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.