Seventh and eighth electrons, you guessed it.

It's a very strange thing, why you might ask, why because quantum mechanics.

Quantum mechanics does this.

This is when I say that electrons can't occupy the same state.

Every time I put new electrons into the box, those new electrons have

to be in a new state that has, has not been occupied before.

We're going to label these states by the number of peaks they have.

This one has one, two, three, four peaks.

We're going to name it as k equals 4 for this one.

This one had a k equals 3, and we're going to try to figure

out how much energy each electron has in each one of its states.

And I'm going to do this by using a very, very poor analogy.

That really is a pretty bad representation of how you really calculate

the energy of the state, and yet it, it works moderately well.

So, so if you know your quantum mechanics better, I apologize.

If you don't know quantum mechanics, think of it

this way, it's a good way to think about.

The first and second electrons, which are somewhere in

the box with, with a probability something like this.

Moving around with some velocity, we don't know what it is, we'll call it v-not.

So for k equals 1, the velocity is v-not.

So the electrons are moving around here

with some effective velocity, something like that.

Now the third and fourth electrons, think of it this way, either here or here.

There's some probability that they're over here, and

some probability that they're over here, and they

are, in some sense, having to move faster

to jump back and forth between these, these possibilities.

They have something like twice as much region to cover,

they have to be moving something like twice as fast.

I know, again, if you know your quantum

mechanics, you're probably about to revolt at this point.

But, but go with me.

Three humps, one, two, three.

going to make the same argument, if three times as

many peaks to have to jump around between to

get around all those three peaks with equal probability,

they have to move something like three times the speed.

[BLANK_AUDIO]

And you can see how this continues on.

All right what good does this do me?

I'm actually interested in energy, and I'm interested in the kinetic energy.

As you remember, kinetic energy is one half mv square so the energy of

these electrons, I'm going to ignore things like

one halves, I'm even going to ignore things like

ms, I'm going to even ignore things like V naughts, I'm going to say that the energy

of this electron is proportional to the

velocity squared, which is equal to k squared.