So consider this, you may know.
You shine some white
light through a prism,
and you find that it is
broken into different colours.
I don't have all the colours
available readily here,
but you get the idea.
It becomes a rainbow.
What else?
Green, maybe.
OK.
And so we're observing that
this white light contains these
different colours, and the thing
that's different about these is
that they have
different wavelengths.
And I suppose that presupposes
that you appreciate that light
can be considered as a wave.
In fact, it's all
part of what we call
the electromagnetic spectrum.
And it's just that the visible
light is a small range of it
that our eyes are
able to detect.
So the whole spectrum
covers a wide range
of different wavelengths.
And quickly,
electromagnetic radiation
can be thought of as having
two components, electric
and a magnetic
component of the wave.
It's not really particularly
relevant for-- whoops.
I was going to do that in
white-- for this discussion,
OK?
But what's really important
is that you appreciate that
there's-- so there's the two
components in there 90 degrees
from each other.
But anyway, there's
a wavelength.
There's a length to
this oscillation, OK?
And that's what we're
going to focus on here.
And so, in fact, if you look
at this whole electromagnetic
spectrum-- that is, all the
different wavelengths that
are possible-- you'll
see that there's
a lot of familiar
radiation in there.
So you could go from-- let's
cover some wavelengths here
kind of at the atomic level.
So maybe 10 to the
minus 11 metres, OK?
Roughly that scale, tiny, tiny,
little, short wavelengths.
Or what about if you go to
really long wavelengths,
kilometre scale,
on the other end?
And you'd find that, in
fact, visible light, well,
visible light just falls
somewhere in that range.
And, in fact, visible
light specifically
spans from red, at about 700
nanometers-- so 700 times 10
to the minus 9 metres
in wavelength--
to blue light that's
around 400 nanometers.
OK.
400 nanometers, 10 to the
minus 9 metres, right?
And that's just a tiny, little
range of this whole spectrum.
To show you what I
mean by this range,
well, blue-- actually, in
fact, the end of the rainbow
is violet, right?
Violet, well, what if you go a
little bit shorter wavelength
than that?
You might get to ultraviolet.
And, in fact, this
little discussion
enables us to--
potentially, if you've
heard about
ultraviolet radiation--
you know, UV-- you may know you
can protect yourself from it.
There's quite a bit of
energy in that radiation,
and it can damage the
tissues of your skin.
It can give you
sunburn or skin cancer.
So there's more
energy associated
with the little--
the energy that's
coming-- that's being
transmitted in this light.
You go a little bit
more shorter wavelength,
you get into x-rays.
What about on the other end?
Red, well, what about a
little bit past it, past red?
How about infrared, a
little bit longer wavelength
than red light, and so on?
And you can get radio
waves and things in here.
So my point here is
there's a whole spectrum,
and what we can detect
with our eyes is just
a tiny, little portion of that.
So I spoke about
the energy that's
contained in this radiation.
And, in fact,
energy is quantised,
that it's transmitted
in these little packets,
little, small-- sometimes
we call them photons.
And so you can actually
calculate that photon energy
with an equation, which some
of you may be familiar with,
E equals hc over lambda, where
lambda is the wavelength.
OK?
And so that's a little equation.
And h is the Planck's constant.
c is the speed of light.
And as I said, lambda--
although that's a pretty
bad-looking lambda, isn't it?
Let's fix that lambda up.
For some reason, of
all the Greek letters,
I have most trouble with lambda.
Anyway, that's the
wavelength there.
OK.
Wavelength.
I'll give you an example
of this in a moment.
So that tells you
the amount of energy,
and you could calculate
the amount of energy
in joules or-- in fact, I'll
show you another quantity
that's quite useful sometimes.
So let's actually look at this.
Let's look at the
visible spectrum.
OK?
Let's look at the
visible spectrum.
And so we know the
visible spectrum--
this is an interesting
little quick calculation
to give you some values.
Visible light spans from
400 to 700 nanometers.
OK?
And what type of energy
does that involve?
So we'd have to calc it
E equals hc over lambda,
where h is the Planck's
constant, as I said.
And that has a value
of 6.63 times 10
to the minus 34 joule-seconds.
And c has a value of 3 times 10
to the eight metres per second.
But when we're dealing with
things like with electrons,
it's-- and with energy at
this level, it actually--
sometimes the joule is not the
most practical thing to use
if you want to get numbers that
you can kind of-- that kind
of roll off the
tongue, if you will,
that are easy for our
human brains to remember.
So what we can actually do is
we could take a value in joules,
like the Planck constant there--
6.63 times 10 to the minus 34--
and do a little
conversion to it.
So we say that's
in joule-seconds.
Well, what if we divided that
by the charge on an electron?
OK?
So that's 1.602 times
10 to the minus 19.
Units of charge,
that's a coulomb.
OK?
And that's the charge
on an electron.
What if we excite the-- or
sorry-- if we take an electron
and accelerate it
through a volt?
Well, a joule per coulomb
is just a volt. So,
in fact, joule per coulomb,
that-- correction-- that
cancels out.
And we could define this charge
on an electron accelerated
through one volt. That is,
you get one volt like this,
and we're accelerating an
electron across that one volt.
Well, we could go ahead and
define that charge times
that voltage, one volt,
as an electron volt.
And then we find that
we get a value that's
a little bit more useful often.
And I'll show you that again
with the visible spectrum.
So that works out
to 4.135 times 10
to the minus 15 electron
volt-seconds for the Planck
constant.
So now what we can do is
we can say, all right.
Let's take this 400
and 700 nanometers,
calculate the photon energy.
And if we do that, we'll
find that the photon
energy for, say,
blue light, OK, is
going to be 4.135 times
10 to the minus 15
electron volt-seconds divided
by-- sorry, correction--
and multiply here by 3 times 10
to the eight metres per second
and then divided
by the wavelength.
And we said, well, the
wavelength of blue light
was 400 nanometers.
So 400 times 10 to
the minus 9 metres.
And let's see what happens
when you cancel out seconds.
Cancel out.
And we end up with
electron volts.
And we find that blue
light has a photon energy
of about 2.8 electron volts.
And similarly, if we
did that for red light,
go through the
same exercise, we'd
find that red light is
around 1.9 electron volts.
And, in fact, you
can actually get
a little bit of
visible spectrum,
and you can see into violet,
a little bit higher energy
than this.
So a nice little result that
you may want to remember
is that visible light, in these
useful units of electron volts,
spans about 2 to
3 electron volts.
So when you consider,
say, optical transparency
and what this visible light
is doing to a material--
does it have enough energy
to excite an electron,
for example-- it's
useful to bear
in mind that visible
light has photon energy
from 2 to 3 electron volts.
All right.
Thank you.
