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.