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PROFESSOR: Last time,
we spoke about photons

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in the context of
an interferometer.

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The Mach-Zehnder interferometer.

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And we saw the very
unusual properties

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of photons and interference,
and how relatively simple

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interference a effect
can be used to produce

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a very surprising measurement.

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Today we're going to backtrack
and go from the beginning,

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and think about photons as
physicists did 100 years ago,

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and how, by thinking
about photons,

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they pretty much came up
with quantum mechanics.

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So we want to trace this back.

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And the best place
to start, probably,

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is with a photoelectric effect.

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The photoelectric
effect is an experiment

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done by Hertz in 1887, in
which he irradiated plates.

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That means shine light,
high energy beams of light,

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on metal plate, and he found
that electrons were released.

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Those were called
photo electrons.

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And therefore, you would
get a photoelectric current

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from those electrons.

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So this is the effect
we want to discuss now,

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is the photoelectric effect.

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And it's Hertz, 1887.

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So first a description.

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So polished metal plates
irradiated may emit electrons.

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And these are called
photo electrons sometimes.

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Photo electrons is
just an electron that

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was released due to a photon.

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And therefore, we get a
photoelectric current.

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OK so so far, so good.

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But what was special
about this experiment?

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The first step that was
special was that there

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was a critical frequency.

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If you would take a sample
and you would irradiate it

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with light, and you
would begin with light

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with very low frequency,
nothing would happen.

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And all of a sudden after
a certain frequency, boom.

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You would get a current.

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So there is a threshold
frequency, nu0,

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such that only for Nu greater
than nu0 there is a current.

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So no current for
lower frequencies.

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Now as it turned out,
nu0 depends on the metal

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you're irradiating.

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And even more, it's a
complicated thing to calculate.

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It depends on the
surface of the metal,

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so that's why Hertz apparently
had to polish the metal.

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And this frequency, if
the metal is irregular,

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may depend on where you shine.

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So you'd better prepare
the metal very nicely.

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And it may even depend
on the crystalline nature

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of the metal, because
it's a many body effect.

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You see, anticipating
the resolution,

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there is this piece of metal and
there are a few free electrons

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running around.

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And they run around among
the crystalline structure

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of the metal.

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And removing them, it's
going to take some energy,

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and that energy depends on
the metal and the arrangement

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and all kinds of things.

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So this nu0 depends on the
metal and the configuration

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of atoms at the surface.

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Third property was
kind of interesting.

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The magnitude of the
current was proportional

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to the intensity of the light.

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Magnitude current
is proportional

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to the light intensity.

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And perhaps the last one and
fourth, a rather important one,

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a very crucial
property, is that you

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could observe the energy
of the photo electrons,

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and it seemed to be independent
of the light intensity.

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So energy of the
photo electrons is

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independent of the
intensity of light

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The number of photo
electrons would

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depend on the
intensity of light,

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but not the energy of
the photo electrons.

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Now there is more to that,
but I think it was not

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quite exactly noticed by Hertz.

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So Hertz probably didn't
notice all these things.

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But the last one, that maybe
we can put in brackets here,

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is that the energy of the
photo electrons E gamma--

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oh, no-- E of the electrons
increases linearly

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with the frequency of the light.

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So this photoelectric
effect was not

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easy to understand if you
thought of light as a wave.

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And Einstein came
up with an answer

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that he almost said
what was going on,

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but didn't quite use the word.

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He said that light comes
in bundles of energy.

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And in a beam, you have
bundles of energy quanta.

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Didn't quite say
light is a particle.

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He himself was a little
non-committal, I think,

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about this concept.

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But Einstein, in 1905, gives
the natural explanation

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and says that light
is composed of quanta.

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He would have to
wait until 1920s

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until the name photons came
up, given by a chemist, Lewis.

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So he called them quanta.

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These are later photons, and
I will use the name photons

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from the beginning.

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With energy, E equal h nu,
where nu is the frequency and h

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was Planck's constant.

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Planck had already
introduced the constant

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in trying to fit the
black body spectrum.

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The black body spectrum,
the intensity of light

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is a function of frequency
in black body radiation,

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had a particular curve.

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Planck tried to fit it and he
realized he needed one constant

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and he called it h.

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That's Planck's constant.

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And the same constant
that Planck introduced,

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reappeared in
Einstein's proposition.

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This is Planck's constant.

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So the picture that
Einstein and others had

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was that you would have
kind of a potential

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here and plot energy
over here, and maybe this

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is some distance.

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And you have a metal and there
is the electrons captured here.

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And here is zero energy.

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So they have negative
energy, they're captured.

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And you need some
amount of energy, w,

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which is called the work
function, that depends

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on the type of metal you have.

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And if you could
supply that energy, w,

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to any one of these electrons
that are bound in this metal,

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they would come out and
not be attracted any more

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and would be able to fly free.

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So it is like an
escape velocity,

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you're bound by the
gravity of earth.

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You need something velocity,
some energy to shoot you out.

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Same thing here.

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So this w, or work function,
is defined as the energy needed

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to release an electron.

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And that work
function is that thing

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that depends on the metal
you have and the structure

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and how well you've
polished the surface.

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So if this is true,
then Einstein,

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if he was right
with this property,

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there would be the following
statement that you could make.

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The energy of the electron,
which is, roughly speaking,

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one half mv squared, would
be equal to the energy

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that the photon [INAUDIBLE],
minus the work function.

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So you supply a photon.

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Some of the energy goes
into the work function,

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but the rest of the energy
goes into giving free energy

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to these electrons.

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So you have the
energy of the photon

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minus w, which is what you
need to just take it out

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with 0 velocity.

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And then the rest of
the energy of the photon

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would be transmitted as
kinetic energy of the electron.

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So if this is true, this
would be h nu minus omega.

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And this was considered
a prediction,

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because that statement that
the energy of the electron

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increases linearly
with the frequency,

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was not quite obvious to people.

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Experiments were
not fine enough.

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Measuring the energy of
the emitted particles

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was not all that easy either.

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So this was
Einstein's prediction.

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And the experimental
confirmation

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took 10 years to come.

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It was verified by
Millikan in 1915.

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So Millikan, in 1915, measures
the energy of the photo

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electrons, verifies
Einstein's conjecture,

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and actually produces,
by measuring so carefully

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the energy of the photo
electrons, produces

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a measurement of h, which
is the best to that point.

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And h is measured
to better than 1%,

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so a very accurate
measurement of h.

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And perhaps you would say,
OK, so this is all wonderful,

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now everybody
believes in photons.

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But that's quite
far from the truth.

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They didn't believe
in photons too much,

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because Maxwell had
been too successful.

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And Einstein himself knew that
once you started believing

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in particles like
photons, you had

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this subject with this case of
loss of determinism and waves

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that we have sometimes
as particles and things

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he didn't like much.

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So people were quite reluctant
to believe in these things.

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It's quite amazing.

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So it took a while still.

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So let's do a simple exercise
to introduce some numbers here,

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and show you how to do some
very simple computation.

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So let me do an example.

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You shine UV light with lambda
290 nanometers on a metal

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with work function 4.05 EV.

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What is the energy, E
of the photo electrons,

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and what is their speed?

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Now it is a goal of mine, and of
the instructors in this course,

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that a calculation
like that, you should

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be able to do without
turning on your iPhone

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and checking what the h bar is,
and getting a few constants,

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and what is an EV
or all these things.

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Well nowadays, you can
just check Wolfram Alpha

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and they will give
you the answer

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for this, in beautiful,
beautiful calculations.

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Just copy the
question like that,

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pretty much, I think it
will answer it for you.

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But you should be
able to do back

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of the envelope calculations,
in which you estimate things

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quickly.

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And with one significant
digit, you don't even

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need a calculator to do this.

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So let's see how
one does this thing.

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So the first thing to
do is to figure out what

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is the energy of this photon.

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That's the first problem.

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So the energy of
a photon is h nu.

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But nu it's not lambda.

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So nu time lambda is c,
so this is hc over lambda,

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where c is the speed of light.

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OK, hc lambda, we could
do it if we knew h.

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I must say, I never remember
what h is in normal units.

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Joule seconds, six
point something,

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I don't quite remember it.

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So what do I do?

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I use h bar, which
is h over 2 pi.

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So h is 2 pi h
bar c over lambda.

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And here is where you--

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here is the first
thing that maybe you

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want to remember by heart.

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h bar c is a pretty
nice number, it's

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about 200mev times a fermi,
If you want it more precise,

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it's 197.33, if you
want to get five digits,

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but it's pretty close
to 200 mev fermi.

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And what is a fermi?

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It's 10 to the minus 15 meters.

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OK, so with this number,
I claim you can do

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pretty much all you want to do.

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So here you have 2pi
times 200 mev times

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10 to the minus 15
meters divided--

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I'll put 197 here--

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divided by lambda, which
is 290 nanometers, which

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is 10 to the minus 9 meters.

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So 10 to the minus 9
and 10 to the minus 15

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is 10 to the minus 6 up.

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And this is a million
ev, which is 10 to 6 ev.

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So all these meters cancel
and there's just an ev left.

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So this is 2 pi times
197 over 290 ev.

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And you certainly could estimate
this like 2 over 3 times 2 pi,

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which is 6.

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And that's about four.

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And if you want to
do it more carefully,

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it comes out to 4.28 ev.

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And the nice thing is that
the answer comes in ev's.

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And the work
functions, everybody

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gives them in ev's, so
it's a convenient thing.

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So at this moment, you
have this electron energy

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of the photon being this.

252
00:21:04,940 --> 00:21:09,380
So energy of the
electron is energy

253
00:21:09,380 --> 00:21:15,380
of the photon minus the
work function, which is 428

254
00:21:15,380 --> 00:21:31,640
minus 405 ev, and it's 0.23 ev.

255
00:21:31,640 --> 00:21:34,730
That's a kinetic
energy and that should

256
00:21:34,730 --> 00:21:39,710
be a non-relativistic
electron because the rest

257
00:21:39,710 --> 00:21:46,170
mass of an electron is
about half a million ev.

258
00:21:46,170 --> 00:21:51,360
It is 511,000 ev.

259
00:21:51,360 --> 00:21:54,520
So this is fairly
non-relativistic, but how slow

260
00:21:54,520 --> 00:21:55,020
is it?

261
00:21:55,020 --> 00:21:57,340
Is it moving a
centimeter per second?

262
00:21:57,340 --> 00:22:00,490
No, it's moving pretty fast.

263
00:22:00,490 --> 00:22:06,120
You can write this as
one half mv squared.

264
00:22:06,120 --> 00:22:08,110
And then what do you do?

265
00:22:08,110 --> 00:22:12,750
You put one half m
of the electron c

266
00:22:12,750 --> 00:22:18,010
squared v squared
over c squared.

267
00:22:18,010 --> 00:22:31,180
And this is one half of 511,000
ev times v over c squared.

268
00:22:31,180 --> 00:22:37,570
So do the arithmetic, it's
20.46 over that, square root

269
00:22:37,570 --> 00:22:40,840
and multiply it by
the speed of light.

270
00:22:40,840 --> 00:22:43,000
You can do this
roughly in your head.

271
00:22:43,000 --> 00:22:52,540
And the velocity comes out
to 284 kilometers per second,

272
00:22:52,540 --> 00:22:55,020
so it's pretty fast.