this video is sponsored by brilliant.org I never understood why radioactive
elements even exist today hear me out
okay if you take the most common isotope
of radium radium 226 it turns out that
it has too many protons and neutrons
making it too unstable and so it spits
out an alpha particle reducing the total
number converting itself into radon
turns out radon is more stable compared
to radium now here's my question if
radium can become more stable by
converting into radon by giving you an
alpha DK why doesn't all all the radium
Isotopes dek into radon the moment they
are formed what are they waiting for
shouldn't all the radium isotop
instantly Decay and that should be the
case for all the radioactive elements
the moment they are formed they should
instantly Decay and become more stable
right so why do they even exist that's
the whole question but they don't do
that they don't instantly DEC instead if
you have for example a bunch of radium
with you which you shouldn't have by the
way because it's super radioactive but
if you did radium 226 then it turns out
that if you wait for about 16,000 years
only half of it would have decayed and
if you wait for another 16,000 years
half of the remaining would have decayed
that's how the DK goes it doesn't happen
instantly this by the way is called the
halflife of radium 226 all the
radioactive elements have some halflife
like this but the question is why does
the DK happen so slowly now don't get me
wrong I'm glad that radioactivity
doesn't happen instantly it goes as the
way it goes because it's the reason why
the core of the earth it's one of the
reasons why the earth's core is still
hot so without it you and I wouldn't
have existed but still the question is
why does that happen that way the most
common explanation I got for this silly
sounding question to my teachers was
that hey radioactivity is a Quantum
process Quantum is inherently
probabilistic so it's kind of like
rolling a die and waiting for a six for
example the chances of that happening is
very small and so you have to wait a
long time for that but that is a very
handm kind of an explanation it was very
analogous and I didn't get a deep
intuition behind what's really going on
during a dek what causes where does the
halflife even come from and why are
certain elements stable while other
Isotopes unstable in the first place
like none of that made any sense to me
until I came across George gamma's work
and then my mind was blown so if I do
this video right not only will we gain a
deep intuition behind Alpha DK which
we'll focus on in this video but we will
also ReDiscover a profound quantum
mechanics principle which has
far-reaching consequences so if you're
ready for this let's begin
so gamma what's going on why doesn't
radium just throw out the alpha particle
instantly and just get done with all the
DK well gamma says because there's a
barrier over here see the alpha particle
inside the radium is attracted by the
strong nuclear force that is the
dominating force over there so if you
want to pull that out then you need to
push it against the strong nuclear force
until you get out of the nuclear range
so that requires energy you need to put
energy to get it outside the nuclear
range once it's out over there then
nuclear force no longer exists then the
kum's repulsion will take over and then
the alpha particle will come out so it's
kind of like a ball being stuck inside a
well if you want a ball to go from here
to here it has to First overcome this
barrier and to do that you need to put
in energy to overcome that barrier in
the same way over here you need put in
energy to overcome that barrier but once
you overcome it then it's a downhill
from there and I'm like okay that kind
of makes sense so the alpha particles
require a minimum energy to overcome the
nuclear force of attraction makes sense
so the my next question is how do the
alpha particles get that energy to
overcome the barrier and Gamma says they
don't I'm like what what do you mean
they don't radium radium nuclei do emit
alpha particles once in a while so
clearly they must be overcoming the
barrier what do you mean they don't GMA
says well we have experimentally seen
that they don't overcome the barrier I'm
like what do you mean how H how do you
even say that what kind of experiments
do you people do to to come to the
conclusions like this and Gamma says
that's a good question mahes let's let's
take some numbers over here and this is
the interesting part folks okay so if
you take some numbers over here for
example let's consider the potential
energy over here to be zero okay then
the potential energy of the ball when it
comes over here well we can calculate
that if we know the mass of the ball we
know the value of gravity and we know
this height mg we can calculate the
potential energy of the ball when it
comes here let's just for the sake of
simple numbers call that to be 10 units
okay now gamma asks Mahesh under these
circumstances how much minimum energy
does this ball need so that it can
overcome the barrier and I'm like well
it needs a minimum of 10 units of energy
right so that if it has 10 units of
energy all of that can be converted into
potential energy if it has less than
that it will not even reach over here if
it has more than that then it will reach
over here okay and then once it reaches
over here it goes downhill what happens
to all that potential energy I'm like
all that potential energy gets converted
to kinetic energy so when it comes over
here all that 10 units would have gotten
converted into kinetic energy so the
kinetic energy over here must be at
least 10 units it can be more if you had
pushed with more energy it would have
had some kinetic energy here as well but
it should at least have 10 units of
kinetic energy when it comes over here
long story short if the ball makes
through you should detect that ball to
have more than 10 units of kinetic
energy does that make sense and I'm like
yeah that makes sense and in fact this
also works the other way around if you
want to push that ball into the well it
should again need a minimum of 10 units
of kinetic energy so that it can
overcome this barrier makes sense right
okay now guess what just like the ball
this alpha particle inside the radium
nucleus can be modeled to be you know
being stuck in a well well not a
physical well but a potential well that
is created by not gravity but strong
nuclear forces and kums forces okay so
just like before there is a barrier it
needs to overcome in order to escape
that makes sense right but what's cool
is that just like how we we calculated
using MGH the barrier potential energy
the minimum energy needed to overcome
the barrier even here we can calculate
what that minimum energy is and all you
need to do that is kum's Law and that I
found is pretty awesome just by using
kum's law you can even calculate how
much is the minimum energy you you know
the alpha particle requires to overcome
which is pretty amazing you know if you
ask me but anyways we not go through the
calculation if you do that calculation
then it turns out that the barrier
potential is about 25
Mega electron WS okay so gamma asks
Mahesh this means how much minimum
energy does this nucleus need alpha
particle need to escape and I'm like
well just like before it needs a minimum
of 25 Mega electron WS of energy if it
has that then all of that energy will
get converted into potential energy when
it is just over here it just escape the
nuclear clutches and then finally when
it goes downhill when it you know gets
repelled all of that potential energy
gets converted into kinetic energy so
how how much kinetic energy should it
have when over here well since all of
this got convered to kinetic energy it
should have at least 25 Mega electron WS
of kinetic energy right it can have more
because you know it could have had more
energy to begin with but it could at
least have 25 Mega electron WTS of
energy so long story short alpha
particles should come out of radium
nuclei at at least a kinetic energy of
25 Mega electron WS right that makes
sense because it has overcome the
barrier but guess what we can measure
this experimentally and we when we did
we found that they don't come out with
25 Mega electron volts of energy in fact
what we find is that they come out
experimentally when we measure with the
energies of close to 4.9 Mega electron
WS which is significantly smaller than
the barrier potential and Gamma says
look Mahesh if they had overcome the
barrier how can they have such low
energies there's no energy loss anywhere
in between so how can they have such low
energies and I'm like yeah that's a
that's a interesting question how are
they going through the barrier with such
little energies maybe something's
something's weird with radium and it
turns out this is not just the case with
radium every single Alpha DK if you look
you'll find that the kinetic energies
usually come out at the range of 4 to 8
Mega electron ws and the barrier
potential is close to 25 to 26 Mega
electron Vols so something is going on
over here these alpha particles should
not be able to escape over here they
should just keep going bouncing back and
forth with that little energy they
shouldn't be able to overcome the
barrier so gamma how can these Alpha
particles even with such little energy
overcome that massive barrier well GMA
you'll also be supporting my Channel all right back to Alpha DK problem so our
main question is the alpha particles
inside the helium nuclei do not have
sufficient energy to overcome the
barrier so they just should be just
going back and forth how can they escape
the barrier well gamma says first of all
let's convert this into an energy level
diagram where the vertical represents
energy levels it's slightly more
intuitive to think of it this way so
again we're saying the same thing if you
want to escape the barrier then the
alpha particle needs to have an energy
Above This level only then it can easily
Escape it if it has energy level below
this barrier like like what we have over
here then it should just be bouncing
back and forth it shouldn't be able to
escape it so how does it do that well
gamma reminds us mahes alpha particles
are not tiny balls bouncing back and
forth they are quantum objects and all
of the cool properties of of the quantum
objects is the uncertainty principle
their positions are not very well
defined there is a minimum uncertainty
in that and so rather than thinking of
our alpha particle as tiny balls
bouncing back and forth like this it's
slightly better to think of it somewhat
this way where their position is not
very well defined this is also not
completely accurate but it's slightly
better than thinking of them as a ball
now because particles don't have a well
defined location it's possible that when
the alpha particle is very close to the
barrier due to its uncertainty it can be
found outside the barrier purely from
the uncertainty the chances of that is
very low but if you just wait long
enough let's just do that let's just
keep waiting waiting there you see that
just purely by chance it found itself
outside and once it goes outside then
the kum's force takes over and then it
just gets released this is how purely
from the fact that particles have
uncertainty they could be overcoming the
barrier without actually having the
energy to do that now classically there
is no way this could happen if a ball
had less than the energy necessary to
overcome the barrier it wouldn't be able
to or you know go there at all unless it
dug a tunnel through it then and only
then it would be able to go through and
that's why what whatever is happening
over here is we give a name to it we
call it tunneling we call it quantum
tunneling but of course you and I
understand it's it's not like the alpha
particle is creating some kind of a
mystery tunnel no no no this is at the
end of the day coming from the quantum
principle that we know the uncertainty
principle or to be more precise we
should actually think in terms of wave
functions turns out that the wave
function does not go to zero it dies out
but it has a very tiny amplitude outside
so it has a very tiny probability uh you
know of finding the particle outside but
like I like to think more in terms of of
the uncertainty principle even though
it's less accurate it's slightly more
intuitive and the uncertainty principle
also comes from the wave function so I
like it this way so long story short
alpha particles tunnel through the
barrier even though they don't have
enough energy and they do that purely
from the fact that their locations are
uncertain so this was the model that
gamma proposed okay so this is pretty
profound so can you now answer original
question why don't all the radium nuclei
instantly Decay well the answer is
because the alpha particles are stuck
inside a potential well they don't have
the energy to overcome the barrier but
there is a small chance there's a small
probability that they can you know be
just due to uner principle be found
outside now that probability is insanely
small however if you wait more time that
probability increases isn't it that
probability adds up right if the longer
I wait the more attempts it gets and the
probability keeps adding up so as I wait
wait wait the probability keeps adding
up becomes more and more and more and
eventually for radium it turns out that
if I wait about 16,000 years the
probability of it tunneling through adds
up all to be
50% this is the reason why if I have a
bunch of radium which you shouldn't have
by the way because super radioactive but
if you do and if you wait for 16,000
years half of it would have decayed
because the tunning probability adds up
to 50% so what's mind blow you know
what's mind-blowing is we now have a
deeper Insight of where halflife even
comes from halflife is actually the
amount of time you have to wait until
the tunneling probability all adds up to
give you
50% that's where it all comes from
that's beautiful isn't it and this also
means now we have a theoretical way to
model halflife we just have to compute
the time we have to wait for the tuning
probability to add up to become 50% it's
very hard to do it and there are a lot
of complic
but in certain cases we have found
theoretically the half lifee values to
be very close to the values that we find
experimentally which is amazing that's
an amazing success for gamma's theory
that is incredible model gamma but wait
I promised you complete intuition right
so here's a final counter question if
radioactive elements give you Alpha DK Y
at tunneling and become stable why don't
all Heavy Isotopes do the same thing we
know that ion is one of the most stable
elements in the universe so all the
heavy elements after ion if they you
know gave you an alpha decay then they
would be lighter and they would be more
stable so shouldn't all Isotopes after
ionb radioactive why do we even have
stable isotopes in the first place I
love the way my questioning is changing
right the more I learn the more
fundamental our question is becoming
which is awesome but what's your answer
for that gamma and Gamma say that's a
great question so first let's look at
the alpha decay of a few other
radioactive isotopes so for example if
you consider uranium 238 then it also is
a radioactive isotope it gives you alpha
particles and there the alpha particles
comes with the energy of about 4.3 Mega
electron volts so you see it's slightly
less energetic than that of radium so
what would you expect to happen for its
tunneling probability I'm like see if
the energy is lower you can you can see
that hey the barrier width is larger so
tunneling is harder which means I would
expect the tunneling probably to be
slightly smaller and Gamma says no mahes
if you actually solve the ringers
equations which we're not going to do
but if you do you find that a small
change in the barrier width gives you
orders of magnitude changes in the
probability so you're right tuning is
going to be harder but the probability
would not be slightly smaller it would
be ERS of magnitude smaller which means
the amount of time now we have to wait
for the tuning probability to add up to
be 50% would be orders of magnitude
higher so the half life of uranium 238
would be not just a little bit more than
16,000 years it would be orders of
magnitude more than 16,000 years and
that's exactly what we find the half
life of unit 238 is 4 and a half billion
years and gamma's Theory can now explain
why such a astronomical difference in
their Half Lives even though there's a
small difference in their you know
energies of the alpha particle it's all
because of the tning probability there
is small changes in the barrier with
gives you astronomical changes in the
tning probabilities okay let's look at
one more just for fun if you now
consider ionium 212 which is also an
alpha DK Source the alpha particle here
comes at 8.9 Mega electron Wes oohoo
what do you expect to happen for the
halflife here mahes I'm like oh my God
the barrier width is now much smaller
than before and so the probability must
be astronomically larger it must be that
much easier to Tunnel through and so the
amount of time I have to wait for the
probability to add 50% must be
astronomically smaller so the halflife
should be I don't know extremely small
and that's exact what we find the half
life of penium 22
is3 microc this is all starting to make
sense isn't it okay now to answer your
question Mahesh let's consider one of
the stable isotopes like gold 197 you
are right if it were to give you an
alpha DK it would be lighter and it
would be more stable and you can now
hypothetically calculate with what
energy the alpha particle would come out
all you have to do is figure out the
energy before the DK and figure out the
energy after the DK which you can do
calculations and again encourage you to
do that yourself and if you do it you
would find the alpha particle would come
out with the energy of
A9 Mega electron W mahes what's the
tunneling probability of that oh my God
such a small decrease gave you such
astronomical decrease in the halflife
now look at this this is so small the
Turning probability would be so low I
don't know the halflife could be I don't
know trillions to the power trillions to
the power trillions of years or
something like that so technically
technically gold would DEC if you wait
long enough time in fact every single
element after iron would DEC give you
Alpha DC if you waited long enough time
but the time scales we're talking about
are so ridiculously large that for all
practical purposes we say they are
stable this makes sense right so the
reason why stable isotopes heavy stable
isotopes are stable is because the
energies of the alpha particles are so
low that the time we have to wait the
Turning probability becomes almost you
know negligibly small that we can call
them stable in the time scale we imagine
this is profound like isn't this making
sense like I love how much explanatory
power gamma's model has amazing isn't it
but guess what I told you turning has
far-reaching consequences and another
consequence of tunneling is that it
keeps the Sun Alive GMA asks what powers
of the Sun and I'm like that's easy
Fusion protons are fusing together but
remember protons also are repelling each
other so there's a kums barrier so just
like like before if they have to fuse
they have to overcome they need to have
enough energy to overcome that barrier
and come within the nuclear range and
only then they can fuse and just like
before we can calculate what that
barrier potential is just by using kum's
law and then by using a little bit of
thermodynamics you can figure out at
what temperature would these protons
have enough energy to overcome that
barrier and that temperature happens to
be somewhere close to 10 billion Kelvin
and the sun's core temperature is about
15 million Kelvin which is way lower
than the necessary temperature so as it
as crazy as this may sound the sun is
actually too cold for Fusion to happen
classically speaking that doesn't have
enough energy then how does sun fuse the
protons together tunneling that's the
only way they can cross through the
barrier and fuse together so tunneling
is literally what's keeping the sun
alive it's what allows sun to fuse
protons at a much lower temperature than
classically needed amazing isn't it now
at this point you may be like mahes this
is all great and mind-blowing and stuff
but it's still a theory isn't it well
think again because we have actually
harness the power of tunneling and one
of my favorite examples is the scanning
tunneling microscope which can be used
to map out the surface features at the
atomic level and the way it works is if
this is the surface that we need to map
we just bring a needle very close to it
and put a voltage then even though there
is no conducting Gap there's a barrier
over here electrons can tunnel through
if the barrier is is small enough to
give you a tunneling current and we can
measure that current using computers and
so we now start mapping them and keep
moving the needle forward and if we
encounter a hill the barrier has become
smaller the T tunneling current becomes
larger substantially and that's how the
computer will detect and say aha there
must be a hill because I detect a very
high current and therefore to get back
the same current I need to pull the
needle back and that's how we can figure
out how the you know where the tip of
that Hill is and similarly if we
encounter a valley the potential barrier
has increased the tunneling current will
decrease substantially and again the
computer will say aha the tunneling
current has decreased therefore there
must be a value over here and so I need
to push down the needle forward to get
back the same current and this way by
trying to keep the current same we can
map out the entire surface and we can do
that at the atomic level in fact here's
a picture what you're seeing is the
surface reconstruction of a you know a
clean gold you can literally see the
reconstructions of the atoms over here
that is incredible isn't it but finally
finally Quantum tunneling is also a huge
challenge for our Electronics because
see so far our technology has been
growing substantially our computing
power and memory you know storage
capacity has been growing all because we
were able to shrink the size of a
transistor transistor is a basic
building block of a computer right but
after a particular size if you make it
too small then the electrons will tunnel
through the insulating barrier which
they're not supposed to and then your
transistors will stop working which
means there is a theoretical limit to
how small you can make these transistors
giving you a theoretical limit on how
much computing power or how much memory
you can have in a given area we have not
yet reached that limit today but we will
at someday leech that and therefore
there is active research going on in
figuring out new technology that can
somehow overcome tunneling and for that
quantum mechanics is the key tunneling
is a huge reminder of how successful the
quantum theory really is and learning
this way where you ReDiscover things is
really the most awesome way the most fun
way to deepen your insights so you can