we're going to introduce ourselves

to the idea of photoelectron spectroscopy.

It's a way of analyzing the electron configuration

of a sample of a certain type of atom.

And so what you'll often see

and you might see something like this on an exam,

is a photoelectron spectrum

that looks something like this.

And so the first question is,

well, what's even going on?

How is this generated?

Well, I'm not gonna go into the details,

but the big picture is

the analysis will be done by taking a stream of that atom,

and so that atom, there's an atom stream

going in one direction,

and then the other direction, let me label this,

so that's the atoms

that we're trying to analyze,

and then the other direction,

you send high-energy photons

that are going to bombard those atoms, photons.

Now these photons are high enough energy,

in fact, they're typically x-ray photons

so that when they collide,

the photons are high enough energy

to overcome the binding energy

of even the core electrons

and as those electrons get knocked out,

they move away

and they enter into a magnetic field

that will deflect those electrons

and then make them hit a detector.

And so you can imagine

the electrons that are closer to the nucleus,

those have the highest binding energy,

and so more of that energy from the photon

is going to be used to knock it off

so less of it is going to be there

for the kinetic energy,

so those closer electrons aren't going to get as far

and the outer electrons,

those have the lowest electron binding energy.

They're the easiest to knock off

and so you have more of the photon's energy

is going to be transferred into kinetic energy.

And so they're going to get further away

and they're going to hit the detector

at a further point.

And so one way to view the photoelectron spectrum

is it gives you a sense of roughly how many electrons

have various binding energies.

And you can see that the binding energy increases

as we go to the left.

Now the reason why this makes sense,

the binding energy is inversely proportional

to how much kinetic energy these electrons have

as they actually get knocked off.

And so this spike on our spectrum at the extreme left,

these are the innermost electrons,

and then these would be electrons further out

with the next lower binding energy,

and then lower binding energy after that.

And so we can analyze this

to actually come up with the electron configuration

of this mystery element right over here.

What do you think that would be?

Pause this video and try to think about that.

Well as I mentioned,

this spike right over here would correspond

to detecting the innermost electrons,

and so the innermost electrons

are the one S electrons,

and we know that those aren't the only electrons

'cause there's electrons that have lower binding energies,

and so we know that would have filled up

that innermost shell

and so we know that they have two one S electrons

and then we can then think that this next spike,

that's going to be the two S electrons

and we have more electrons than that

so we must have filled up the two S sub shell

and then this next spike,

this looks like two P.

And the reason why this really makes a lot of sense is

notice the detector is detecting more electrons there,

and we also have more electrons,

and so that must have been filled

and that makes sense,

and actually the way this was constructed,

it's not always going to be this perfect,

but you can see you have roughly three times as many two P

electrons as two S electrons, which makes sense.

The two P sub shell can fit six electrons.

Two S sub shell fits two.

So this next spike is going

to be the next highest energy shell,

which is going to have a lower binding energy.

It's easy to knock the,

it's easier to knock those electrons off.

And so this looks like it's going to be the three S two

and then this next spike,

this looks like three P six

and then that one gets completely filled

and we have one more spike after that

and that spike seems to get roughly the same number

of electrons as all of the other S sub shells

and we know from the Aufbau principle

that the next we fill is four S

and it looks like there's two electrons there

because this spike is about the same

as the other filled S sub shells.

And so just like that,

we're able to use a photoelectron spectrum

to come up with the electron configuration

of this mystery element.

Its electron configuration is one S two,

two S two,

two P six,

three S two,

three P six,

four S two.

And what element has this electron configuration?

Well, we've worked on it in other videos,

but I can get my periodic table of elements out,

and we can see, let's see.

One S two gets us to helium,

then you have two S two, two P six gets us to neon.

Three S two, three P six gets us to argon,

and then four S two gets us to calcium.

So our mystery element is

calcium,

and if someone were to ask about valence electrons,

that would be this outermost spike right over here.

The spike of electrons with the lowest binding energy.

They have the lowest binding energy

because they're the furthest out there.

They are the easiest to knock off,

and because they're the easiest to knock off,

most of that photon energy is leftover

after overcoming the binding energy

that gets converted into kinetic energy.

So those electrons get deflected further.

And the base of what we see here

are the photoelectron spectrum of calcium.

What would we expect the photoelectron spectrum

of potassium be?

And just as a reminder,

potassium has an atomic number of 19,

so it has 19 protons in the nucleus,

while calcium has 20 protons in the nucleus,

and we're going to assume

that we're talking a neutral potassium atom,

so it's going to have 19 electrons, as well.

Pause this video and think about

how it might be different.

When we think about potassium,

it's going to have a very similar photoelectron spectrum

as calcium,

but because it only has 19 versus 20 protons,

it has less positive charge in the nucleus,

so it pulls a little bit less hard

on our various shells.

So in potassium,

you're still going to have one S two,

but it's going to have a slightly lower binding energy

because it's not pulled into the nucleus as much.

And I'm not drawing it perfectly.

It might not be this much.

Actually, you know what?

It's probably more slight, probably.

Something like this,

but it's going to be a little bit to the right.

Similarly, two S two is going to be a little bit

to the right,

and then two P six is going to be a little bit

to the right,

and once again, I'm not drawing it completely perfectly

'cause I don't have the exact data here.

Three S two

would be a little bit to the right.

Once again,

only 19 protons versus 20 for calcium,

so we're pulling a little bit less inwards,

so we have a lower binding energy

for any given shell or sub shell,

and three P six is going to be a little bit to the right,

like this,

and then what is the four S sub shell going to look like?

Well, it doesn't have two electrons in the four S sub shell.

It only has one,

'cause it only has 19 electrons and not 20.

And so it's going to be a little bit to the right.

It has a lower binding energy

and it's only going to be half as high

because you only have one electron, not two.

So it's going to look something like that.

That would be the photoelectron spectrum

of potassium, roughly speaking.

Now we've already talked about that your outermost shell

shows where your valence electrons are.

So if we're thinking about potassium,

it would be right over there.

Now that also tells us,

when we're thinking about the binding energy over here,

so this binding energy,

that tells us how much energy do we need

to remove an electron?

And so when you're removing that first electron,

that's your first ionization energy.

Once you remove that first electron,

because of all of the interactions between the electrons,

your photoelectron spectrum would change

so you can't think about your second

or third ionization energies,

but your first ionization energy,

you just have to think about it's the binding energy

of your outermost electrons.