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Where were we,
last time?

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Last time, we said we were
setting aside the problem of the

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structure of the atom.
We were setting it aside

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because we were stuck,
and what we had to do was to

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look at another area of
discussion.

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And that is this wave-particle
duality of light and matter,

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because it is that discussion
that is going to give us the

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clues about how to proceed.
We are putting aside the

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discussion of the structure of
the atom all the way until next

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Wednesday, because next Monday,
I was reminded,

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is a student holiday.
[APPLAUSE]

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And so we started.
We talked about the wave-like

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properties of light.
We said that the property of

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superposition,
the fact that you can put waves

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at the same point in space and
their amplitudes add.

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Since waves have both positive
and negative amplitude,

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that means that you have
constructive and destructive

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interference.
And it is those interference

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phenomena, then,
that are evidence for wave-like

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property.
And we did the two-slit

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experiment to try to give you an
example of interference

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phenomena.
We were trying to understand

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those interference phenomena,
and did so in terms of this

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diagram here.
The interference phenomena that

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we saw was an array,
actually a row of bright spots,

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dark spots, bright spots,
dark spots.

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And we drew these semicircles
here around each one of the

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slits.
They represent a little bit of

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the wave that emanated through
those slits.

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Because those slits are small,
then, those waves emanated

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equally in all directions.
That is why these semicircles

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represent the wave maxima.
And what we discovered is that

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if we looked along this line
here, this line which led to

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this bright spot,
that all of the waves along

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this line were constructively
interfering.

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That is, we had the maximum of
the two waves at the same point

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in space, or the minimum of the
two waves at the same point in

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space.
And we noticed that everywhere

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along this line,
where we had that constructive

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interference,
the difference in the distance

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of the waves traveled was one
lambda.

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We noticed, here,
that everywhere along this line

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that led to a very bright spot,
we had constructive

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interference.
And the difference in distance

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traveled by those two waves was
two lambda.

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And, likewise,
up here, along this line,

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the difference in the distance
traveled was zero lambda.

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And from just that,
in a sense, qualitative

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observation, we drew a
conclusion.

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And that conclusion was in
order to get maximum

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constructive interference,
a condition that had obtain,

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is that the difference in the
distance traveled by the two

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waves has to be an integral
multiple of the wavelength.

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N could be 0,
1, 2, 3, etc.

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And so, the very bright spot
here that always bisects the two

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slits, since N is 0,
we call that the zero-order

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interference feature,
or the zero-order fraction

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feature.
The bright spot that is either

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to the left or to the right or
up or down of that center bright

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spot is the first-order
diffraction feature or the

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first-order interference
feature.

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And then the second bright spot
up or down from the center is a

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second-order diffraction
feature.

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And so on and so on.
And in recitation section,

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what you also should have done,
is you should have reasoned

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through what the condition was
for destructive interference.

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That is in between these bright
spots, you have dark spots as a

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result of destructive
interference.

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And that results because,
say, right here you get a dark

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spot --
Right here at that point you

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would see the maximum of one
wave at the same point in space

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as the minimum of the other,
and so they exactly cancel.

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And so by just analyzing what
waves were destructively

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interfering, you should have
come up with a general

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expression for destructive
interference,

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of N plus one-half,
that quanity,

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times lambda.
That is your general condition

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for destructive interference,
the difference in the distance

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traveled by the two waves.
This kind of diagram here we

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are also going to see on Friday,
because this interference

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phenomenon is the property
associated with waves.

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And what we are going to do is
see this diagram again when we

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scatter electrons for particles.
We are going to see that

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particles, also,
will destructively and

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constructively interfere.
They also have wave-like

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properties.
That is what we will do on

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Friday.
We have established,

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now, the wave-like properties
of radiation,

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so I would like to move on and
talk about the evidence for the

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particle-like nature of
radiation.

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The evidence for the
particle-like nature of

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radiation comes from an effect
called the photoelectric effect.

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Shortly after Thompson
discovered the electron,

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scientists were noticing that
if you took a metal and shined

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radiation on that metal,
that indeed electrons were

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emitted.
Electrons came off.

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These were called
photoelectrons.

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However, the radiation that you
shined on the metal had to have

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a frequency nu that was greater
than or equal to some threshold

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frequency, nu nought.
That is, if you took radiation

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of some frequency here,
nu, that was less than this

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threshold frequency,
well, you did not get any

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electrons off.
Well, another way to kind of

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understand that data or that
effect is to just plot the

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number of the electrons that
come off as a function of the

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frequency of the radiation.
And so at low frequency,

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there are no electrons,
but all of a sudden you get to

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nu nought, and then electrons
start coming off.

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And no matter how high you
increase the frequency here,

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the number of electrons that
come off remains the same,

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remains constant.
And it turned out that for the

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metals that were looked at,
at that time,

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the threshold frequency,
here, was in the UV range of

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the electromagnetic spectrum.
Well, in addition to just

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measuring the number of
electrons and generally

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observing this effect,
scientists did not understand

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what was going on.
So they just started measuring

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everything they could think
about measuring.

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And one quantity that they
measured was the kinetic energy

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of these electrons that were
being emitted.

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And so you take kinetic energy
here, KE, as a function of the

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frequency.
They found that at low

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frequency, again,
there is no kinetic energy,

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because there are no electrons.
And then at some frequency,

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all of a sudden electrons
started coming off.

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And the kinetic energy of those
electrons seemed to increase

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with the frequency once past
that threshold frequency,

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nu nought.
Well, this was really another

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one of these conundrums,
here, at that time,

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because classical physics,
classical electromagnetism,

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classical physics had no way of
explaining these data.

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And, in fact,
what classical physics

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predicted is that the kinetic
energy of these electrons,

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that that kinetic energy should
have nothing to do with the

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frequency of the light.
That is, the kinetic energy was

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constant.
As you increased the frequency

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of the light,
classical physics would tell

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you that the kinetic energy
should not be affected by the

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frequency of the light.
There was nothing in the

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classical way of thinking,
classical electromagnetism that

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connected the frequency of the
light to the kind of energy,

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to the kinetic energy.
There was no way for blue light

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to make the electrons have a
larger kinetic energy,

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and for blue light to have an
effect on the kinetic energy,

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00:10:57 --> 00:11:04
and red light to not have an
effect on the kinetic energy.

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In addition,
what classical physics

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predicted is that the kinetic
energy of the electrons should

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be dependent on the intensity of
the light.

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That is, the more and more
intense the radiation on the

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metal, the more and more kinetic
energy those electrons should

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have.
Because, after all,

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if you increase the intensity
of the light going into the

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metal, you are putting more and
more energy into it.

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That should be reflected in
just how energetic those

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electrons were picked out.
The more energy in,

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the electrons ought to come out
with larger and larger kinetic

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energy.
Of course, the observation was

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that the kinetic energy of the
electrons had nothing to do with

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the intensity of light.
The kinetic energy of the

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electrons did not increase as
you made the light brighter and

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brighter.
As you put more and more energy

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in, the kinetic energy remained
the same.

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It didn't have an effect.
This was a real conundrum here.

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The known classical physics was
making predictions really just

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contrary to what was being
observed.

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These data, here,
of the kinetic energy versus

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the frequency,
were around for a few years

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before Einstein took a look at
them in 1905,

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a hundred years ago.
And he looked at these data for

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many different metals.
Here is some data for metal A,

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for example,
and here is some data for metal

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B.
And, in both cases,

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it certainly looked like the
kinetic energy was linearly

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dependent on the frequency of
the radiation.

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But what was different for the
two different metals was the

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threshold frequency here,
nu nought.

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What Einstein did was,
he went and fitted a straight

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line to these data,
y equals mx plus b.

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And when he did that,

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and he went to calculate the
slope here, m,

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of these lines,
he thought "very interesting."

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Because the slope of those
lines was 6.626x10^-34 joule

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seconds.
The slope of those lines was

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something called Planck's
constant, h.

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You say so what?
Well, the reason he was so

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interested in this is because
just a few years earlier,

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there was a scientist by the
name of Max Planck who was

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interested in understanding what
was called the black-body

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radiation data.
What is a black-body?

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Well, let's just,
for simplicity purposes,

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think of the black-body as the
burner on an electric stove.

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What you know is that if you
turn up the voltage on that

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burner, the burner gets hot.
It increased in temperature.

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And you increase the
temperature, and sooner or

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later, that burner is glowing
bright red.

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And you increase the
temperature some more,

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and the burner is glowing a
brighter red.

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And you increase it some more,
and it is glowing orange.

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And you increase it some more,
which you shouldn't do,

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and it's glowing yellow.
And then if you could increase

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it some more,
it's glowing white.

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What is happening,
as you increase the

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temperature, is that the
radiation from that black-body,

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this is the black-body
radiation, is increasing in

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intensity.
But, more importantly,

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the frequency is getting larger
and larger.

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Dark red, bright red,
orange, yellow,

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white, those are all
frequencies.

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The frequency is shifting to
higher and higher values.

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00:16:04 --> 00:16:10
And what was actually done at
that time is that the intensity

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of that black-body radiation,
oh, and this material is not in

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your notes, because you are not
responsible for it.

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00:16:21 --> 00:16:27
I am just trying to make this
surprise that Einstein noticed

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about the slope.
I am just trying to put it in

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some context,
why he was so surprised and

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amazed at it.
This black-body intensity here,

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people had dispersed that
radiation and looked at the

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frequencies that were coming
off.

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00:16:46 --> 00:16:49
This is intensity versus
frequency.

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00:16:49 --> 00:16:54
Here is a general shape of that
intensity versus frequency.

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00:16:54 --> 00:17:00
That was observed for some
temperature T one.

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00:17:00 --> 00:17:05
That was a low temperature.
And then, when the temperature

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00:17:05 --> 00:17:10
was increased and the intensity
versus frequency was observed,

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00:17:10 --> 00:17:14
well, the frequencies generally
got higher.

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00:17:14 --> 00:17:18
This is higher temperature.
Intensity goes up.

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00:17:18 --> 00:17:22
And you increase the
temperature some more,

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00:17:22 --> 00:17:25
and you get even higher
frequency.

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00:17:25 --> 00:17:30
T three is the highest
temperature.

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00:17:30 --> 00:17:36
And that is what the data were.
What Planck was trying to do

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was to understand the origin of
that black-body radiation.

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What he said was that in these
black-bodies,

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00:17:48 --> 00:17:52
in these materials,
what there must be are

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oscillators that are giving off
this radiation.

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00:17:59 --> 00:18:04
But he had another little kick
to these oscillators.

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00:18:04 --> 00:18:10
These oscillators were giving
off radiation or energy in

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00:18:10 --> 00:18:13
chunks, in quanta,
in particles.

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And using that idea,
plus some statistical

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00:18:18 --> 00:18:23
mechanics, he was able to
calculate the shapes of these

244
00:18:23 --> 00:18:26
curves.
That is, he indeed got,

245
00:18:26 --> 00:18:32
for the lowest temperature
here, a curve that looked like

246
00:18:32 --> 00:18:36
this.
And for T two,

247
00:18:36 --> 00:18:39
he got a curve that looked like
this.

248
00:18:39 --> 00:18:44
And for T three,
he got a curve that looked like

249
00:18:44 --> 00:18:47
this.
He got the shape right,

250
00:18:47 --> 00:18:50
but he wanted to get the
intensity right,

251
00:18:50 --> 00:18:53
too.
What he realized he had to do

252
00:18:53 --> 00:18:57
was he essentially needed to
have a scaling factor,

253
00:18:57 --> 00:19:04
actually, in front of his
frequencies of his oscillators.

254
00:19:04 --> 00:19:07
He wanted a constant.
And so he said,

255
00:19:07 --> 00:19:13
what constant do I have to have
in order to make all of these

256
00:19:13 --> 00:19:18
data fit the observation?
That constant is Planck's

257
00:19:18 --> 00:19:22
constant, his own 6.626x10^-34
joule seconds.

258
00:19:22 --> 00:19:26
There it is.
That is Planck's constant.

259
00:19:26 --> 00:19:31
That is it.
There is nothing deeper here.

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00:19:31 --> 00:19:36
It is a natural constant.
It comes from our observations

261
00:19:36 --> 00:19:39
of the world,
of nature.

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00:19:39 --> 00:19:42
That is it.
It is a fitting constant.

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00:19:42 --> 00:19:47
And so that is why Einstein was
so amazed, here,

264
00:19:47 --> 00:19:54
when he realized this number is
the same as what comes out of

265
00:19:54 --> 00:19:57
here.
There must be something very

266
00:19:57 --> 00:20:04
fundamental about this h,
this Planck's constant.

267
00:20:04 --> 00:20:09
That is the story.
Isn't that amazing?

268
00:20:09 --> 00:20:16
What Einstein then proceeded to
do, of course,

269
00:20:16 --> 00:20:24
is to write down the equation
of the straight line that he

270
00:20:24 --> 00:20:33
just put through these data.
And so that equation is the

271
00:20:33 --> 00:20:38
kinetic energy equal to nu,
which is our x,

272
00:20:38 --> 00:20:44
h, which is the slope.
And then what he found was that

273
00:20:44 --> 00:20:50
the intercept here,
of course, is minus h times nu

274
00:20:50 --> 00:20:56
nought.
This is plus minus h times nu

275
00:20:56 --> 00:21:02
nought.
And that is the equation of a

276
00:21:02 --> 00:21:05
straight line.
Of course, he realized,

277
00:21:05 --> 00:21:11
if this is energy on this side,
boy, there better be energy on

278
00:21:11 --> 00:21:14
this side.
And so this h times nu

279
00:21:14 --> 00:21:18
better be an energy.
And since this nu was the

280
00:21:18 --> 00:21:22
frequency of the incident
radiation, therefore,

281
00:21:22 --> 00:21:27
h times nu better be the energy
of the incident radiation,

282
00:21:27 --> 00:21:32
E sub i.
That is where this expression,

283
00:21:32 --> 00:21:36
energy equals h times nu
comes from.

284
00:21:36 --> 00:21:40
Nothing more.
That is where it comes from,

285
00:21:40 --> 00:21:45
the photoelectric effect.
This was the first time that

286
00:21:45 --> 00:21:50
there was any relationship
between the frequency of the

287
00:21:50 --> 00:21:53
radiation and the energy of the
radiation.

288
00:21:53 --> 00:21:58
In classical electromagnetism,
there is no relationship

289
00:21:58 --> 00:22:03
between the frequency and the
energy.

290
00:22:03 --> 00:22:08
This was the first time in
which that relationship was

291
00:22:08 --> 00:22:12
observed.
And what this is saying is the

292
00:22:12 --> 00:22:16
following.
This is saying that you can

293
00:22:16 --> 00:22:23
have any frequency of radiation
you want, but the corresponding

294
00:22:23 --> 00:22:30
energy comes in these chunks of
h times nu.

295
00:22:30 --> 00:22:35
h is a quantization constant.
Radiation, nu,

296
00:22:35 --> 00:22:41
is continuous,
but the energy that corresponds

297
00:22:41 --> 00:22:48
to any given frequency of
radiation is h times nu.

298
00:22:48 --> 00:22:56
This E equals h times nu,
here, is thought of as a

299
00:22:56 --> 00:23:02
quantum of energy.
A particle of energy.

300
00:23:02 --> 00:23:08
A chunk of energy.
Later on, it became the photon,

301
00:23:08 --> 00:23:15
the energy of a photon.
If this h times nu here

302
00:23:15 --> 00:23:20
was an energy,
well, this h times nu nought

303
00:23:20 --> 00:23:25
also better be an  energy.

304
00:23:25 --> 00:23:32
It is the threshold energy.
Let's draw an energy level

305
00:23:32 --> 00:23:36
diagram to try to understand
that.

306
00:23:36 --> 00:23:40
I am going to plot an energy
here.

307
00:23:40 --> 00:23:44
Let's draw an energy level for
an electron.

308
00:23:44 --> 00:23:49
This is an electron,
here, bound to the metal.

309
00:23:49 --> 00:23:56
And we know that it takes some
energy to rip this electron off

310
00:23:56 --> 00:24:01
of the metal.
Up here, at higher energy,

311
00:24:01 --> 00:24:03
is going to be our free
electron.

312
00:24:03 --> 00:24:06
I will just call it
electron-free,

313
00:24:06 --> 00:24:11
not bound to the metal anymore.
And the energy that is required

314
00:24:11 --> 00:24:15
to pull the electron off,
from the bound state to its

315
00:24:15 --> 00:24:20
free state, is this threshold
energy, h times nu nought.

316
00:24:20 --> 00:24:23
This threshold energy is like

317
00:24:23 --> 00:24:27
an ionization potential.
You know what the ionization

318
00:24:27 --> 00:24:32
potential is.
Just the energy required to

319
00:24:32 --> 00:24:35
pull an electron off an atom or
a molecule.

320
00:24:35 --> 00:24:40
However, when we are pulling an
electron off a chunk of a metal,

321
00:24:40 --> 00:24:43
we actually have another name
for it.

322
00:24:43 --> 00:24:47
It is called the work function.
That is just historical,

323
00:24:47 --> 00:24:51
but it is the same thing as an
ionization potential.

324
00:24:51 --> 00:24:54
And we often give it the symbol
phi.

325
00:24:54 --> 00:24:58
That threshold energy,
ionization energy for a metal,

326
00:24:58 --> 00:25:01
is the work function,
here, h times nu,

327
00:25:01 --> 00:25:06
phi.
The important point here is

328
00:25:06 --> 00:25:11
this.
In order to get an electron off

329
00:25:11 --> 00:25:17
of the metal,
what you have to have is

330
00:25:17 --> 00:25:24
energy, E sub i.
That energy E sub i has to be

331
00:25:24 --> 00:25:32
equal to at least the threshold
energy, h times nu nought.

332
00:25:32 --> 00:25:37
If you come in with energy of

333
00:25:37 --> 00:25:41
this radiation,
of this wavelength and that

334
00:25:41 --> 00:25:45
frequency, you pulled the
electron off,

335
00:25:45 --> 00:25:50
and then the electron is off
the metal and it just kind of

336
00:25:50 --> 00:25:53
stays there.
It doesn't move away.

337
00:25:53 --> 00:25:57
But you can also come in with
energy here, E sub i,

338
00:25:57 --> 00:26:03
that is greater than this work
function, than the threshold

339
00:26:03 --> 00:26:07
energy.
And you can pull the electron

340
00:26:07 --> 00:26:09
off.
But then, the electron is

341
00:26:09 --> 00:26:14
actually going to move away from
the metal, and the energy with

342
00:26:14 --> 00:26:18
which it moves away from the
metal, its kinetic energy,

343
00:26:18 --> 00:26:23
is just the incident energy
minus this threshold energy.

344
00:26:23 --> 00:26:27
It is the excess energy here.
And I am going to write it as

345
00:26:27 --> 00:26:33
the kinetic energy.
From that energy level diagram,

346
00:26:33 --> 00:26:37
this energy,
the incident energy,

347
00:26:37 --> 00:26:43
has to be equal to the work
function, h nu nought,

348
00:26:43 --> 00:26:48
plus the kinetic energy.

349
00:26:48 --> 00:26:54
Or, if I turned this around,
the kinetic energy is equal to

350
00:26:54 --> 00:27:02
the incident energy minus h nu
nought.

351
00:27:02 --> 00:27:06
The actual expression for the
energy that Einstein found,

352
00:27:06 --> 00:27:08
I just turned that equation
around.

353
00:27:08 --> 00:27:11
This is an equation that you
have to know.

354
00:27:11 --> 00:27:14
I will not give this to you on
an exam.

355
00:27:14 --> 00:27:17
Now, you don't have to memorize
it.

356
00:27:17 --> 00:27:21
You just have to reason it.
Draw yourself an energy

357
00:27:21 --> 00:27:23
diagram.
You know conservation of

358
00:27:23 --> 00:27:26
energy.
The sum of these two energies

359
00:27:26 --> 00:27:30
has to equal the incident
energy.

360
00:27:30 --> 00:27:37
Then you will be all set.
Now, what is very important

361
00:27:37 --> 00:27:44
here is the following.
If I come in with radiation

362
00:27:44 --> 00:27:50
that is, say,
a half of the threshold energy.

363
00:27:50 --> 00:27:58
Suppose I come in with two
photons, where each photon is

364
00:27:58 --> 00:28:03
one half h nu --

365
00:28:03 --> 00:28:08


366
00:28:08 --> 00:28:12
The bottom line is that you are
not going to get an electron

367
00:28:12 --> 00:28:15
off.
Even though you are coming in

368
00:28:15 --> 00:28:19
with two photons,
which together are going to

369
00:28:19 --> 00:28:23
give you the threshold energy,
you won't get a photon off.

370
00:28:23 --> 00:28:28
You have to come in with at
least the energy of the work

371
00:28:28 --> 00:28:33
function.
A photon has to have at least

372
00:28:33 --> 00:28:37
this energy to get an electron
off.

373
00:28:37 --> 00:28:42
That is the particle-like
nature of radiation.

374
00:28:42 --> 00:28:47
Energy comes in chunks,
in particles of energy,

375
00:28:47 --> 00:28:53
in quanta of energy.
Likewise, if I came in here

376
00:28:53 --> 00:29:00
with a photon that had twice the
energy of the work function or

377
00:29:00 --> 00:29:05
the threshold energy,
I would still only get one

378
00:29:05 --> 00:29:11
electron off.
I would not get two electrons

379
00:29:11 --> 00:29:15
off, even though energetically
you would be able,

380
00:29:15 --> 00:29:19
in principle,
to get two electrons off.

381
00:29:19 --> 00:29:23
But you won't.
You will only get one electron

382
00:29:23 --> 00:29:26
off.
Whenever you send a photon in,

383
00:29:26 --> 00:29:31
if it has enough energy,
that is if its energy is equal

384
00:29:31 --> 00:29:35
to or greater than the work
function, you will get an

385
00:29:35 --> 00:29:40
electron off.
There is one electron for every

386
00:29:40 --> 00:29:44
photon.
You never get two electrons for

387
00:29:44 --> 00:29:48
every photon,
or you can never get one

388
00:29:48 --> 00:29:52
electron for two photons that
are lower energy.

389
00:29:52 --> 00:29:56
That is the particle quantum
nature of radiation.

390
00:29:56 --> 00:30:00
That is important.
Yes?

391
00:30:00 --> 00:30:08


392
00:30:08 --> 00:30:18
What is the form of the photon?
What do you mean by form?

393
00:30:18 --> 00:30:25
Oh, you want a picture of the
photon.

394
00:30:25 --> 00:30:33
You're looking at them.
You cannot draw a picture of a

395
00:30:33 --> 00:30:39
photon because you want to
relate it to something that is

396
00:30:39 --> 00:30:42
within your classical
experience.

397
00:30:42 --> 00:30:48
And you cannot do that.
It isn't a classical particle.

398
00:30:48 --> 00:30:53
That is what you're working
with right here.

399
00:30:53 --> 00:30:59
You are trying to use your
experiences, that are everyday

400
00:30:59 --> 00:31:05
experiences, to explain
something that isn't within your

401
00:31:05 --> 00:31:13
everyday experiences.
You don't have a frame or a

402
00:31:13 --> 00:31:18
format to do that.
Yeah?

403
00:31:18 --> 00:31:30


404
00:31:30 --> 00:31:33
Yes.
If you have a constant flux of

405
00:31:33 --> 00:31:39
photons onto the surface,
you will have a constant flux

406
00:31:39 --> 00:31:44
of electrons.
Now, there is a probability.

407
00:31:44 --> 00:31:50
It is not necessarily the case
that every photon gets in,

408
00:31:50 --> 00:31:56
will eject electrons,
because there are other kinds

409
00:31:56 --> 00:32:02
of competing processes.
Whatever the rate with which

410
00:32:02 --> 00:32:07
the photons come in.
It depends on the flux of the

411
00:32:07 --> 00:32:11
photons.
And we will have some problems

412
00:32:11 --> 00:32:17
like that, where we are going to
assume that the probability of

413
00:32:17 --> 00:32:23
the electron coming off is going
to be one, so one electron for

414
00:32:23 --> 00:32:26
every photon.
But, in reality,

415
00:32:26 --> 00:32:32
there are competing processes.
Are all electrons being

416
00:32:32 --> 00:32:35
ejected?
Actually, some electrons.

417
00:32:35 --> 00:32:39
Again, this goes to the
probability.

418
00:32:39 --> 00:32:47
Some are actually kind of going
in, too, into deeper the metal.

419
00:32:47 --> 00:32:53


420
00:32:53 --> 00:32:55
Not the probability,
right.

421
00:32:55 --> 00:33:01
The rate at which the electrons
come out with is dependent on

422
00:33:01 --> 00:33:06
the intensity.
The more photons you send in,

423
00:33:06 --> 00:33:12
the larger the number of
photons per second coming in,

424
00:33:12 --> 00:33:18
the larger the number of
electrons per second coming out.

425
00:33:18 --> 00:33:23
This is a plot,
here, of the energy of the

426
00:33:23 --> 00:33:26
electrons.
That's all right.

427
00:33:26 --> 00:33:30
Other questions?
Yeah?

428
00:33:30 --> 00:33:35


429
00:33:35 --> 00:33:36
Eventually.
Yes.

430
00:33:36 --> 00:33:39
Absolutely.
There are other problems that

431
00:33:39 --> 00:33:43
will come in.
Usually, your light source

432
00:33:43 --> 00:33:48
isn't so energetic that you
could possibly do that.

433
00:33:48 --> 00:33:53
Now, also usually what happens
is that you've got your metal

434
00:33:53 --> 00:33:58
grounded, so that as you lose
electrons, new electrons come in

435
00:33:58 --> 00:34:03
and fill it up to the fermi
level.

436
00:34:03 --> 00:34:06
And so you don't charge up your
sample.

437
00:34:06 --> 00:34:10
In an experiment,
if you had your metal just not

438
00:34:10 --> 00:34:15
grounded and you did shine some
radiation, what would happen is

439
00:34:15 --> 00:34:18
the metal would start to charge
up.

440
00:34:18 --> 00:34:23
Then, that would make it
difficult to get electrons off.

441
00:34:23 --> 00:34:25
Yes?

442
00:34:25 --> 00:34:35


443
00:34:35 --> 00:34:37
Yes.
How strongly those electrons

444
00:34:37 --> 00:34:42
are bound to the metal depends
on the electronic structure of

445
00:34:42 --> 00:34:44
the metal.
And we are going to talk a

446
00:34:44 --> 00:34:49
little bit about what determines
the strength of the interaction

447
00:34:49 --> 00:34:53
for electrons on atoms and
molecules, but it is similar to

448
00:34:53 --> 00:34:57
what it is for metals.
That is coming in a few days.

449
00:34:57 --> 00:34:59
Yes?

450
00:34:59 --> 00:35:04


451
00:35:04 --> 00:35:05
Yes, there is.
Right.

452
00:35:05 --> 00:35:08
You don't actually have to have
a metal.

453
00:35:08 --> 00:35:11
You could do it.
There are usually higher

454
00:35:11 --> 00:35:14
frequencies on insulators and
semiconductors,

455
00:35:14 --> 00:35:17
right.
It is harder to see the effect,

456
00:35:17 --> 00:35:19
but it can be done and has been
done.

457
00:35:19 --> 00:35:24
Well, what I want to do right
now is to show you an experiment

458
00:35:24 --> 00:35:27
we are going to do.
We are going to do a

459
00:35:27 --> 00:35:30
photoelectron experiment.

460
00:35:30 --> 00:35:45


461
00:35:45 --> 00:35:53
And the experiment is this.
We have a device up here.

462
00:35:53 --> 00:36:00
What we have is an aluminum
plate.

463
00:36:00 --> 00:36:05
And that aluminum plate is
mounted on this blue metal rod.

464
00:36:05 --> 00:36:10
And in the middle of this rod
is a needle on a pivot.

465
00:36:10 --> 00:36:14
And this is a fairly
frictionless pivot.

466
00:36:14 --> 00:36:17
This black ring,
here, is just a support

467
00:36:17 --> 00:36:22
structure, an insulating support
structure.

468
00:36:22 --> 00:36:27
What we are going to do is put
some excess charge on this

469
00:36:27 --> 00:36:32
aluminum plate.
And that excess charge is going

470
00:36:32 --> 00:36:35
to run down this metal rod and
then onto this needle.

471
00:36:35 --> 00:36:40
And because that excess charge,
the electrons on the needle and

472
00:36:40 --> 00:36:43
the electrons on the metal rod
are repulsive,

473
00:36:43 --> 00:36:45
since this is rather
frictionless,

474
00:36:45 --> 00:36:49
that needle is going to move
because of the repulsive

475
00:36:49 --> 00:36:52
interactions between these
electrons.

476
00:36:52 --> 00:36:56
What we're then going to do is
try to do the photoelectron

477
00:36:56 --> 00:37:00
experiment.
We are going to take some UV

478
00:37:00 --> 00:37:07
radiation and shine it on this
metal and drive the electrons

479
00:37:07 --> 00:37:09
off.
And we should see,

480
00:37:09 --> 00:37:14
then, the needle swing back to
its original position.

481
00:37:14 --> 00:37:20
I need a couple of volunteers
in order to do this experiment

482
00:37:20 --> 00:37:22
here.
Come on up.

483
00:37:22 --> 00:37:24
All right.
Fantastic.

484
00:37:24 --> 00:37:27
I think that is all right.
Good.

485
00:37:27 --> 00:37:32
Okay.
One of you needs to be the

486
00:37:32 --> 00:37:35
charger, and the other needs to
be the discharger.

487
00:37:35 --> 00:37:38
Which one?
You want to discharge?

488
00:37:38 --> 00:37:41
Discharge, okay.
You come over here.

489
00:37:41 --> 00:37:45
And what you are going to do is
discharge the aluminum plate

490
00:37:45 --> 00:37:48
after we get some excess charge
on it.

491
00:37:48 --> 00:37:52
You are going to do it just by
holding it up to here.

492
00:37:52 --> 00:37:57
You have to get it kind of
close because it is not a very

493
00:37:57 --> 00:38:03
intense UV source.
Could you get the video cam on

494
00:38:03 --> 00:38:09
the side or on the center to get
where we are putting it?

495
00:38:09 --> 00:38:13
I guess we are putting it on
the side, right?

496
00:38:13 --> 00:38:15
Okay.
There we go.

497
00:38:15 --> 00:38:19
There is the device.
You are the charger.

498
00:38:19 --> 00:38:24
What we are going to do,
to get the excess charge,

499
00:38:24 --> 00:38:30
we are taking a piece of
natural fur.

500
00:38:30 --> 00:38:33
We are going to rub it on this
Lucite rod.

501
00:38:33 --> 00:38:37
You have to keep your fingers
on the yellow tape here.

502
00:38:37 --> 00:38:41
And we are going to transfer
some of the natural oils here

503
00:38:41 --> 00:38:44
onto this rod.
And there are plenty of

504
00:38:44 --> 00:38:47
negative ions around here and
free electrons.

505
00:38:47 --> 00:38:52
That oil likes those negative
charges, and so there are going

506
00:38:52 --> 00:38:57
to be excess negative charges on
this Lucite rod.

507
00:38:57 --> 00:39:03
And then you are going to come
over here and just touch the

508
00:39:03 --> 00:39:08
edge of this and let the
electrons flow onto there.

509
00:39:08 --> 00:39:13
Are you right-handed?
You have to rub that really,

510
00:39:13 --> 00:39:16
really hard.
[LAUGHTER] Great.

511
00:39:16 --> 00:39:19
Go over there.
Touch the end.

512
00:39:19 --> 00:39:23
Cool.
Why don't you give it another

513
00:39:23 --> 00:39:30
jolt here and we will really
move that needle over.

514
00:39:30 --> 00:39:31
Okay.
Discharger.

515
00:39:31 --> 00:39:33
We have to give it another
jolt.

516
00:39:33 --> 00:39:36
That is okay.
You may have touched it with

517
00:39:36 --> 00:39:40
something else and discharged it
a little bit.

518
00:39:40 --> 00:39:43
No, that's okay.
You have to get the hang of

519
00:39:43 --> 00:39:46
this, here.
You are doing fantastic.

520
00:39:46 --> 00:39:49
Take it off.
That's what it is.

521
00:39:49 --> 00:39:53
You are holding it on too long.
Okay, that is pretty good.

522
00:39:53 --> 00:39:57
Put it in front there.
Get it a little bit closer.

523
00:39:57 --> 00:40:02
Here comes the UV radiation.
We did it.

524
00:40:02 --> 00:40:06
Try it again really hard.
Just touch it.

525
00:40:06 --> 00:40:09
Take it off.
Do it again.

526
00:40:09 --> 00:40:14
You need to do it again.
You've got to get it right

527
00:40:14 --> 00:40:16
here.
Not too much,

528
00:40:16 --> 00:40:18
not too little.
Okay.

529
00:40:18 --> 00:40:22
It is doing it.
Discharge in front.

530
00:40:22 --> 00:40:27
Electrons off.
Now we have to do a control

531
00:40:27 --> 00:40:33
experiment.
That is, you have got to charge

532
00:40:33 --> 00:40:38
it up again, but now,
when you put the light there,

533
00:40:38 --> 00:40:44
what I am going to do is hold
up a Pyrex plate in between the

534
00:40:44 --> 00:40:49
light and the metal.
It is going to block the

535
00:40:49 --> 00:40:53
radiation, and it should not
discharge.

536
00:40:53 --> 00:40:57
You need to get on there.
Fantastic.

537
00:40:57 --> 00:41:02
There it goes.
Here is the plate.

538
00:41:02 --> 00:41:07
Get it to a little bit lower.
Do a good discharge.

539
00:41:07 --> 00:41:12
[APPLAUSE] Fantastic.
Thank you very much.

540
00:41:12 --> 00:41:15
Thank you for being a good
sport.

541
00:41:15 --> 00:41:19
That is the photoelectron
experiment.

542
00:41:19 --> 00:41:24
Hey, it works.
Well, what I want to do now is

543
00:41:24 --> 00:41:32
just spend a few minutes working
on a few problems.

544
00:41:32 --> 00:41:36
I think these are pretty
straightforward,

545
00:41:36 --> 00:41:42
but I just want to make sure
that everybody is on the same

546
00:41:42 --> 00:41:47
page here in terms of being able
to do the homework.

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00:41:47 --> 00:41:53
Here is the first problem.
The first problem says,

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00:41:53 --> 00:41:57
how many photons?
And remember what we said a

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00:41:57 --> 00:42:02
photon was?
E equals h nu.

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00:42:02 --> 00:42:07
This is the number of joules.
Implied is the number of joules

551
00:42:07 --> 00:42:11
per photon, although we don't
usually write this,

552
00:42:11 --> 00:42:15
but that is what that is,
joules per photon.

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00:42:15 --> 00:42:20
You may want to write it as you
do these problems.

554
00:42:20 --> 00:42:28
How many photons associated
with radiation of a wavelength

555
00:42:28 --> 00:42:35
lambda equals one picometer,
which is 1.0x10^-12 meters,

556
00:42:35 --> 00:42:42
how many of these do you need
in order to create,

557
00:42:42 --> 00:42:49
say, a laser pulse of energy
that is one joule?

558
00:42:49 --> 00:42:55
Lasers are pulsed,
so I am talking about a pulse

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00:42:55 --> 00:43:02
of energy, one joule.
You want to draw yourself a

560
00:43:02 --> 00:43:06
picture, here.
We are drawing a picture of one

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00:43:06 --> 00:43:08
pulse of energy,
one joule.

562
00:43:08 --> 00:43:13
Now, we have not been given the
frequency, here,

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00:43:13 --> 00:43:17
of this radiation,
but we know the wavelength,

564
00:43:17 --> 00:43:21
and we know the relationship
between frequency and

565
00:43:21 --> 00:43:25
wavelength.
It is just c over lambda.

566
00:43:25 --> 00:43:30
I know what lambda is.
I can calculate nu.

567
00:43:30 --> 00:43:34
And, when I do that,
I find that the energy of the

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00:43:34 --> 00:43:40
photon, hc over lambda,
that energy of the

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00:43:40 --> 00:43:44
photon is 1.99x10^-13 joules per
photon.

570
00:43:44 --> 00:43:50
And I am using one more figure
than is significant since this

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00:43:50 --> 00:43:55
an intermediate step in the
calculation.

572
00:43:55 --> 00:44:02
If I want a pulse of one joule
of energy and I am asked how

573
00:44:02 --> 00:44:10
many photons do I need to get
that, and each photon is

574
00:44:10 --> 00:44:16
1.99x10^-13 joules,
well, that means that I am

575
00:44:16 --> 00:44:24
going to need 5.0x10^12 photons.
There was a question here?

576
00:44:24 --> 00:44:30
All right.
Let's work another one.

577
00:44:30 --> 00:44:34
Here, we want to define what we
mean by power.

578
00:44:34 --> 00:44:40
This says the power of
radiation from the continuous

579
00:44:40 --> 00:44:44
laser is three milliwatts.

580
00:44:44 --> 00:44:50
We have some laser,
and the power of that radiation

581
00:44:50 --> 00:44:55
coming out is three milliwatts.
Well, what is power?

582
00:44:55 --> 00:45:02
Power is energy per unit time.
It is the energy delivered or

583
00:45:02 --> 00:45:06
the energy expended per unit
time.

584
00:45:06 --> 00:45:11
The unit of power that we are
going to use is a watt.

585
00:45:11 --> 00:45:16
A watt is a joule per second.
We are told that we have

586
00:45:16 --> 00:45:22
radiation of three milliwatts.
That is 3.0x10^-3 joules per

587
00:45:22 --> 00:45:25
second.
And the question asks,

588
00:45:25 --> 00:45:30
how long will it take for a
total energy of one joule to be

589
00:45:30 --> 00:45:36
supplied?
Well, one joule.

590
00:45:36 --> 00:45:47
And we have the rate of energy
supply as 3x10^-3 joules per

591
00:45:47 --> 00:45:54
second.
That gives us 330 seconds.

592
00:45:54 --> 00:46:04
That is straightforward.
Finally, we have one more.

593
00:46:04 --> 00:46:11
It says, how many photons per
second of, again,

594
00:46:11 --> 00:46:17
the same radiation,
of the wavelength of one

595
00:46:17 --> 00:46:22
picometer.
That means, again,

596
00:46:22 --> 00:46:29
we are dealing with photons
that have an energy of

597
00:46:29 --> 00:46:39
1.99x10^-13 joules per photon.
How many photons per second,

598
00:46:39 --> 00:46:45
the rate of photons at the
wavelength do you have to have,

599
00:46:45 --> 00:46:49
or do you have,
if the power of the radiation

600
00:46:49 --> 00:46:54
is three milliwatts?
Well, the power of the

601
00:46:54 --> 00:47:00
radiation is 3.0x10^-3 joules
per second, --

602
00:47:00 --> 00:47:06
-- and we have 1.99x10^-13
joules per photon.

603
00:47:06 --> 00:47:11


604
00:47:11 --> 00:47:18
In order to have this kind of
power, what we have to have

605
00:47:18 --> 00:47:25
being emitted is 1.5x10^10
photons per second.

606
00:47:25 --> 00:47:34


607
00:47:34 --> 00:47:38
All right.
The photoelectric effect is one

608
00:47:38 --> 00:47:43
of the experiments that
demonstrated the particle-like

609
00:47:43 --> 00:47:46
nature of light,
of radiation.

610
00:47:46 --> 00:47:52
Particle-like nature because
you have to have these chunks of

611
00:47:52 --> 00:47:57
energy to make some process
occur.

612
00:47:57 --> 00:48:03
Next time, we are going to look
at and will just talk briefly

613
00:48:03 --> 00:48:09
about the other experiments that
demonstrated the particle-like

614
00:48:09 --> 00:48:14
nature of radiation.
And that other experiment is

615
00:48:14 --> 00:48:18
the demonstration that a photon
has momentum,

616
00:48:18 --> 00:48:22
even though it doesn't have any
mass.

617
00:48:22.562 --> 48:25
See you Wednesday.
See you Friday.