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CATHERINE DRENNAN:
Click in your response.
All right, let's
just do ten seconds
on the clicker question.
OK, so 82%.
I like it when we get into
the 90s, just FYI, for these.
So since this is similar
to one we did last time,
it's just to remind you again
of the first part of problem
set one where we
have this material
that you need to
learn how to cover.
So does anyone want to tell me
how they got the right answer?
And this is not going
to be a great prize.
There's going to be
better prizes later.
This is an American Chemical
Society pen for this one,
since we had a similar
question last time.
I should've told
you it was going
to be a better prize later.
Now no one's going to--
everyone's going to wait.
See if that's turned on.
No, I guess not.
AUDIENCE: So you find
the limiting reactant
by dividing the amount
of moles for both
by the molar coefficient.
And you see that it's
at the O. And then
you just do 12 times
the molar fraction,
which is just one AL203 for
every 3FEO and you get 4.
CATHERINE DRENNAN: Great.
So if you haven't
practiced these yet,
go ahead and practice.
Yeah!
[APPLAUSE]
CATHERINE DRENNAN: OK, so
let's think about what we
were talking about on Friday.
We were talking about
discovery of the electron
and the nucleus, and realized
through the experiments
that the atom is
mostly empty space.
But there is this
concentrated small part
of the nucleus that can
deflect alpha particles,
or ping pong balls.
And this is a really
small concentrated part,
so that would be like the head
of a pin in a room somewhat
bigger than this, or a pea in
the size of a sports arena.
The nucleus is very tiny
compared to the atom.
And the atom is, again,
mostly empty space.
So this discovery was amazing
of these subatomic particles
and was really changing what
people were thinking about.
So at that time, they
started to realize
in doing these experiments
and the experiments I'm
going to tell you today that
they needed a different way
of thinking about matter.
And to explain the
observations that scientists
were making at the time, they
needed to think about the fact
that radiation had both
wave-like and particle-like
properties.
And matter had, also, wave-like
and particle-like properties.
And also that
energy is quantized
into these discrete
bundles called photons.
So we're going to be talking
about these new discoveries
and the data that
didn't fit today,
and how we came up with
this new mechanics that
helped to explain the properties
that were being observed.
So we're going to start
today with a wave particle
duality of light.
So we're going to talk
about light as a wave.
And we're going to first talk
about the characteristics
of waves, which is
a little review.
And then we're going to talk
about light as a particle
and get into the
photoelectric effect, which
was a really important
series of experiments
that help scientists
understand what was going on.
So first we'll just have a
little review about waves.
So some of you come from places
that probably don't have oceans
nearby.
You are now living in a place
that does have an ocean nearby,
so you can go take the
blue line to Revere Beach.
I always find doing a
chemistry problem set is
very relaxing on the beach.
And you can watch
the water level
go up and down in this
repeated periodic fashion.
So if you haven't
experienced water waves,
you should absolutely do that.
So waves have this
periodic variation.
So you could have
average water level,
the water level will
go up and then go down
and go up and go down from
high levels to low levels.
This same behavior is observed
for other types of waves,
such as sound waves.
So here you would have
the average density,
and the sound wave can go to
higher density, lower density,
higher density, lower density.
And this same periodic
behavior is also observed
with white light or
electromagnetic radiation
is also a periodic function.
But here you have this periodic
variation of an electric field.
So we have, whether
it's water waves
or if we have sound
waves or light waves,
we always have this
periodic behavior.
And you can define
this periodic behavior
by a number of different terms,
which we'll talk about now.
Mostly we'll be focused
on light waves today,
but these terms can apply to
other types of waves, as well.
So we have amplitude.
And that's the deviation
from the average level.
So you can have a
positive amplitude
or a negative amplitude here.
So this is the
height of the wave.
You also have wavelength where
the abbreviation is lambda.
And this is the distance
between successive maxima,
so the distance from this
maxima to this maxima
is one wavelength.
We also have frequency of the
wave, which helps to define it.
Oh, I should say wavelength
can be up here or down here.
They should be exactly the same.
So frequency or nu is the
number of cycles per unit time.
So we talk about wavelength,
amplitude, and frequency.
And as you turn the
page, we can also
talk about the
period of the wave.
So 1 over the frequency
is called the period,
and it's the time it takes
for one cycle to occur.
So the time that you
go from one maximum
to the other maximum
for one cycle
is the period of the wave.
As with most things in
chemistry, there are units,
always think about your units.
So units of frequency
are cycles per second,
and that's also called a hertz.
So you will often
just see per second,
but sometimes you'll see
hertz in these problems.
So those can be used
interchangeably.
And one other term is
intensity, which is
equal to the amplitude squared.
So for all of these
waves, there are
these certain characteristics
you think about.
The amplitude of the wave, the
wavelength, and the frequency,
the period of the wave, and
also the intensity of the wave.
So now if we're thinking
about light waves, which
we will be most of
the time, we can also
think about the speed of
that light that is traveling.
And so at time 0
if we're thinking
about the time it is going to
take this little orange dot,
to move this pink
here that's labled,
to move from here to
here, move one wavelength.
So it has moved to
this second location.
The time it takes
to do that is going
to be 1 over the frequency.
If we think about then the
speed at which this will happen,
that it'll go from
here to here at time 0
to time 1 over the frequency or
one period as we just defined,
now we can fill
out this equation.
And see that the
speed is going to be
equal to the wavelength, lambda.
So that's the distance
traveled, the wave
traveled one wavelength.
And the time it took,
the time elapsed
was one period or 1
over the frequency,
and then we can define
one of the equations
that you probably
don't really need
to have defined for you, which
is that the speed of light
is equal to the wavelength
times the frequency.
And this is in usually
units of meters per second.
So most people already know
what this speed of light,
we're talking again about
light here, is equal to.
And it has a constant speed.
So electromagnetic radiation
has a constant speed,
the speed of light.
And the speed of light
is abbreviated c,
equals the wavelength
times the frequency,
which is 2.9979 times 10 to
the 8th meters per second.
So most of you have
seen this before
and are well aware of it.
This also has some of
the conversions on here.
Speed of light is
quite fast and often
people have the expression
how fast [INAUDIBLE].
You're working at
the speed of light.
And that's a pretty
valid thing to indicate
that you're doing things
very, very quickly,
because that is fast.
And in fact, if we had the
earth here and the moon here,
light would go like that.
And it should take about
1.2 seconds to do that.
So speed of light, very quickly.
All right, so what's also
important in thinking
about this is that
the speed of light
is a constant, which
is going to mean
that these terms are related.
So first before we move on,
let's do a clicker question.
And you can all test
out that your clickers
are working again.
How are we doing?
OK, let's do 10 more seconds.
OK, 92%, that's awesome.
All right, does
someone want to explain
how they could eliminate one
and two versus three and four
and get this one right?
AUDIENCE: Sure, well it
looks like this problem
is asking us to look at
two different things,
the wavelength of these
waves and the frequency.
And you can look at the
distance between the two peaks
in both of the waves to see how
short or long the wavelength
is.
Wavelength A has a
much shorter distance
between peaks than B does.
And then you're also looking
for nu, the frequency.
So within a period of time you
can fit more waves of A than B,
so it has a higher frequency.
[APPLAUSE]
CATHERINE DRENNAN: So,
this prize here is LEGO.
And LEGO has decided
to make girl chemists.
So this is a little
LEGO girl chemist
that comes with pretty
colored erlenmeyer flasks.
So that's very special.
OK, yeah, so the
trick of that question
you just looked which was
the longer wavelength.
And then you could rule
out that from the picture
and also realize that
there's connections because
of the constant speed of
light between the frequency
and the wavelength.
So when you're talking
about wavelengths of light,
c is always equal to a
product of the wavelength
times the frequency.
So they're not
independent of each other.
And if you know one,
you will know the other.
So this is something you'll
come in very handy as you're
doing these problems.
OK, so let's talk about
light for a minute
and look at these
different colors of light.
So we go from red
at long wavelengths
to violet at the
shorter wavelengths.
And so here the
wavelength is decreasing.
And then if we think about
the corresponding frequencies,
up here then if we
have long wavelengths,
what are we going to have
in terms of the frequency?
Yeah, so we will have lower or
shorter frequencies going up
to higher frequencies up here.
So again, we have
this relationship
because the speed of light
equals the wavelength
times the frequency.
So you are not
responsible for memorizing
all of the wavelengths,
but you should
have a sense of the
order of the wavelengths
and certainly the relationship
between wavelength
and frequency.
And there's going to
be a number of problems
later when we're talking
about colors of light that
are admitted from things or
colors that are absorbed where
it's really convenient to
have the order of wavelengths
memorized.
So I thought I would
just help you out
with this by this
nice little song
from They Must Be Giants in Here
Comes Science's album, which
should help you always remember
the order of the wavelengths.
So let's just see
if this will play.
MUSIC: R is for red.
O is for orange.
Y is for yellow.
And G is for green.
B is for blue.
I for indigo.
And V is for violet.
And that spells Roy G. Biv.
Roy G. Biv is a colorful man.
And he proudly stands
at the rainbow's end.
Roy G. Biv is a colorful
man and his name spells out
the whole color spectrum.
Roy G. Biv is a--
CATHERINE DRENNAN: OK, so I
think you get the idea there.
And it sticks in your head.
And you may remember this
for the rest of your life,
even if you don't want to.
That's a very catchy song.
In fact, my
six-year-old daughter
learned it when she
was about three,
and then we get very
upset if anybody
drew the colors that were
not in the appropriate order
of the rainbow.
And she would come around
and correct their work.
Anyway, it made her into a
little bit of a holy terror
but we're working on that.
So in addition to the visible
light, which is actually
a very small part of
the range of waves
and so we have
visual light in here,
we can also think
about other waves that
go from then long wavelength
here and low frequency
to short wavelength
and high frequency.
So we have radio waves on
the long wavelength end
and we have then microwaves.
Microwaves are I think college
students' best friends.
And as I am teaching this
course, since many of you
are freshmen, I feel the
need to compare my many years
of experience at MIT with you.
Point number one, just
use the popcorn button
on the microwave.
Don't think about how long
is it-- just use the popcorn
button on the microwave.
I used to live in
Simmons for a while.
3:00 AM fire drills or
fire things because someone
did not push the popcorn
button on the microwave
while making popcorn.
Anyway, life lesson
number one, microwaves.
So molecules behave differently
in these different kinds
of waves.
So you can rotate infrared,
you're looking at vibrations.
Of course here, visible light.
We also have UV light.
So when you go to the
beach on the green line
this weekend to do
prom set number two
and look at the
waves, you'll want
to wear your sunscreen because
UV is, in fact, dangerous.
So wear sunscreen,
advice number two.
Then we have x-rays.
Hopefully most of you do
not know one of the uses
to detect broken bones.
And as you'll hear
later on, x-rays
can also be used to solve
structures of molecules
at atomic resolution.
And then on the very
short wavelength,
then, we have
gamma rays as well.
So again, you're not
responsible for memorizing
all of these numbers,
but you should
have a sense of the order of
these different types of rays
of the electromagnetic
spectrum, what's at short,
what's at long wavelengths.
All right, so waves
have other properties.
And one of the most
important properties of waves
is that they can superimpose.
So if you have two
waves, one drawn up here,
and one drawn down here, that
are in phase with each other,
which means that their
troughs are at the same place,
their peaks are
at the same place,
you can get constructive
interference
and that would look like this.
So you have these waves
come together in phase
and you get this much larger
constructive interference.
This property can
be very important
as we'll talk a little
bit more about later.
You can also have what's called
destructive interference,
so when you have
out of phase waves.
And the clicker, you can tell
me what that should look like.
OK, ten seconds.
Now looks like it's back
to being a darker color
box in the corner.
Just likes to vary
it up on its own.
OK, that's one second.
Woo!
All right, 98%.
We don't have to
explain that one.
That one was pretty clear.
So here you had they were
completely out of phase.
So you had total
destructive interference.
So that just looks
like a straight line.
So the combination of
constructive and destructive
interference
actually has a number
of practical applications.
So people who are
very interested
in constructive and
destructive interference
include people who are designing
symphony halls or classrooms.
Actually, this is one
of the better classrooms
in terms of the acoustics.
And the Boston Symphony
is actually, supposedly,
the third best in the world
in terms of acoustics.
MIT students get nice
discounts, go check it out.
Another practical
application was
in designing noise
canceling headphones.
I brought a pair if some of
you have never tried them
and you want to come down after
class, you can give them a try
and see what you think.
These headphones,
the Bose headphones,
were developed by a
former MIT professor.
He passed away last year.
He taught at MIT, taught
acoustics, for many years.
And he was riding on an airplane
once and it was just so loud.
And he was thinking, wow, I
was wondering if there a way
I can design some good
headphones to cancel
this noise.
And he did and many billions
and billions and billions
of dollars later.
So as you are an
MIT student, you
get a discount on
these headphones.
So if you're going to buy them,
buy them while you're here.
Also, when he died, the majority
share of his stock went to MIT.
So you will buy
them, get a discount,
and you'll also be
giving MIT money
by buying these because we
get a lot of money for this.
So I feel like this brings
up a really important point
that I just want to stress.
And I'll probably
mention a couple
of times that the material
that you learn in your classes
here at MIT, and
in this class, you
will learn a lot of
really useful things.
Some of that will lead to money.
And as you make
lots of money, you
should remember where you
learned that and know that I
take both cash and checks.
Another practical application
is actually in my own research.
So we have a series
that I'm going
to be using I mentioned to
bring some different faces in.
The first video I'm going
to show you in this series
is actually me.
So it's not a different face.
But when I asked other
people to make videos
about how they
were using chemical
principles in their
research, they said OK,
but you're going to do
one, too, right, Cathy?
So I was like, yes, I
guess I'm going to do one.
And that just happens
to be the first one
that I'm going to show.
So another practical use of
constructive and destructive
interference has
to do with x-rays.
And you can use constructive
and destructive interference
to determine the structures
of very tiny things, protein
molecules or nucleic
acids in your body.
So I'm going to try
to run this movie now.
We'll see, this as a demo.
Good to try it out with me and
see how this is going to work.
CATHERINE DRENNAN (VIDEO):
My name is Cathy Drennan
and I'm a Professor of
Chemistry and Biology at MIT.
And I'm also a Professor and
Investigator with the Howard
Hughes Medical Institute.
And my lab uses the principles
of diffraction in our research.
A wave shoots through
some kind of grating.
You can have light, say light
waves, shooting through.
And when the light waves
hit the metal lattice,
they'll be diffracted.
And some of those waves will
be in phase with each other
and will constructively
interfere
and you get a bright spot
in a diffraction pattern.
Other waves will be out of
phase and they'll destructively
interfere and you'll see nothing
as a result of those waves.
From this pattern of
spots and no spots,
you can understand something
about the structure
of the grating that
it went through.
So if I had two
different gratings,
the diffraction patterns
would be different for these.
And so from looking at
the diffraction pattern,
you can figure out how the
metal or whatever was arranged
that generated that pattern.
This property works
whether it's a metal
grating or a lattice that's
made up of protein molecules.
Because the protein
molecules are small
and crystals are
small, we use x-rays
and short wavelength,
high energy.
But because everything
is really tiny,
we need really bright
x-rays to do this.
And I don't mean high energy
bright, I mean intensity.
So we need more
photons per second.
So we have to go
to a place called
the synchrotron, a
research facility, that
has really intense x-rays.
And then we shoot those
x-rays through our crystal,
collect this
diffraction pattern,
and then figure out what the
shapes of these molecules are.
The structure can
tell you so much.
I mean, there can be
big questions of field
about how something works.
And all of a sudden, you see
what the molecule looks like
and you're like, ha, of course.
Sometimes there's a
problem with the DNA
that then gets translated
into a defect in the protein.
But people often
don't know why does
it matter, why does it
matter that the protein is
this or that?
But we can look at
it and figure it out.
So we can compare what the
protein structure looks
like for a healthy individual
with the protein structure
from someone who has a mutation.
All of a sudden
you might see, wow,
the vitamin that this protein
needs can't bind anymore.
So we can have a
sense of what's wrong.
And then sometimes
you can figure out
how to treat it once you
know what the problem is.
Sometimes there'll
be a protein molecule
that everyone
knows is important.
Everyone wants to know
what it looks like.
But you might be
the one who does it.
You might be the one to
figure out what it looks like.
And you'll be the first one.
You'll see these patterns,
these diffraction patterns,
and you'll build this model
and all of a sudden you'll
be like wow, that's not
what people expected.
And it'll just be this
incredible discovery.
So you're an explorer
of the molecular world
when you're a crystallographer.
[APPLAUSE]
CATHERINE DRENNAN: Thank you!
OK, so that's the
first in the series.
We're going to have
another one this week,
as well, because we
have a lot of history.
So we've got to counter it
with a lot of current research.
And so you'll be learning about
quantum dots also this week.
OK, so those are some of
the characteristics of waves
that are really important and
we talked about light as a wave.
Now we're going to talk
about light as a particle.
Light as a wave is a
little bit easier to grasp.
Light as a particle is a
little bit more confusing.
And it took a while for
people to really appreciate
that light had particle-like
properties, i.e.
It was quantized.
And this really came out of
the photoelectric effect.
So what were people doing?
And this is around the time of
the discovery of the electron
and the nucleus.
And what scientists
were having fun doing
were taking beams of UV light
and hitting metal surfaces,
and seeing if they
could inject electrons,
which have been discovered.
It's like, let's get
some electrons out
of those metal surfaces.
We know they're there, let's see
them come off and characterize
their properties.
So they found that if they had
some UV light and the frequency
of that UV light was below
something, below a threshold
that they referred to as
the threshold frequency.
So we have a new zero here.
If the frequency was lower
than this magic number
for frequency,
nothing would happen.
But if they increased
the frequency,
if it was greater than or equal
to this threshold frequency,
then all of a sudden
they would see something.
They would see an
electron being ejected.
And the electron would come
off with a certain amount
of kinetic energy,
K.E. And kinetic energy
is equal to a half times mass
times the velocity squared.
All right, so they decided
let's characterize this.
Lets very some parameters
and see what happens.
So they looked at constant
intensity of this light
and they changed the frequency.
And then they looked at
the number of electrons
that were coming off.
And so below this
threshold frequency,
no electrons came off.
I just told you about that.
Then when they were
at the threshold,
they saw electrons
coming off and then they
increased the
frequency even more,
but they weren't getting
any more electrons.
Hm.
OK, this was interesting.
So they thought what
else can we measure here.
And they knew how to
measure the kinetic energy.
So it's like, let's
start measuring
the kinetic energy of these
electrons that are coming off.
So they plotted kinetic energy
of the ejected electrons
as a function of the frequency
of the incoming light.
And again, below the
threshold, they saw nothing.
But above the threshold, they
saw the kinetic energy increase
proportionally to the increase
in the frequency of the light.
And this didn't
really make any sense
from what they knew at the time.
They didn't have a way to relate
kinetic energy and frequency.
So they really weren't
sure what this was about,
but they were having
fun doing experiments.
It's like, let's keep going,
let's vary more properties.
So then they decided
to look at how
the kinetic energy
of the electron
was affected by changing
the intensity of the light.
And they thought that if
you increase the intensity,
you'd have more
energy in your system,
you should have
more kinetic energy.
But that did not
seem to be the case.
They increased the
intensity, the kinetic energy
stayed the same.
They were having trouble
wrapping their head around it.
But they said, all right, well
let's collect some more data.
So now they decided to look at
the number of ejected electrons
as a function of the intensity.
And they really
didn't think there
should be much difference.
Increase the intensity,
number of electrons
should be the same.
But experiments
showed otherwise.
So when they increased
the intensity,
more electrons came off.
And this is where they
were in the field.
It almost seemed
like everything they
did was opposite of
what they expected.
It's a pretty exciting
time actually in science
when you're getting results
that are unexpected.
And some of this data
sat around for a while.
And then Einstein decided
to take a little look at it
and see what he
thought of this data.
And people were studying
all sorts of things.
They're taking different metals,
you have a different metal,
you have a different
threshold frequency.
And so people were
characterizing different metals
and figuring out the
threshold frequency
for all the different metals.
And then plotting the
kinetic energy of the ejected
electrons as a function
of the frequency.
And you look at this,
you realize huh,
there's different
threshold frequencies
for the different
metals, but they all
seem to have these
straight lines that all
seem to have the same slope.
And sometimes when you
look at the discoveries
of really amazing
people like Einstein,
you're thinking
well, basically what
he did was solve the
equation for a straight line.
You realize hey, maybe I can
contribute to science, as well.
So we had a whole lot
of straight lines here.
And when you have that, you
can solve for the slope.
So that's what he did,
he solved for the slope.
And he got this
number, 6.626 times 10
to the -34th Joule seconds.
And he saw that number
and he's like, I've
heard that number before.
Planck came up with that number
when he was studying black body
radiation.
So totally different
phenomenon, but yet
the number comes
up again, Planck's
constant, also known as h.
Now that seemed like a
really strange coincidence.
So there must be
something to this number.
So if you look at
this plot, we can also
think about what the y-axis is.
So the y-intercept is minus
Planck's constant times
that threshold frequency.
And when you have
all of this, you
can now write the equation
for the straight line in terms
of all of these variables.
And so y-axis here
is kinetic energy.
So we'll solve that equation
now in terms of kinetic energy.
So kinetic energy is
going to be equal.
We have our x-axis here.
The x-axis is frequency.
And again, now, the
slope of the line we know
is Planck's constant,
so that's h.
And the y-intercept,
or b, was -h
times the threshold frequency.
And this is a very
important equation.
So just to define
those terms again,
we have the frequency
here, Planck's constant.
Planck's constant times
the frequency is an energy.
It is the energy of
the incident light
or the incoming light, e sub i.
And on this side over here, we
have that threshold frequency
again.
We also have Planck's constant.
So Planck's constant times
a threshold frequency
is another energy term,
which is called the threshold
energy, or more commonly
a work function.
So the kinetic energy
equals the incident energy,
the energy of the incoming
light minus the work function,
which has to do with the
threshold frequency which
depends on the
metal in question.
So this was a really
important equation.
And Einstein realized
that the energy of light
is proportional to its
frequency and it's proportional
by Planck's constant.
And this really
changed how people
had been thinking about energy.
And all of a sudden, a lot of
those observations made sense.
Now, Einstein of course had
many important discoveries
in his career.
But this one was the one
that he personally felt
was the most revolutionary.
I don't know.
People are always
their worst critic,
but even he realized
that this was important.
And in terms of units, because
units are always important.
Notice usually you'll see
energy in joules or kilojoules.
And Planck's constant has
the units of joule seconds.
And frequency is per
seconds or hertz.
So in this equation,
your units work out.
So from this idea then
we have this notion
that light is made up of
these energy packets which
people call photons where
the energy of that photon
depends on its frequency.
So we can go back to
the photoelectric effect
now and start thinking
about those observations
and try to rationalize now
what we had been seeing.
So here's this new model
for the photoelectric effect
where we can think about the
energy of that incoming photon,
or that incident photon.
If it's greater than
the work function,
then you'll eject an
electron from the metal.
And any left over energy
is the kinetic energy
of that ejected electron.
So we can think about that here.
That here we have
the energy coming in
of the incident photon.
We have to get over
that threshold frequency
or overcome that work function.
So you have this minus
this, and the leftover
is the kinetic energy.
So we can also
write it this way,
that the kinetic energy
equals the incident
energy minus the work function.
So if you just have
enough energy to do this,
you have very small
kinetic energy.
But if you have a
lot of extra energy
once you overcome
the work function,
you'll have more kinetic energy.
We can also write the
equation this way,
that the incident energy
equals the kinetic energy
plus the work function.
OK, so let's just try a
clicker question on this.
And we're going to go back
and look at those graphs
and think about what they mean.
All right, let's do
ten more seconds.
Yeah, OK.
So here the trick was to think
about what the work function is
and how much energy was
coming in of the photon.
But here the energy is lower
than the threshold needed,
so you're not going to
get any electrons ejected.
Let's try one more.
Let's see if you
can get up to 90%.
So now we've changed
the energies.
Or the energy, but not
the threshold energy.
OK, ten more seconds.
Yeah, 98%.
Yeah, so now we're over
the threshold energy.
So we need to subtract
the threshold energy
and the remaining is
the kinetic energy.
OK, so these are the kinds
of questions we have on this.
And now let's go back and
think about these plots again.
So we don't have these a
second time in your notes,
but you have them one time.
And let's just think about
how this makes sense now
with the new equations that
Einstein helped us achieve.
So in the top here, we have
the surprising observation
that when you increase
the frequency of the light
that the kinetic
energy increase.
Well, now this makes
sense, because if you're
increasing the
frequency of the light,
you're increasing the incident
energy of the photons coming
in.
And so if you're
increasing this frequency,
so you're increasing
the incident energy.
And once you're above
the threshold energy,
you'll have more extra
kinetic energy coming off
as the frequency, or the energy
of the incident light comes up.
So that makes sense.
All right, what about intensity?
We haven't really talked
so much about intensity.
So let's consider
intensity for a minute
and think about the number
of electrons, as well.
So both of these
are about intensity.
So let's think about
the number of electrons
ejected from a metal surface.
We're going to come back
to those plots in a minute,
sorry to make you go back
and forth in your notes.
And that's going
to be proportional
to the number of photons.
So the more photons
you have coming in,
the more electrons are
going to have coming out.
That is, if the photons
have the appropriate amount,
if they're over the threshold
frequency over the threshold
energy, then you're going
to have an electron ejected
from the metal surface.
So for each photon that
has greater incident
energy than the
threshold, you'll
have an electron being ejected.
So what is intensity?
Well, the intensity is really
the photons per second.
So it's proportional to
the number of photons being
absorbed by the
metal, and therefore,
the number of electrons
coming out of the metal.
So intensity's units
are often in watts.
You also can do a conversion
in joules per second.
So the higher the
intensity, the more
photons with the
appropriate amount of energy
to overcome that work function,
the more electrons coming off.
So now we can go back and
think about these plots again.
So here the relationship between
intensity and kinetic energy
was flat.
And that was unexpected.
But the kinetic energy
doesn't change here
since the intensity means
more photons per second, not
more energy per photon.
So you're just increasing
the number of photons.
If none of the photons have
the appropriate energy,
you're not going to have
any electrons coming off.
But if you have more
photons per second,
and they have the
appropriate amount of energy,
then you are going to see
these electrons coming off.
So the number of
electrons admitted
does change since high
intensity means more photons.
More photons, more electrons.
So these things that
Einstein helped us with,
these equations, now
made sense of the data
that was being observed.
So the photoelectric
effect was really
important in helping
derive these relationships
between energy and frequency.
And so in particular, the
really important points
here is that light is
made up of these photons,
these discrete energy packages.
And each one of those photons
has to have enough energy in it
to overcome the threshold
to emit an electron.
So energy is proportional
to frequency,
which was a really new and
exciting idea at the time.
E equals Planck's
constant times frequency.
And the intensity of light
has to do with the number
of photons hitting per second.
And if you keep
these things in mind,
you'll do really well finishing
up a number of the problems
on the photoelectric effect,
which are in problem set one.
OK, see you on Wednesday.
We're going to do a demo of
the photoelectric effect.
