of those
actually will be met will be explained
by the
first order rate equations this is
actually the integrated rate equation
for the first order reactions now n T
and sub T is the number of radioactive
isotopes at time T and this corresponds
exactly to the concentrations of the
reactant at time T for the first order
reaction right and this one here
corresponds the number of ready
radioactive isotopes at the beginning of
the nuclear reaction right decay
reaction n sub zero that means that it
corresponds to the initial molar
concentrations of the reactant in
chemical first order reactions and
chemical first order reactions and this
K is the rate constant again and T is a
time that elapsed actually and remember
again for the first order reaction the
half-life is independent of the initial
concentrations and it is always equals
to logarithm natural logarithm of two
divided by the rate constants right and
that means that the rate constant for
the first-order reactions are always
same no half-life is always the same no
matter what is the initial concentration
in this case what is the initial amount
of your radioactive substance and as we
see here half way in fact when we reach
two they have of the reactant in this
case the radioactive isotopes at the
beginning the time elapsed is simply a
half-life this is again the half-life
for the first order reaction this is the
logarithm natural logarithm of two
divided by the rate constant T 1/2 how
half-life is the time required for the
half of the radio nuclei sample to decay
just like chemical reactions nothing but
just the chemical reactions again now
the half-life of these radioactive
nuclei
new clients are given here again if you
look at those let's see if I can see
that here you see for example uranium
238 has a half-life of 4.5 times 10 to
the 9 years now what does that means
that simply means if you start with one
gram of red radioactive uranium 238 and
after billion years that 10 to the 9
right somewhere
4.5 billion years you will still have
the half of that that means 0.5 gram of
uranium 238 still emitted and
radioactive right still emitting there
so the half-life is really important
particularly for the radioactive nucleus
because it tells you how far you will
simply introduce to the radiation
nuclear radiations from those now again
if you look at the other species here
for example 235 half-life is less than
that but it is 10 to the 8 years that's
a long time and then we have for example
strontium 90 half-life is 28.8 years and
if you have iodine 131 half-life is
about 0.02 that means about 2 months
right
about 2 months so and these are the type
of decay that they emit then again alpha
alpha alpha beta beta alpha beta and
beta again now by using this first-order
rate law we can in fact determine the
age of the rocks which contains
reactive isotopes such as uranium right
or we can determine any objects that
contains a radioactive isotopes if we
know what is the radioactive isotope is
now particularly if you have wooden
objects right and they have carbons and
the carbon isotopes we have carbon 12 is
the stable isotope most stabilizers
herbs not radioactive and we have carbon
13 and we also have carbon 14 carbon 14
is a radioactive isotopes it is not
stable and it decays actually and we
have five of the carbon 14 half isotope
radioactive isotope is 5,700 years now
it is limited to the objects up to about
in fact by using this carbon-14
determining the activity of carbon-14 in
the wooden objects we can determine the
age of those objects which is made of
wood as a matter of fact and how far we
can go back again by dating again by
using this carbon-14 dating we can go up
to 50000 year again now we can also use
other isotopes to date the rocks the age
of the rocks actually now as we will see
why this is the limit because when we
use as we will see when I solve the
problem related to this what we assume
that carbon-14 abundance in let's say
ten thousand years or twenty thousand
years or forty thousand years before in
the air is exactly the same as the
carbon food
abundance in the air today and when we
say in when I say in the air what we
have that carries the carbon in the air
is carbon dioxide carbon dioxide right
so simply the ratio of carbon 14 to the
other carbons let's say in 40 years ago
in the atmosphere in a carbon dioxide if
is if it is the same that means that the
living organisms which inhale uses
carbon dioxide from the air will also
have the carbon 14 abundances I should
say in their bodies or in the plants the
same as the air same as the air and by
assuming that actually we calculate the
age of the artifacts which is made from
the wood or other living organisms
actually now and before 50 thousand
years before let's say 55 thousand years
ago we can't be sure maybe that the
carbon-14 ratio to the other carbons in
the carbon dioxide that many years ago
was probably not the same as that we
have today in the atmosphere we have
today in the atmosphere let's just take
an example let's see if I have an
example here I guess now
before that I will solve problems
related to this carbon dating let me
find out the problem that I picked up
now let's let's see I have that no I
don't have it
this is the from the book I picked it up
simple exercise 21-6 is not installed it
says it's simple exercise exercise - no
this is that twenty one six one two just
two and it will be twenty one six and
this is the second one there it says a
wooden object has an activity of carbon
14 measured to be as 11.6 disintegration
per second so it wouldn't object
this is an old object certainly old
measured to be activity of carbon 14
measured let's say activity of carbon 14
equals to eleven point six
disintegration per second
now fresh wood activity carbon-14 is
15.2 disintegration per second now this
is again the first order reaction right
first order reaction and we will use the
first order rate law Ln n T over N 0
equals 2 minus K times T and the
half-life of carbon
I guess another data here T 1/2 for
carbon-14 is given as 5,700 years this
is the half-life
ok now let's think about that let me
explain what this disintegration per
second means that simply means that in
one second that can be measured by using
instruments geiger instruments measuring
the disintegration radiations right this
simply means that in one second
average 11.6 carbon-14 decays right in
one second to the product nucleus
whatever and this one is the fresh wood
that means if you take a piece of wood
outside and measure the carbon-14
activity in that case we have 15.2
disintegration per second now remember
the disintegration per second let's put
it this way and
she simply the number of carbon-14
nuclides now this will simply be
proportional to the number of carbon-14
disintegration per second right because
just like concentration you can think
about that as concentration the more
carbon-14 I have the more
disintegrations will be per second it is
just that rate sort of the rate and so
when that is correct that means that n 0
if I take that and zero the initially
when this object is made from the fresh
would at that time so many years ago
this is the number of carbon-14 let's
say in that object and that will also be
number of nucleotides proportional to
the number of carbon-13 disintegrations
initially let's say number of carbon-14
disintegration per second initially this
is initially what does that means that
means that instead of in this equation
here since the that number of
disintegration is proportional to the
number of the carbon-14 nucleons instead
of the number of carbon-14 nucleus here
and here I can take the number of this
integrations right because they are
proportional there will be a constant
probably those councils will cancel out
so I can simply put up set up my
equation as follow I can have Ln and up
here for NT I will simply
have this number of this integration
which is 11.6 and for n 0 in this
equation here I will take number of
integration per second as 15.2 from the
fresh you see again as the decay or
nuclear reaction continues the number of
carbon-14 decreases and reaches to
simply from here to there and that time
now the question here is why does it
decreases right carbon-14 now as long as
the plant is alive it will simply take
carbon dioxide from the atmosphere
during the day and then converted to the
sugars and then at night
it will give the carbon dioxide to the
atmosphere and there's always an
equilibrium between the carbon-14
concentration in the living organisms
let's say plant and the outside
atmospheric concentrations of carbon-14
in the carbon dioxide atmosphere carbon
dioxide but when the plant dies you cut
the wood for example right and from that
point on there will be no photosynthesis
that means there will be no exchange of
carbon dioxide from the atmosphere with
the wood whatever in the wood when it's
cut off will decrease carbon-14 amount
concentration will decrease as the time
goes on and then from that decrease
actually we calculate the age of the
wood that
it's cut off when they cut off okay so
you see again this is eleven point six
and this is five point seven this will
be equals to minus simply K but instead
of minus K what we can put for the
first-order reactions
Ln two divided by half life right Ln 2
divided by half life so I can put here
Ln two divided by half life which is
5,700 years right and time T this is it
so now I have all the numbers everything
here and the only thing I have to simply
find out the T and if I solve for T here
and it turns out to be let's see how
much what result I found out I find out
two thousand two hundred and twenty
years so this is actually called
carbon-14 Gator
you date the objects but again in order
to carry out this method you have to
have carbon in your object right again
you just assume that carbon
concentration in that object when that
cut off or die was the same as the
carbon-14 concentrations in the
atmosphere at that time right when it's
cut off it stopped the exchange of the
carbon dioxide with the atmosphere that
means the present carbon-14 will decay
decrease and decrease according to the
first-order reaction and we find out
what time is elapsed to decrease the
carbon-14 to the value which is
proportional to this actually as a
matter of fact and we calculate this now
the question here is is there an error
there sure I mean I can say maybe
like pause - fifty years but still it is
pretty good I mean it's really working
pretty good as a matter of fact it he
goes up to 20 thousand years twenty five
thousand years sometimes you know and so
hundred years there
compared to twenty five thousand years
is not that long even that so it really
works fine there is another example I
was going to show not only the carbon-14
that can be used for datin old artifacts
and objects you can also use other
radioactive isotopes such as uranium 238
and by using the uranium 238 you can
determine the age of the rocks
remember the half-life of uranium is ten
to the nine years something right and
actually the age of the earth which is
assumed to be 4.5 billion years came odd
from this age or dating of the rocks
which contains uranium
it contains uranium again assuming that
the uranium we know the activity of the
uranium now there again there is a
problem here I also picked up probably
next time I will work out on it you use
a different approach actually by using
the uranium 238 for Dayton because the
end product there is led you look at the
amount of lead you compare it with the
amount of uranium 238 present in the
rock and from there again using the
first-order rate though integrated rate
law you calculate the age of the rocks
and they turn out to be like three
million something like you know years
and they assume that cooling of the
earth took about a million billion years
so if you measure age of a rock like
three and a three and a half billion
years then
age of the earth must be about
four-and-a-half billion years
right because that's what I assumed 1
billion year to cool off the earth and
formations of those rocks and from that
on you can determine the age of the rock
actually ok any questions yes now this
one here now remember for the first
order reaction the rate constant is
equals to Ln 2 divided by T or T
half-life remember that for the first
order reaction let's write it down T 1
half-life is equal to Ln 2 divided by K
or K is equal to Ln 2 divided by T 1/2
laugh ok so instead of rate constant you
put Ln 2 divided by half life but that's
only for the first order reaction we can
do this for the chemical reaction first
order chemical reactions all nuclear
decay reactions are first order first
order reactions okay I guess we stop
here