That was a long hard clip, we learned a 
lot. 
And there's more. 
One last addition of Physics. 
Before we turn our attention back to 
astronomy and we will be equipped for 
most of the class. 
Though we will have occasion to introduce 
more science, there is a lot to discover. 
so we're back to our understanding of 
light which as I said is extremely 
important to us and the first thing we 
want to consider are the possibilities 
for what happens when light meets matter. 
So we talked about dense objects like the 
earth. 
whence light hits the earth most of the 
light is absorbed. 
We know you shine a flashlight at the 
ground it doesn't go through. 
Objects as dense as Earth take up only a 
very small fraction of space. 
But there are, in fact, large cold clouds 
of dust and gas that absorb radiation, so 
they look very dark. 
So there is the possibility that dense 
enough and cold enough objects simply 
absorb light. 
Or some of the light might be reflected 
when you shine a flashlight beam on the 
ground. 
Some of it bounces up. 
If you put your hand above the beam, you 
will see light coming off your hand, so 
we can get some reflection off of dense 
objects, and that in fact is how we see 
the wold around us, sunlight bounces off 
dense things. 
And, we see them and don't walk into 
them. 
Now in general, how much is absorbed can 
depend on the wavelengths, so different 
materials reflect different amounts of 
the light in different wavelengths. 
This is how dyes and colors work. 
So the sweatshirt I am wearing is red 
because someone imbibed the fibers with a 
dye that absorbs, say, green light and 
that makes the light that it emits look 
this nice dark red color and other 
things. 
the walls behind me are painted with a, a 
paint that reflects mostly blue light, 
and therefore they look blue. 
And so, what that means is that as we 
look around the universe and we see 
colors of things, sometimes if you see 
the colors of reflected light, you can 
conclude something about the chemical 
composition of the thing you're looking 
at. 
There is another interaction of light 
with matter that will be of great 
importance to us, and as we will see we 
will explain interesting things. 
And that is the possibility that if you 
have matter that is not dense. 
That is tenuous enough to be transparent, 
so most of the light goes through [COUGH] 
light scatters off of molecules, atoms, 
dust grains, anything. 
Rayleigh and the mathematical formulation 
was given by Lord Rayleigh in 1871. 
So, it's called Rayleigh's scattering. 
And, what scattering means, means that a 
light being coming in will hit some 
particle and be deflected at some angle. 
What that means is that you looking here 
will see light Coming from over there 
that actually came from over there, you 
will see light coming from the wrong 
direction. 
Now, 
this phenomenon decreases with 
wavelength, long wavelengths scatter far 
less than short wavelengths. 
So blue lights scatters more than red if 
you recall this image of the Pleiades 
cluster N45, we saw this blue wispy light 
all around. 
This is scattered light, these are clouds 
of dust around these stars and the 
starlight is scattering off of them so 
that light from the star that was not 
suppose to hit us on earth that was 
heading somewhere else, 
got scattered by dust over here and so we 
are seeing light, 
starlight coming from the wrong 
direction, because it was scattered by 
the dust. 
this has lots of interesting 
consequences. 
And one of my favorite is the following. 
In this experiment, we're going to 
simulate the interaction of sunlight with 
the atmosphere and we'll learn 
somethings. 
On the left hand side we see the 
apparatus. 
We have a cup of water standing on an 
over head projector. 
The overhead projector has a round hole 
cut in a mask. 
And, so what we see is, we see the cup of 
water and we see the light going through 
the cup of water and projected on to the 
wall. 
Water is transparent and so looking 
through the cup and seeing the dark 
color, we're seeing the darkness of the 
curtains beyond it. 
Just as where the air completely 
transparent, you would look above us and 
see the darkness of space. 
Indeed, if our earth's atmosphere were 
completely clear then, looking at the 
sun, we would see the bright white color 
of a black body object with a peak 
somewhere in the visible. 
The peak is broad enough that there's 
distinguishable difference between the 
way our various receptors are excited. 
So any object with a black body spectrum 
of a few thousand degrees, like an 
incandescent light bulb, will appear 
bright white to us, as would the sun. 
The rest of the sky though when we're 
looking away from the sun would appear 
dark. 
And this famous Apollo image that we see 
of Earth rise over the lunar surface, is 
a great example of this. 
Clearly it is daytime on the moon. 
From the phase of the Earth, you can tell 
that the sun is directly overhead, as 
seen by, the astronauts on the moon, at 
this point. 
And you can see that the moon's surface 
is brightly lit, the sun is overhead. 
And yet, the sky on the moon is 
completely dark. 
Had we looked at the sun, we would see a 
bright white sun. 
Looking away from the sun, the sky is 
dark. 
And, in fact, you can see stars in the 
daytime. 
This is not the situation on Earth. 
And the difference between the moon and 
the Earth is our atmosphere. 
Dissimulate 100 miles of air overhead 
with its 
abundance of scattering opportunities for 
incoming light. 
What I've done is I've stirred some 
reagents into this cup. 
Over time, as they react, they will 
precipitate increasingly large 
concentrations of small crumps of sulfur 
into the water. 
These will service scattering centers, 
and will allow us to emulate a 100 miles 
of atmosphere in six inches and what 
we're going to do is as the concentration 
of sulphur increases we will follow on 
the left hand side what the cup looks 
like. 
this emulates what you'd see in the sky 
looking away from the sun, which right 
now is a dark sky and presumably star 
studded. 
And on the right, we'll see what happens 
when you look directly at the light 
source. 
This will simulate what you would see 
looking directly at the sun. 
You've now achieved a sufficient 
concentration of sulfur precipitate that 
there's a lot of scattering going on in 
that cup and the water is no longer 
transparent. 
In fact we don't see the dark curtains 
through it, we see that it's glowing and 
as predicted, blue light scatters more 
than any other color. 
So the color of this cup is glowing, is a 
bright sky blue and as the precipitate 
continues to increase in concentration, 
that glow will get brighter and brighter. 
What we are seeing is sunlight scattered 
off the 
scattering centers in the sky, water 
molecules, dust particles, air molecules 
themselves, causing the sky to glow blue 
when you're looking away from the sun, 
and this is a very dramatic demonstration 
of what it is we're seeing. 
Looking on the right, we see that what 
has happened to the transmitted sunlight. 
This is, remember, what you see when you 
look straight at the sun. 
Some of the blue light that would have 
reached your eyes had it not been 
scattered, has been scattered in other 
directions in interactions with the 
atmosphere. 
This leave the sunlight that reaches your 
eyes, blue depleted and blue depleted 
white light, you recall, looks to our 
eyes yellow. 
It's a combination of green and red with 
less smaller amounts of blue. 
What we perceive that is as yellow light. 
This is the reason the sun looks yellow. 
We've now achieved a high enough 
concentration of scatterers, and in fact 
when we look at the cup, it not only 
glows very brightly, pretty in fact 
appears white. 
We see all colors of the light scattered 
towards our eyes. 
This is some what the color of bright 
white cloud in the sky. 
A cloud contains many ice crystals, light 
is reflected and scattered off of the 
ice, we see all colors reflected from a 
white cloud, so that's the reason we are 
seeing this. 
But, we still have as you can see at the 
edges where the camera is less saturated, 
there is still a preponderance of blue 
light in the scattered light. 
And this is very dramatically evident on 
the right when we see that the 
transmitted sunlight is now really a dark 
yellow as the light loses blue components 
to scattering, what's left is yellow, 
that is some reminiscent of the color of 
the Sun as we see it. 
We also see that as more and more light 
get scattered, the observed sunlight is 
dimmer. 
Indeed, the atmosphere dims the Sun by 
distributing some of its light in all 
kinds of other directions, the Sun is 
much brighter on the moon where there is 
no atmosphere. 
Finally, having waited for the 
concentration of scattered rays in the 
cup to increase to the point where as you 
see in the left, the cup glows bright 
white. 
you can see that what's going on is that 
not only have the blue hues of the 
incoming white light been scattered away 
but in fact its lost much of it's green. 
And the remaining color of the 
transmitted light as we see on the right 
is darker than yellow in fact it's an 
orange. 
As scattering continues to increase we 
will lose more and more of the green and 
eventually the transmitted sunlight will 
appear almost red. 
This might remind you that there are 
circumstances under which indeed, the sun 
in the sky appears red. 
I hope you found that demo as fascinating 
as I always do. 
What did we see? 
We saw that the atmosphere scatters blue 
light in preference over other colors 
making the sky glow blue. 
And because of depletion of blue light 
the sun appears yellow so light of all 
colors impinges on the atmosphere and the 
blue light scatters so that if we look 
away from the sun over here we see blue 
light scattered in our direction among 
others from the sunlight that hit over 
here but the rays that penetrate are the 
greens and the reds together blue 
depleted white light appears to us to be 
blue. 
And then, as we increase the 
concentration of scatterers, effectively 
making the atmosphere contain more 
impurities. 
Or be thicker, we saw, 
when we got more scattering, 
we lost the green as well as the blue, 
and that left the sun looking distinctly 
red. 
And of course the sun looks red to us at 
sun rise and sunset when its low in the 
sky. 
The reason for this is both because at 
sun rise and sunset we're looking not 
through a 100 kilometers of atmosphere, 
but through a 1000 kilometers of 
atmosphere. 
And more over most of the impurities in 
the atmosphere, the bigger scatteres are 
at low altitudes. 
And the grazing rays of the rising or 
setting sun have more opportunity to 
encounter them. 
And scatter and so the blue scatters 
early than the greens than the yellows 
and so on. 
And only at the end of the day, red light 
penetrates all the way through to our 
rise. 
So that same demo shows us why the sky is 
blue, why the sun looks yellow, and why 
sun sets are red. 
Now, I can't resist the few other 
brilliant examples of scattering on 
Earth. 
One is crystals of ice, because of their 
geometry, tend to scatter like 
preferentially at particular angles. 
There is, are many forms of ice crystals, 
one hexagonal form that forms in high 
altitude clouds tends to scatter light at 
an angle of 22 degrees and so very often 
you see at night the moon with a 22 
degree ring around it. 
So again this is moonlight that was not 
aimed at you but someone 22 degrees away 
from you was deflected and is hitting you 
and so you see this beautiful ring around 
the moon. 
You can get a ring around the sun but the 
sun is to brilliant. 
On the other hand, the geometry of water 
droplets in the, optical properties of 
water. 
Say that water droplets like to scatter 
light through an angle of 140 degrees, 
approximately. 
What this means is that the light is 
returning in the direction of the Sun and 
it forms a big circle with a radius of 40 
degrees around the direction 
diametrically opposed to the Sun. 
And so, if the sun is high in the sky 
this is typically below you, and you 
don't see anything. 
But if the Sun is low you can see parts 
of a big circle in the sky in the 
direction, 
opposite the direction of the Sun. 
And because the light has gone through 
water and the optical properties of water 
depend on the wavelength different colors 
of light get deflected by slightly 
different angles and we get the brilliant 
phenomenon of the rainbow. 
And as I said the best rainbows are 
always early in the morning or late in 
the afternoon. 
The Sun is low and the rainbow therefore 
high. 
If you want to see a rainbow at, midday, 
with the sun overhead. 
You have to be able to be looking down at 
the clouds. 
As this paraglider pilot is doing. 
the round rainbow, in this case double 
with the shadow of your glider in the 
middle is called the glory. 
And it is, indeed, a glorious sight. 
The sun as we know, has a black body 
spectrum. 
It's a black body with a temperature of 
6,000 degrees. 
And it looks white in general. 
The black body spectrum is sufficiently 
broad. 
And anything with a temperature of a few 
thousand degrees. 
The sun and incandescent lamp. 
Such that the maximum is anywhere near 
the visible will not create sufficient 
differences between the way it activates 
our green, blue and red receptors to give 
us a great sensation of color, so the sun 
appears to us white, remember its 
wavelength of maximum emission is right 
smack in the middle of the visible 
spectrum of the green, and it makes a 
beautiful 
rainbow of colors. 
And here, someone has laid out the solar 
spectrum line by line by line. 
So this is to be read like a book. 
It's a very detailed spectrum of the sun. 
And indeed, there's a black body spectrum 
here centered on the green. 
But there are these gaps. 
There are holes. 
There are specific wavelengths along the 
spectrum in which there are holes. 
Something is eating the black body 
spectrum is continuous. 
Something is absorbing the light at 
particular wavelengths. 
And this was a discovery by Fraunhofer in 
1814. 
And a few years later, Kirchoff and 
Bunsen discovered that if you heat a 
tenuous gas, a gas under low pressure and 
very low density, 
then the la, glass will glow if you 
either. 
Heated by burning or ionize it by passing 
a current through it. 
When the gas is sufficiently tenuous, the 
light that it glows with is actually not 
black body spectrum but only discrete 
spectral lines. 
And Kirchhoff is the one who figured out 
the regularity that relates these two 
pictures, and let's see how that works. 
We have a incandescent light here, or if 
you want any black body, say a star, and, 
like the Sun. 
If you are looking at the star, then you 
will see in your spectrometer a 
continuous black body spectrum with the 
maximum emission determined by the 
temperature of the star. 
To the left, is a cloud of tenuous gas. 
So low pressure, low density. 
And if you observe the emissions from 
that cloud of tenuous gas, you get this 
line spectrum that 
Kirchhoff and Bunsen discovered. 
There will be discrete wavelengths, 
discrete places. 
It's called the line spectrum for the 
obvious reason of its appearance. 
There will be discrete places in the 
spectrum where this cloud will emit. 
On the other hand, if you observe the 
continuous emitter, the black body, 
through the cloud, you will see the 
rainbow the full continuous black body 
spectrum of the black body that's behind. 
And at precisely the same wavelengths 
where you saw emission you will see 
absorption. 
In other words, an atom or a molecule is 
characterized by a specific set of 
wavelengths at which it can either emit 
light or absorb. 
Now when you bunch a whole collection of 
atoms densely together, then these lines 
are broadened gradually as you increase 
the density. 
And eventually when the density becomes 
large enough they merge into the 
continuous spectrum of a black body 
spectrum that absorbs all light at any 
wavelength and emits in a continuous 
black body spectrum. 
But if the density is low and the 
pressure is low enough then you find 
discreet emission as well as discreet 
absorption. 
So these wavelengths are properties of 
the 
Gases in the cloud, that we're talking 
about. 
Naturally, this discovery was a huge boon 
to chemistry. 
Because what it allowed, Kirchhoff and 
Bunsen to do was to heat various gases. 
Observe the emission line spectrum. 
And conclude, identify the wavelengths of 
emission with those from known atoms, 
known elements and they could find the 
element, the elementary composition, the 
chemical composition of the substance 
that they were observing. 
Thus was born the field of spectroscopy. 
And, so as we see, as we seen, observing 
the line spectrum allows you to identify. 
So, you can go over, an expert can go 
over the spectrum, and identify that this 
line and that line corresponds to the 
wavelengths at which we know Thrice 
ionized Iron. 
Atoms. 
Absorb radiation. 
So, the, degree, the darkness of these 
lines, the amount of, absorption, 
indicates something about the 
concentration of, thrice-ionized iron. 
And so on and so forth. 
You can go through the solar spectrum, 
and identify, all the elements that are 
there. 
And then in 1868 an interesting discovery 
is made by Jansen ad Lockyer. 
independently they look at the spectrum 
of sunlight during an eclipse and they 
discover a line in the yellow, right over 
here in this region of the spectrum. 
And it does not correspond to any known 
element. 
and so after some further checks they did 
decide that they've discovered a brand 
new unknown element. 
And since it was discovered in the 
spectrum of the sun they name it 
appropriately helium. 
yeah, the helium you put in your birthday 
balloons was first discovered to exist in 
the spectrum of the sun. 
We'll talk later about why it's so hard 
to find helium on earth. 
But the first indications of the 
existence of such a substance were in the 
spectrum of the Sun. 
So, observing the line spectrum of an 
astronomical object will tell us about 
it's chemical composition. 
And as we shall see a whole lot more. 
So spectra will be with for a good part 
of the class. 
Understanding why particular atoms 
emitted particular wavelengths was an 
interesting problem, but before that 
could be solved a revolution in our 
understanding of the structure of the 
atom had emerged. 
By this time G.G.Thompson had discovered 
that one of the constituents of matter 
was something he called electrons. 
They were responsible for the conduction 
of electricity in metal. 
Hence the name. 
And they were negatively charged. 
And one suspected that an atom being 
electrically neutral would have some 
positive charge and some electrons. 
And indeed Rutherford in 1909 sets out to 
discover this structure with his students 
Geiger and Marsden. 
And what he discovers is astonishing. 
He discovers that most of the mass of the 
atom. 
Is contained in a positive nucleus whose 
size is of the order of ten the minus 
fifteen meters. 
For the sake of comparison, the size of 
an atom is on the order of ten to the 
minus ten meters. 
So angstrums. 
So o, only one hundred thousandth of the 
radius of an atom, a number you have to 
cube list to get the volume, is taken up 
by most of the mass. 
So there's a very tiny, very heavy, very 
compact nucleus. 
And it's surrounded Rutherford 
understands, by electrons. 
The charge of the nucleus is the atomic, 
is the atomic number of the element 
depending on the atom. 
And there are corresponding number of 
negatively charged electrons, so the 
whole thing is neutral. 
And with Rutherford concludes is it the 
electrons are essentially orbiting the 
nucleus in keplerian orbits, which is 
what gives this large size with the mass 
concentrated very tightly in the middle. 
This is a beautiful example of 
universality. 
The force law between electrons and 
protons is Coulomb's law. 
It's quadratic. 
You get exactly the same elliptical 
orbits that you see in the solar system. 
And so, 
this is the picture of the atom that 
we're so familiar with. 
And then we understand, 
once we understand this that atoms can 
bind chemically by trading, 
sharing electrons or deforming the 
distribution of their electron orbits. 
The development of chemistry from this 
point is very quick. 
And chemistry is the science of 
electronic rearrangement. 
What we understand now is why it is that 
elements are immutable. 
The number of carbon atoms that goes into 
a reaction is always equal to the number 
of carbon atoms that emerge. 
And that is because the nucleus is not 
effected. 
carbon nucleus specifies that this is 
going to be a carbon atom, because it has 
the right the charge, set it out some 
where and it will acquire electrons until 
it is neutral, so nucleus identifies the 
chemical structure of the element. 
And, because the nucleus does not 
participate and these electronic 
rearrangement issues, elements are 
immutable and the project of alchemy of 
converting the element gold into the 
element lead or the other way around is 
completely hopeless. 
this is a brilliant and successful 
picture of the world and Newton's 
universe is becoming richer and at the 
same time better understood. 
And there are those who speculate at the 
end of the nineteenth century that 
physics is all about resolved, but there 
are few negling problems. 
One of them that we can understand is 
this issue of atoms. 
So imagine the simplest of all atoms, a 
hydrogen atom, it has a nucleus with 
charge one and one electron orbiting it. 
This electron is in motion, and in fact 
is accelerating. 
It's moving in a circle. 
And an accelerating charge will create 
changing electric and magnetic fields. 
This means it will create radiation. 
The radiation will carry off energy. 
The electron will lose energy. 
And as we know, you have some particular 
ener-, amount of energy determines your 
orbit. 
As you lose energy, you fall to lower and 
lower orbits. 
So, what you expect the, electron to do 
is just spiral in towards the nucleus 
while continuously emitting radiation. 
Atoms obviously are observed to be 
stable. 
And the stability of the atom is a big 
riddle. 
Similarly, why is it that atoms only emit 
at discrete frequencies? 
You can easily imagine that an electron 
revolving around an atom would radiate at 
the frequency. 
The periodic nature of the radiation 
would be related to the periodic nature 
of the motion. 
But Keplerian orbit as we know, exist at 
any radius. 
And given a radius, you can figure out 
the frequency from P^2 = KA^3. 
And so, since you can orbit at any 
radius, you can orbit at any frequency. 
And therefore you will atoms to be able 
to emit radiation at all wavelengths. 
What is this, this discrete line 
spectrum? 
And then there is some experimental 
puzzles. 
These are sort of theoretical thought 
puzzles. 
Their experimental situations in which 
light is observed a particle like 
behavior. 
Remember Newton said light was a 
particle, and it was one of the rare 
times he was wrong, but not quite. 
And so this is first 
conjectured by Plack in 1900 to explain 
some details of the shape of a black body 
spectrum. 
And then by Einstein in 1905, to explain 
the photo electric effect. 
And the picture that emerges is that a 
beam of light can be thought of under 
some circumstances as a stream of 
particles and if the light wave has 
frequency f, 
then, each of those particles carries an 
energy which is proportional to the 
frequency f and the constant of 
proportionality this object h is known as 
Planck's constant, and it has units of 
course of energy per frequency or energy 
times time and it's a very small amount 
of energy times time. 
So, h is a very small number means that a 
beam with a Nontrivial flux of energy 
contains huge numbers of these photons, 
as these light particles are called. 
And, because there are so many of them, 
the fact that at any given moment a 
particle is or isn't impinging on the 
detector doesn't happen. 
But, if you have a beam of very low 
power, then this quantization as Einstein 
calls it, the fact that the energy of 
beam is carried in discrete packets might 
become apparent. 
And to complicate things. 
So we have this object that has been 
observed to be a, li, wave, because 
[INAUDIBLE] that light undergoes 
interference exhibiting some particle 
properties. 
And then in 1927, Davison and Germer in 
the US, do an experiment in which they 
basically observe that electrons exhibit 
interference. 
Electrons manifest the particles, exhibit 
some of the properties that we set with a 
hallmark of wave behavior. 
So there's this weird duality emerging 
between waves and particles. 
What is a particle sometimes.behaves like 
a wave, a wave sometimes behaves like a 
collection of particles. 
And all of this is resolved over the 
course of the teens and twenties of the 
twentieth Century, by a beautiful and to 
this day somewhat 
puzzling theory called Quantum Mechanics, 
Which leads to a complete revolution in 
our understanding of nature. 
This is the first time that we go way 
beyond anything Newton could have 
imagined, let alone written down. 
and this is, 
modern physics, as we call it, twentieth 
century physics, and in quantum mechanic 
particles, all the states of a particle, 
rather than being described by their 
positions at velocities, are described by 
something called a wave function. 
and this wave function has the, the 
property that its value at any position 
in space at any given time predicts the 
probability of finding the particle the 
probability density technically of 
finding the particle at that point of in 
space at that particular time and notice 
I said probability and I said state so 
the full state of the universe only 
predicts the probabilities for particles 
to be here there or anywhere else, there 
are not definitive predictions its not 
that our ignorance prevents us from 
knowing it in quantum mechanics. 
The Universe does not know where a 
particle is, and yet the 
deterministic evolution, that was so, 
satisfactory, about Newtonian mechanics, 
is in some, deep sense retained here, in 
the sense that the evolution of the wave 
function itself, is, completely 
deterministic. 
the results of measurements however, can 
only be predicted with probability. 
Again, when the numbers of particles are 
on the order of a boule, then the law of 
large numbers guarantees that these 
distributions will be very sharply 
peaked. 
And the probability that, I am not here 
right now but some where else, is 
exceeding the low and I don't need to 
worry about it. 
Now associated to this, a particle as a, 
to a particle is associated to a wave, 
this wave has a wave length. 
The wave length is determined by the 
particles momentum. 
And again that Planck's Constant thing 
shows up 
The wavelength is related to the momentum 
by this relation lambda h / p. 
So again h is a very microscopic number, 
macroscopic values of momentum lead to 
negligible wavelength and therefore the 
wave behavior of a macroscopic object is 
completely negligible and you won't see 
it only microsco macroscopic distance 
scales can you observe real quantum 
behavior. 
Now, we won't have time to discuss either 
the nature of this beautiful theory, 
sadly. 
Or all of its consequences. 
But a few that are important to us, first 
I said this resolves the issue of the 
Discreet spectrum. 
Indeed solving the equation for this wave 
function for electrons in an atom, you 
find that electrons can only occupy a 
discreet set of energy levels. 
The energy of an electron can be, in an 
atom, can be one of a few discreet 
values. 
And in a hydrogen atom, for example, this 
is the form that these energy levels 
take, K is constant, and the energies are 
of course negative. 
These are all bound states, and 
The energy levels are some constant 
divided by n^2 where n can be one, two 
etc. 
So, one is the lowest energy. 
And as n gets bigger, you get states of 
larger and larger energies tending to 
zero as n becomes large. 
Then, the point is that the dominant 
interaction between an atom and radiation 
is the emission or absorption of a single 
photon. 
One atom emits one photon. 
One light particle. 
And at the same time the electron jumps. 
Undergoes what we call a quantum 
transition between energy levels. 
And then energy conservation guarantees 
that for example if a photon is emitted 
while jumping from level N to level M in 
which case the energy N must be bigger 
than M. 
Then. 
Energy conservation says, the energy 
taken away by the photon, which is HF, is 
the difference between the initial and 
final energy. 
The energy lost by the atom is equal to 
the energy takem away by the photon and 
plugging in our value. 
We get this answer. 
And indeed these frequencies, you can 
convert them to wavelengths, are observed 
in the spectrum of the hydrogen atom, for 
example. 
And so the, the discreet energy levels 
are very nicely explained by this and 
many other phenomena are explained. 
As, one outcome of this that is very 
crucially important to us, is the Pauli 
exclusion principle. 
Pauli exclusion principle states that 
electrons are a kind of particle later 
termed fermions. 
And it tells us that at most two 
electrons can occupy a given energy level 
or a given state. 
And for those who like to think about 
these things, electrons have spin, they 
can have two different spins states. 
One electron can actually occupy a given 
state but that state information includes 
which of the two spin states it's in. 
the fact that electrons cannot be 
compressed and you can not have more than 
one electron in a given state explains 
many things. 
It explains the structure of the periodic 
table, and all the regularities that 
Mendeleev had found in the chemistry of 
elements in similar positions in the 
period table are explained by 
understanding the structure of energy 
levels, and pairing it with this Pauli 
exclusion principle. 
It also explains why when I slam the 
table with my hand. 
My hand doesn't go through the table. 
remember that my hand is mostly empty 
space. 
Each atom of my hand is mostly empty 
space. 
So it's not that there's literally a 
collision between atoms. 
Now, what's really going on, is that both 
in my hand and in the table, all the low 
lying energy levels are filled. 
In order to take a mole of electrons from 
my hand and mix them into a mole of 
electrons that are the local part of the 
table, you need to excite a mole of 
electrons to slightly higher energy 
levels that are not yet occupied. 
Per electron that's not lot of energy, 
but a mole is ten to the 23 electrons, is 
a lot of electrons It takes a lot of 
energy to excite so many electrons to the 
next energy level and if I hit the table 
hard enough, it generates enough energy 
to excite a mole of electrons to the 
requisite energy level. 
Then I've exerted so much energy that 
either the chemical bonds in my hand or 
in the table will break and one of the 
two objects will just fall apart rather 
than 
moving right through each other. 
So this Pauli exclusion principle 
explains many, much of our day to day 
experience. 
It'll also become very important in 
understanding some phenomena in 
astrophysics. 
Whew. 
That was a busy week. 
we have found a ton of new science and we 
have come a long way since Newton not to 
mention Aristotle. 
There are many phenomenon's both on earth 
and off of it that we understand and the 
main tool that allows us to be so 
insightful is that atoms are 
fundamentally the same wherever you go. 
The behavior of a hydrogen atom on earth 
right here is indistinguishable from the 
behavior of a hydrogen atom out in the 
crab nebula or inside the sun. 
There may be physical circumstances that 
are different in the Sun. 
But if we can emulate those circumstances 
hydrogen atoms or hydrogen atoms, helium 
atoms or helium atoms. 
The laws of Physics are the same here, 
there and everywhere and so these laws 
that we have discovered by measuring 
things in labs on Earth can be and are 
applied to the way things behave in the 
heavens. 
Remember we said that we are going to do 
our Aristotle one better by looking for 
laws that are valid on heavens as they 
are on Earth. 
And indeed, these are the laws that we 
are going to find. 
There's a satisfaction in understanding 
all these things. 
And I hope that you will take away from 
this discussion a new way of looking at 
things you see here on Earth. 
But the purpose of this class was to talk 
about things away from Earth, and we're 
finally ready. 
When we come back next week, we will 
start to take all this amazing new 
arsenal of tools we've developed, and 
apply it to actual astronomical 
phenomena. 
In the meantime, get some good rest. 
You've have certainly earned it.