All right, but we're going to talk about spins today.

Not about sticks.

So I want to continue our discussion of the concepts

and theory behind NMR spectroscopy and again,

this is not going to be about math or anything to that extent.

But we're going to be thinking very, very qualitatively.

All right, so when we last left things we had said

that there are two spin states

for a dipolar nucleus like a proton or C13.

There's spin up and spin down,

and if you have an applied magnetic field there's a small

energy difference between the spin up state,

what we're calling the Alpha state and the spin down state,

what we're calling the Beta state.

And because that energy difference is

so small unlike IR spectroscopy or electronic spectroscopy,

UV Vis spectroscopy where the energy differences are very big

and all of your molecules are in the ground state,

here there's only a miniscule number of nuclei

in the lower state more than the number in the upper state.

We said if there are -- if we take 2 million protons,

out of those 2 million protons depending

on the applied magnetic field, it will be 50 or 80

or thereabouts difference in population.

In turns out that difference in population is going

to be extremely important because it is only

that differential population that's going

to be able to get us a signal.

All right, so if we think about things

in an XYZ coordinate frame, and I'll talk more

about NMR spectrometer in a second and how it works.

But imagine for a moment we have some coordinates,

so the X coordinate is coming out of the plane,

the Y coordinate is in the plane and the Z coordinate is pointing

up and we're going to have our applied magnetic field BNOT

pointing upwards.

That kind of makes sense.

These super conducting magnets are always vertical

because you've got this big pot of liquid helium surrounded

by a vacuum vessel, surrounded by liquid nitrogen,

surrounding by a vacuum vessel.

And, those small amounts of population,

that small differential of population with spin up is going

to give rise to a net magnetization.

Now, in other words a way to think about this is for most

of our cases we're going to have one nucleus pointing up,

one nucleus pointing down in their spin

and there's no net vector here.

Those vectors cancel each other out.

But for that small differential of access vectors you're going

to have some net magnetization along the Z-axis.

Now, the ay it works, when you apply a magnetic field is you

actually have those vectors that are processing around.

So in other words they are processing

at that resonant frequency, at the Lamar Frequency

at 500 megahertz for 117,500 Gauss magnet.

So we actually can represent this by saying okay,

we've got spin sort of pointing in every which way,

and I'll just draw two directions.

They're all processing around.

So remember, remember this is only the differential population

that we're worried about because already for every one

where you have one up and you have an opposing one spin

down those vectors are going to cancel each other out.

Now the other thing is they're not quite on axis.

In other words they're not like this.

It's like a gyroscope if you've ever hung it from a string,

the gyroscope doesn't --

who's hung a gyroscope from a string as a kid?

The gyro in physics lab or something.

The gyroscope doesn't hang vertically,

it kind of hangs off axis and goes around like this.

But if you think about it, since those spins are not bunched

up for every one that's processing

like this there's another one that's opposite it.

So in other words if were just like this you'd say,

oh there's a net magnetization along the Z axis

but also a net magnetization along the Y axis.

But there are other spins that are like this

and they're all going around.

So everything is canceling

out except the net magnetization along the Z axis.

All right, what I want you to imagine right now is

that we're going to place a coil along the X axis and we're going

to put energy into that coil.

We're going to apply a magnetic force.

And I want you to think classically

because the quantum mechanical thing is going

to be we'll flip the spins.

I'll show you that in a second.

But you have your net magnetization along the Z axis,

and think back to classical physics.

If I apply a force along the X axis, right hand rule and all

of that good stuff, we rotate our vector downward.

So after we apply a pulse, I'll just say a pulse.

If here's out net magnetization,

when we apply an RF pulse our net magnetization moves along

the Y axis, and so I guess if I want

to actually represent it I'll just say XYZ,

and I'll say here's our net magnetization.

And as you'll see in a moment we're going

to have continued procession.

And again, if you're worried about the fact that all

of our vectors are not lining up, that they're all processing

like this, just think as I apply a pulse

and drive my magnetization from the Z axis onto the Y axis,

the vector sum is right along the Y axis even though there are

some that are like this, I drive it down.

They're countering each other.

There are some like this, I drive it down.

They're countering each other.

And so our net magnetization ends up a long the Y axis.

Does that make sense?

All right, lets come back to our spins to see what this means.

So, the way I was trying last time

to represent this very small difference

between the Alpha state and the Beta state was

to show some vectors, some spins pointing up in the Alpha state.

And some spins pointing down in the Beta state,

and to try to represent this miniscule difference

in population what I did for the purpose

of my drawing was I drew 6 with spin up in the alpha state and 4

with spin down in the Beta state.

>> [Inaudible] nuclei right?

>> Those are representing exactly the spins

of individual nuclei.

So in other words, if we had a mole of --

or more realistically if we had a millimole of CHCL3,

proiochloroform [assumed spelling] in our NMR tube,

what this would represent would be the different,

the nuclei of the hydrogen there and we would have out of

that millimole of nuclei we would have a small access

in the Alpha state and they would all be processing.

All right, so if we apply an RF pulse, and now I'm going

to be a little bit specific, if we apply a pulse long enough

that it's what's called a 90 degree RF pulse or a pi over 2.

That's just radians and degrees, your choice

and they get used interchangeably.

What that does is it equalizes the population of Alpha

and Beta state, so I'll represent

that by 5 spin up and 5 spin down.

And this situation is exactly the situation that we have

at the end of my little drawing

over on the left-hand blackboard.

In other words here's our net magnetization.

And so the key is now we have no net magnetization spin up,

no net magnetization spin down,

but the very important point is we have the net magnetization

focused along the Y axis.

It is not diffuse, it is not pointing in all directions.

We actually have net magnetization in the XY plane.

And if we apply a longer pulse, a more powerful RF pulse,

so again I will represent our 6 little arrows

and 4 little arrows representing our differential populations

of the Beta state.

If we apply a more powerful RF pulse,

what we call a pi RF pulse

or a 180 degree RF pulse I can invert the population.

In other words I will represent that by 4 arrows pointing up

and 6 arrows pointing down.

And if I want to draw that on my diagram,

can anyone tell me what I do with my net magnetization

on my little XYZ diagram at this point?

>> Down.

>> It's going to point down, exactly.

All right, and this is the damming thing.

Well, one of the many damming things

about NMR spectroscopy is no matter what you do

with your pulses you are limited to the difference in population

that occurs between the Alpha and Beta state,

and later when we start to talk

about 2D NMR spectroscopy we're going to learn about one

of the common techniques now, which is to go ahead

and have polarization transfer.

Now, think about what I said before

in the equation relating the Boltzmann Distribution

to the energy difference.

And remember how the magnetogyric ration

for carbon was a quarter the magnetogyric ration for protons.

That means that roughly the Boltzmann Distribution is going

to be a quarter as big on differential population

for carbon as it is for protons.

So when we get into techniques like HMQC,

which is a two-dimensional technique one of the tricks

of this technique is to transfer the larger

but still miniscule population difference

from proton to that of carbon.

But again, what's damming is you never can get away from the fact

that out of 200 million --

out of 2 million protons at 500 megahertz there's no way

to exceed that I think I said 81

out of 2 million population difference with the exception

of some very specialized techniques that involve

for example unpaired electrons and free radicals or xenon atoms

for that matter, and special optical techniques.

All right, so we have our differential population

and we know that if we apply a pulse

of the right length we can drive that population

to have a net magnetization in the XY plane.

Now let's take a look at how we get a signal

out of the spectrometer.

All right, and again we have a coil and I'm going to represent

that coil as being along the x-axis.

That's a little bit of an over simplification.

And now we have our net magnetization in the XY plane.

And as I said, it processes and so I'm trying,

of course it's hard in three dimensions.

I'm trying to represent this as procession in the XY plane.

I'm trying to represent that with a curvy little arrow

but what I'm really saying is you have your net magnetization

and it's moving around, those vectors are moving around

and we'll just take a single nucleus like chloroform.

It's processing at the frequency,

we'll call it V, call it new.

So like at 500 megahertz sometimes it's called the

Lamoure Frequency.

So for example at 500 megahertz for a 117,500 Gauss magnet.

NMR spectroscopy was actually discovered by the physicists

and rejected by the physicists because they figured

that there would be this universal property of a proton,

of how fast it processed in any given magnet and we --

when we come next time to the concept

of chemical shift we'll see that the frequency,

the magnetic field that the proton field is modulated

by the nature of the molecule, by the environment

in the molecule hence different types of protons process

at different frequencies.

Chloroform processes at a different frequency that TMS,

the CH2 groups of ethyl alcohol process

at a slightly different frequency than the CH3 groups.

These differences in frequency are very, very small

but they were upsetting to physicists

because psychics figured this has to be universal property

of protons and when they saw it varied by magnetic environment

in the molecule they gave it the contemptuous term

"chemical shift" [laughter].