So, what we discovered is that the power 
of the sun requires a source of energy 
that we have not discussed yet. 
It is not electromagnet energy in the 
internal structure of an atom. 
It is not gravitational energy. 
Where else can you mine potential energy? 
This was a puzzle until the twentieth 
Century and the answer, of course, is 
nuclear energy and so we'll have to learn 
a little bit about the structure of the 
nucleus and we talked, when we mentioned 
the nucleus and it's contruction out of 
Protons that are positive and neutrons 
that are neutral. 
That there's a big puzzle. 
That's a collection of positive charge 
without any negative charge. 
And there's a very strong electrostatic 
repulsion between all these charges. 
Remember electric forces like 
gravitational forces decay with distance 
like one over R squared. 
These are the forces at distances of ten 
to the minus fifteen meters. 
The size of a nucleus, 
these protons are very close up against 
each other. 
There's a huge repulsive force between 
them but nuclei I don't fall apart. 
Something must hold them together. 
So it's natural to conjuncture and later 
to verify the existence of a very strong 
attractive force, that binds the nucleons 
to each other. 
And over comes this electrostatic 
repulsion. 
How strong is the force? 
Well, strong enough to over come the 
electrostatic repulsion between protons 
and the nucleus. 
And that's a very strong force indeed. 
on the other hand, we know that this 
force cannot extend beyond the confines 
of the nucleus too far because if it did 
then the the nuclei of two neighboring 
atoms would attract each other and 
collapse on top of each other and so 
unlike gravitation and electromagnetic 
ray interactions that are long range 
interactions, volumes interact, every 
parts of the universe attracts every 
other part gravitationally the nuclear 
force is a short range force that ranges 
larger than the size of the nucleus, it 
effectively decreases to zero. 
and so there's no interaction between 
neighboring nuclei. 
We don't have a problem. 
We have this very strong force. 
And this brings up the idea, that maybe 
just as rearranging electrons lead to the 
liberation of electrostatic potential 
energy. 
Maybe rearranging nucleons inside a 
nucleus can liberate nuclear energy. 
And we've learned a lot about nuclear 
energy. 
the way, they have parameterized the 
amount of potential energy liberated at 
creating a nucleus similar to the way we 
computed the gravitational energy 
liberated in creating the song. 
Is to say imagine starting with a bunch 
of nucleons, put them together. 
Of course, you'll have to input a lot of 
energy to get them close to each other 
because at large distances the 
electrostatic repulsion will dominate. 
But once they get close there's a strong 
attractive force. 
They'll crash into each other and 
liberate a lot of energy producing the 
nucleus. 
The question we want to ask is if we have 
a whole bunch of nucleons, what's the 
most efficient way to pack them together. 
To do that, we measure the total 
liberated energy. 
nuclear minus electrostatic. 
The total difference, the total energy 
gained by constructing nuclei out of nu, 
a bunch of nucleons, and that's, we want 
to do that energy per nucleon, so that if 
you have a, some fixed number of nucleons 
what's the most efficient way to pack 
them. 
And one would think that because we have 
this very strong attractive interaction, 
that certainly a hydrogen atom is not a 
good way, to produce efficient packing. 
A hydrogen atom is a proton it's not 
interacting with anybody it hasn't, 
liberated any potential energy. 
but one would think that very heavy 
elements like uranium. 
Big nuclei, where there is a lot of 
nuclear interactions would be the ones 
that liberate the most energy and what 
this plot shows us, we have here atomic 
number or number of nucleons running mass 
number running to the right and the 
average energy liberated per nucleon 
going up. 
And we see that the most stable 
configuration is not a bunch of uranium 
nuclei, but a bunch as many as you have 
nucleons for of iron nuclei, the sort of 
intermediate range, intermediate size 
nucleus is the most efficient packing. 
And the explanation for this is an 
important one, the explanation for this 
is very close to the discussion we had of 
the cross over between short range 
chemical forces that are short range but 
are very strong and enact on the surface 
and ling range gravitational forces at 
about a size of kilometer in the solar 
system. 
A similar thing happens with nuclei. 
What goes on is that if you have a great 
big uranium nucleus, then a proton that 
is located on this side of the nucleus 
and a proton on that side of the nucleus 
basically are too far apart to really 
interact through the strong force, so 
they do not attract each other. 
Remember, the attraction falls to O. 
in some sense each of these protons on 
the edge of a very large uranium nucleus. 
Interact only with his neighbors what 
that means on the other hand the electric 
forces between these protons decay only 
as the distance squared those are long 
range forces so these guys definitely do 
repel each other through electro static 
forces. 
And therefore the sort of efficient way 
to arrange the energy just as we saw this 
is really analogous to the discussion 
what holds a mountain together is to 
cleave this nucleus in two, perhaps. 
we now have, lost all the nuclear energy 
that was involved in the bonds along the 
place we cut. 
But when these two positive sub-nuclei 
are created, 
they are two positive charges very near 
each other. 
They repel with the great electrostatic 
repulsion. 
That produces a lot of energy as they 
accelerate away. 
And the net result is a gain of energy 
and so what we see indeed is that the 
most efficient way to pack is iron and 
nuclei. 
Heavier than iron are not efficient 
packing, and by rearranging their 
nucleons, they can re-liberate energy 
well known case is the case of fussion. 
This is the case exactly, where this 
nucleus of californium breaks into 
cadmium and tin and some debris, some 
extra neutrons flying around. 
And in the process, liberates essentially 
the electrostatic repulsion that, once 
these two nuclei are free, they are 
repelled and proceed at great energy to 
move away from each other. 
Another popular mode of breaking up, if 
you're a heavy nucleus, is, we see here, 
rutherfordium, emitting, an alpha 
particle. 
Remember, an alpha particle is a nucleus 
of helium, two protons and two neutrons, 
and the rutherfordium decays to 
seaborgium. 
so both of those modes occur in heavy 
nuclei. 
They liberate a lot of energy. 
This was the radioactive energy that 
powred heated up the, the interior of 
Earth. 
Remember that was the 89 watts per liter 
squared or 87 watts per liter squared 
that were bubbling up from nuclear 
reactions in the core but 
it's not going to be enough to power the 
sun, because in the sun we don't have 
rutherfordium or californium or uranium. 
We have hydrogen and hydrogen remember is 
way on the other side of the divide. 
a hydrogen atom nucleus is just a proton. 
It's not bound to anything. 
Of course if we could make bound states 
of protons, maybe we could gain. 
But there are no bound states of protons 
only. 
helium 2 is not a stable nucleus. 
If you put two protons together, they may 
bind for a short time but the 
electrostatic repulsion will break that 
nucleus apart very quickly. 
And so the first really stable nucleus 
and it's a very stable nucleus indeed, is 
helium 4, that alpha particle. 
If you can make a helium nucleus out of 
the hydrogen, you will have gained all 
this energy. 
that's very good. 
The problem is that to make a helium 
nucleus you need two protons, two 
neutrons. 
The sun is full of protons but there's no 
neutrons essential where do you get the 
neutrons we can't using the srong force, 
convert photons to neutrons but we know 
that somebody can. 
And the reason we know that somebody can 
is because we talked about beta decay of 
nuclei and we see here some of the decay 
of oxygen to fluorine. 
And what's going on here is, since this 
is a positive beta decay, you can look at 
the atomic number and see that in fact, 
one of the protons in the fluorine is 
being converted to a neutron. 
So, fluorine is decaying to oxygen with 
the emission of a positron and there's 
also the inverse reaction, in which here 
carbon-14 converts one of its neutrons to 
a proton becomes nitrogen-14. 
And emits an electron and so we know 
about these decays. 
In fact, the free neutron decays to a 
proton within about fifteen or sixteen 
minutes. 
And so there is this thing called the 
weak nuclear force, probably better 
called the weak interaction, which 
mediates these decays. 
It is possible for one elementary 
particle to be converted to another 
elementary particle. 
And this is a very confusing thing. 
So we have to sort of stop. 
We're not going to discuss the physics of 
the weak interactions, fascinating though 
it is, in detail. 
But we need to have, set some ground 
rules. 
So what is this kind of force? 
Magically convert one particle into each 
other. 
We understand that a force can cause a 
rearrangement of the constituance of a 
particle. 
So one could image maybe that a neutron 
is really just a very, very tiny hydrogen 
atom. 
There already were a proton and an 
electron inside the neutron and then they 
just fell apart. 
The answer is no, it's a very bad idea to 
think of a neutron as a hydrogen atom. 
there was no proton inside the neutron. 
The neutron honestly decayed to a proton 
and an electron. 
and yes the weaker interactions can 
change one particle to each, to another. 
But, there are going to be some rules 
that we need to understand. 
And then there was this third object 
there. 
it's called an anti electron neutrino. 
So the Greek letter nu stands for 
neutrino. 
The bar says anti, and the subscript E 
makes it an electron neutrino. 
And what all that means, we'll have to 
understand. 
so lets set the rules. 
What can, interactions do, what can they 
not do, they cannot do anything they 
want. 
The rules, basically it turns out, are 
restricted to a good old fashion 
conservation loss, that's why we made 
such a big deal about it, when we were 
learning. 
Now, 
there's a tricky business here, we're 
getting into the, stepping into the 
beginnings of relativity, where you allow 
the particles to decay. 
We will spend almost an entire week 
understanding relativity, later in the 
class. 
for now, I'll just say the words we had 
in Utonian physics of conservation of 
energy, and of course, conservation of 
mass 
in relativistic theories, those are 
combined in the conservation of the sum 
of energy and mass. 
Mass is a form of energy. 
There's the famous conversion ratio 
square of the speed of light. 
We will talk about this. 
it is not that relevant to the processes 
that take place in the sun despite what 
you may have heard. 
And so when it's important we will talk 
about relativistic physics. 
But mass and energy are conserved. 
momentum is conserved just as it always 
was. 
angular momentum is conserved if you are 
dealing with elementary particles you 
need to remember that elementary 
particles carry intrinsic angular 
momentum it's called spin. 
You could imagine that a proton always 
spins and there's a. 
This, the rotation. 
Is at a constant rate and points in some 
particular direction. 
And, then there are the other kinds of 
conserved quantities, that are not to do 
with motion. 
We talked about electric charge. 
Electric charges conserve. 
No matter what processes go on 
the total electric charge in any region 
of the universe doesn't change unless a 
charge is flowing in our out. 
And then, there's a new one that we 
discover as we start to develop particle 
mechanics. 
And that is, 
Property called electron number. 
An electron carries electron number. 
A proton obviously has zero electron 
number, as does a neutron. 
An electron number will see its 
conserved, and this restricts what can 
happen in interactions involving 
electrons. 
And the interactions we are going to 
study. 
Weak interactions. 
What make them weak is that they're not 
really a force. 
They are things that happen. 
the strength of the interaction 
essentially measures, how frequently a 
reaction will happen. 
Weak interactions. 
Occur very slowly, they are rare. 
One out of many, many attempts will 
generate a reaction. 
The example is the neutron that survives 
as a free particle for fifteen minutes. 
By particle standards, that's a very long 
time. 
So, who are the players? 
Well, here's a list, we're into particle 
physics now, of all of the particles we 
have or should be discussing. 
and they include well, I'll start at the 
bottom. 
We have our friend 
Photon denoted by gamma, its gamma rays 
and I have written the quantities of 
their conserved charges, of course their 
momenta and energy depends which way they 
are moving but a photon is a neutral 
particle, it carries no electric charge, 
it is not an electron carrier, zero 
electron number and then here we have our 
proton, neutron and electron with their 
known electric charges and with the fact 
that the electron carries a charge not 
carried by any of the others. 
And then. 
There is this other interesting object 
called the neutrino. 
And the neutrino was discovered because 
when neutrons decayed. 
Studying the conservation of energy mass 
it was discovered there was missing 
energy. 
it was Enrico Fermi's idea, I believe, to 
think that maybe there was a neutral 
particle. 
It doesn't interact with anything. 
It is not detected by any of our 
detectors. 
Sails right through the detectors. 
And produces and carries off our 
remaining energy since it was 
electrically neutral and didn't interact 
with anything, it was called a neutrino. 
We now know that these particles exist 
and indeed are part of this. 
And, in fact an electron neutrino carries 
a electron charge, electron number one. 
Travis will become important in what 
follows, because the weak interactions of 
electrons and protons conserve electron 
number. 
What that means, in particular, is that 
when a reaction occurs we need to balance 
all of these quantum numbers. 
They're all conserved so, for example, 
the decay of a neutron into a proton plus 
an electron conserves electric charge. 
Because the neutron is neutral. 
And the total electric charge of the 
products is zero. 
But it does not conserve electron number. 
Electron number was magically created. 
And indeed this means that if you have a 
neutrino and an electron. 
And they react, that can produce a proton 
and an electron. 
Now, I was about to write something on 
the right hand side, because of course a 
free neutron decays without anything 
hitting it. 
this brings up the fact that there's this 
whole bottom line of the table. 
And it turns out to be another important 
principal of physics, that for every 
particle there is an antiparticle. 
An antiparticle is not something mystical 
or mysterious or a particle moving 
backward. 
It's simply another kind of particle. 
Which has the same mass as the original, 
and all the opposite charges. 
So, for example, there is an antiproton, 
which has the same mass as a proton but 
is negatively charged. 
And of course, carries the same zero 
electron charge. 
There's an anti-neutrino, which is 
neutral. 
There are anti electrons, they're called 
positrons. 
That was what was emitted in positive 
beta decay. 
They carry the same mass as an electron. 
But electric charge positive and negative 
electron number charge. 
And the neutrino has its own 
anti-particle. 
And the anti-electron neutrino is neutral 
like the electron neutrino but has the 
opposite sign of electron charge. 
And so, the decay can proceed if an empty 
electron neutrino is produced over here. 
This conserves all the charges. 
Now these neutrini are very hard to 
understand. 
They interact only through this weak 
interaction which as I said, makes for 
rare events. 
So mostly, mostly, they don't interact at 
all. 
In the time I've been talking about this 
slide, some millions of neutrinos have 
penetrated each and every of your 
fingernails. 
You have not felt them because they don't 
interact with anything. 
In fact, the great majority of them will 
sail right through the Earth and come out 
the other end, and keep going through the 
universe. 
they carry very little mass if any. 
In fact for a long time they were thought 
to be massless. 
And they don't interact which makes 
detecting them a very difficult 
proposition as we will see. 
But they're important because they 
balance the charges in weak decays. 
And as we'll see they have some other 
important role in our story. 
I didn't bring them up just to tell you 
about particle decay and there's a the 
property that if you take a particle and 
an antiparticle so you have an electron 
and a positatron. 
That combination has total charge zero 
with respect to all the concerned charges 
except for energy momentum. 
And so if you bring an electron or 
positron near each other, and they're 
addressed, there's just energy. 
That's in their mass, and that can indeed 
be converted to straight radiation. 
The electron and positron annihilate, and 
a burst of gamma radiation flies off in 
both directions and the energy is 
essentially the mass of the disappearing 
electrons. 
This is a process that does occur and you 
will have to understand how that happens, 
as I said, when we talk about relativity 
for now, we recognize that if you have an 
electron and a positron, you can liberate 
energy. 
We'll take all this information, and see 
what it tells us about, how the sun 
works.