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So Einstein in his great 1905 year
took this idea of Planck of E is equal to some constant times the frequency
and applied to the photoelectric effect as we have talked about earlier
Summary of that was
as you increase the frequency of the light
you are going to need more and more
stopping potential in order to stop all the electrons
and now of course we can multiply by a constant e and changes to energy instead, so we basically get this
so looking at that
then Einstein basically said that it is not the oscillators that have energy levels that is quantized
it's the electromagnetic energy that is quantized
that every time the electron absorbs the energy, it takes it by
one chunk worth, and this chunk
is worth h x nu
just like how the smallest amount of charge you can pick up is an electron's worth
the smallest amount of light you can absorb is h x nu and it depends on its frequency
that's the brilliant idea that Einstein have and that starts the whole idea that
light is actually a particle, now I want to stress here at this point
that when you have lights as the particle, it doesn't mean that light travel as a ball of fire
no, it's one photon worth of light looks like this
as it propagates and two photons worth of light looks like this
it's just that we can't possibly have one and a half photon's worth of light
so that's not allowed
that's what we mean by quantization of light energy
and is this idea contrary to popular belief, and not relatively
that got him the Nobel prize, and rightfully so, it's not because relativity was not popular or anything
it's that this is quite revolutionary and basically started
the whole wave-particle duality of different things
ultimately leading to quantum mechanics; it's an important discovery
so while Einstein uses E=hv to quantize the EM waves
on the electrons side, things have advanced a little bit as well
in 1911 Rutherford discovers that there's a nucleus
and subsequently in 1913, Niels Bohr came up with his atomic model
of a dense nucleus with electrons zipping around on the outside
kind of an electron orbit model
now there are certain things that doesn't work with that, and we will go through that in a little bit [later]
similar to how Planck was initially proposing that the electron energy level is also quantized
there has been clues as to
how this energy level is quantized, it comes in the form of
gas emission spectrum, when you heat up gas and only one type of gas and emit some light
and when you seperate the light into all colors of the rainbow, you see these discrete lines
so say for hydrogen, very simple atom, has a few lines, iron has a lot more lines
but nonetheless
you get these discreet lines. Knowing, of course, now
these different frequencies corresponds to different amounts of energy, E = hv
that tells you that
an atom can only give up specific amounts of energy
they can't give up anything they want, they have to jumped from one level to another that is discrete
but to see if for the first time is through the Franck-Hertz experiment, another classic experiment
Franck-Hertz, they are two different people, these experimentalist often work in pairs and seems like they have no first names
but it's Franck and Hertz
so how their experiment goes is actually quite similar to your photoelectric effect experiment
so what they have
is they have an electron gun over here with some kind of accelerating voltage
and they have some plate that provides a stopping potential once again
now this electron gun is going to fire out some electrons and it's going to try
and come up against
some negative charge to see that makes it to the end to give you a current
what's different is, instead of a vacuum, it is filled with
[Mecury vapour] and what can happen is with all these Hg particles
as the electron moves across and collides with our Mecury particle
chances are they are going to lose some energy
if the atom can take time
knowing classical mechanics, atom is much heavier, so we through the calculation of conservation of momentum and energy
we can know how much energy it loses per collision, and so for a given accelerating voltage
you can expect that the current coming out, the number of electrons that makes it to the end, will get higher
as your accelerating voltage gets higher, so the faster the electron initially flies off
the more mecury it can hit before it slows down enough that it doesn't make it through the plate
but what you actually see is that
you rise up as you speed up, but at some point you get a big drop
and then it rises up again and you get another drop, and then it rises up again, and another drop
so why is there that pattern
what ends up happening is
because the electron energy levels are quantized
if you move too slow the mecury can't take you energy
because you are not providing enough energy for it to jump up to the next level, so the electron bounce off elastically
and then when you get fast enough right here
to have enough energy to give the energy to the mecury, that's when you start to inelastically colliding
you lose a bunch of energy and so you don't make it to the end
and then you have to build up again, at twice that energy, you can collide twice and still survive
and 3 times and so forth. Notice that we are not working with different energy levels
just the first energy level, but multiple collisions
but the importance of this experiment here is
we can now say that the electron energy level is also quantized
something Bohr has already worked into his
atomic model in a fairly ad hoc fashion
and we'll do that because actually surprising effective