Lecture 17: The Generation of X-rays, Moseley's Law, X-ray Spectra

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Opera, that's a good one. That's good. It was opera, yes. What opera? No, it wasn't Wagner, but that's a good guess. It's certainly a reasonable style, way over the top. That was Maria Callas singing La Mamma Morta from Andrea Chenier, which was written in 1895, and premiered in the spring of 1896 exactly at the time when the world was going nuts over this mysterious form of radiation that can see inside the human body.

So, I thought that was a good match. The thing's best in class. That's Maria Callas. This is opera for those of you who don't like opera. This, by the way, some of you may recognize if you saw the movie Philadelphia.

This is the piece that's playing when the Tom Hanks character visits the loft, or excuse me, the Denzel Washington character visits the loft of the Tom Hanks character. And this is playing. It's a fantastic piece, way over the top.

And this is Maria Callas who is the woman that restored melodrama to opera. It's fantastic. So go and listen to it. Enjoy it. And, there's Bertha Roentgen's hand, reminding us of the fact that you always irradiate the one you love.

[LAUGHTER] All right, so I have a few announcements. Next week, a week from today, there will be no lecture, instead, celebration of learning. Celebration number two, Wednesday the 27th, coverage through today's lecture.

We'll go through the generation of x-rays but we won't touch anything to do with the use of x-rays and indexing crystals, Bragg's law, any of that stuff. So, anything we talk about today I think is fair game.

And, we'll go back to the early part. So, I think last time we said up until the 22nd. So, I'm going to say the 22nd is fair game. We started talking about the properties of ionic compounds and electron transfer, octet stability.

So, we'll go through all of these. We've covered a fair bit of ground, and will end with x-ray spectra, but not Bragg's Law. OK, second thing I want to remind people that I had a staff meeting yesterday, and many of my recitation instructors said that some of you are puzzled to learn that there's more than one book, that the text is, in fact, three volumes.

And right now, the x-ray readings are coming from this volume here called the course supplement. So, you need to be aware of that, and also some of the best material is in the archive notes on the Web, and also all of these images that I show, they get posted as well.

So, some of you are feverishly taking notes. And that's good, but if you miss something, you can go and take it off the website as well. Last point that came out of the staff meeting last night, a number of people are becoming tardy about taking the weekly quizzes.

You are allowed to miss the weekly quiz for either health reasons or some crisis in the family, but not because she just decided to sleep in or you decided you'd like to take it at a later time. So, I'm giving the TAs discretion to deny you the right to take a make up unless it's proper.

I'm not asking that you come with a medical certificate or anything; we'll take you on your honor. But I do expect you to take those tests when they're offered. If you can't, take it on the day, you can take a makeup up to one week.

After that, we want to close the books on it. And, we're not going to allow you, as is the practice in other classes, to throw away your bottom two or three scores. If you don't take them, you'll get zeros, and that gets averaged in to your homework grade.

I want you to have the discipline of weekly homework and weekly homework quizzes. So, I know that recitation instructors are announcing this, but I want you all to hear it from me as well. It's good for your mental health to take those tests, you know? It keeps you sharp.

So, last day we talked about Roentgen and the discovery of x-rays. Roentgen was working in this laboratory studying gas discharge tubes. And, his special take was high-voltage and low pressure. And, under these circumstances, he was generating, unbeknownst to him until the night of November 8, 1895, photons of wavelength approximately one angstrom.

And, we looked at the relevant physics and concluded that we could explain the generation of x-rays by this energy level diagram, which is the energy level diagram of the target. This is the anode. Remember the gas discharge tube has a cathode, which is charged negatively? And, electrons are made to boil off the cathode, accelerate from rest, and they crash into the anode over here.

And, we think when these electrons crash into the anode, they cause a set of operations that ultimately result in the admission of photons in the x region of the spectrum. So, this is the energy levels of the element here in the target.

And, we reasoned that these incident electrons coming with kinetic energy imparted by acceleration voltages in the range of tens of thousands of volts have enough energy to come in and actually dislodge inner shell electrons.

And, in the extreme, N equals one, K shell electrons. And when that happens, there's vacancies that invite a cascade. So, we have a cascade of electrons in the anode target from higher levels down to lower levels.

And, as you know, going back to the early part of 3.091 when electrons move from high-energy to low energy, photons are emitted. And these photons are the source of the x-rays. These are the x-rays here.

So, we saw that if we had a vacancy in the k shell, we could get electrons moving from L shell down to K shell. And, such a photon was termed a K alpha photon, K because the photon came from an electron cascade into the K shell, alpha because it came from one shell above K.

There's a slight chance that the electron may fall from N equals three down to N equals one. That's a greater energy difference. And, we will get a K photon, but K beta, K beta indicating that the photon fell to K from two levels up.

And, even just to complete the picture, I put K gamma. Well, if there is vacancies in the K shell, if we have enough energy to dislodge electrons from K shell, we certainly have enough energy to dislodge electrons from L shell.

Vacancy here would invite a cascade from N equals three to N equals two. This would be L alpha because L is the destination shell, alpha meaning you came from one shell above. And, in the event that you fall from two shells above, N equals four down to N equals two.

This will be an L beta photon, and thus was the way we left it last day. And, the last thing was that the instant energy values here, and therefore, the instant wavelengths are determined by the chemical identity of the target.

If I change the composition of the target, I have a different internal energy structure, and I'll get a different set of emissions. So, that's what was left at the end of last day. So, now the question is, is there a quantitative relationship between any of this, specifically, is there a quantitative relationship between the chemical identity of the target and any of these wavelengths that are observed? And the answer is yes.

And for that, we go back to Manchester and the person of a young graduate student at the name of Henry Moseley. He was a graduate student working under Rutherford in 1913, 1914. And, he was conducting a study, what we call a systematic study.

For those of you who intend to become graduate students, I want to let you know this is a very dangerous word. What systematic means, it's polite talk for tons and tons of measurements, systematic.

His systematic study was to take the x-ray generator and change the chemical identity of the target. And, he conducted a study of no fewer than 38 elements, systematically changing the chemical identity of the target, and measuring the spectrum, the emission spectrum for 38 elements.

He started as low as aluminum and went all the way up to gold, stopping 38 places along the way. And, he measured the wavelengths of these x-rays, and he found a pattern. What he found was that as the molecular weight or as the atomics, and we are just dealing with elements, as the atomic weight rose, the wavelengths fell.

So, I'm comparing apples and apples. So, let's compare all of the K alpha lines. So, the lambda, K alpha, would fall as the heavier and heavier elements were used. And, here is the plate from one of his papers.

This is a beautiful piece of work. These are the photographic plates along the lines of the Balmer series, only this is from the x region of the spectrum. So, here's calcium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, copper, and brass.

Here's where he's going. There's calcium; didn't have scandium. It was too rare, and still to this day, very, very expensive. So, now he's moving across the transition metals. He gets to copper, and he can't use zinc for reasons I'm going to show you very shortly, namely that the energy in that tube is so high that he's going to melt the zinc.

So, he says instead I'll use brass which is an alloy of copper and zinc. And, so this is the data from his study. And, so here's the first page of the paper. "The author intends to make a general survey of the principal types of high-frequency radiation, examine the spectra of the few elements in greater detail.

The results already obtained show that such data have an important bearing of the question on the internal structure of the atom and further support the views of Rutherford and of Bohr." This is what he's putting up here for us.

And, what I want to show is that when he took his results this is what he found. He tried to get a better functionality of this relationship between wavelengths and atomic weights. And here's what he found worked best.

He found that if he plotted not the wavelength but the wave number, which we've seen before, the wave number as a function of proton number. And, in fact, the square of the proton number he got a linear relationship.

So, and let's just say this would be L alpha, L beta, K alpha, K beta. Let's say you are at copper. So, copper would be 29 squared. So, he would get data for the L alpha line of copper, the L beta line of copper, K alpha line of copper, K beta line of copper.

He might not get all four lines for every element, that he would take sets of data and plot them out. And he found that if he plotted the reciprocal of the wavelength versus the square of the proton number, the points lay on a line.

So, over here would be aluminum, and over here would be gold. And, this was extremely important. This changed so much because look at what he's able to conclude here. Let's read his paper here. "We have here a proof that there is in the atom a fundamental quantity which increases by regular steps as we pass from one element to the next.

This quantity can only be the charge on the central positive nucleus of the existence of which we have already definite proof." And, remember, when Mendeleev enunciated the law of periodicity, he said that the properties of the elements are a function of the atomic weight.

And, people were perplexed by the fact that potassium is less massive than argon. But no one would put argon under sodium. When Mendeleev's law is that you arrange things by atomic mass. Cobalt and nickel are reversed.

What to do? Here's Moseley. "We are therefore led by experiment to view that N, his capital N is what we call proton number, is the same as the number of the place occupied by the element in the periodic system." "This atomic number," he's coining the term.

"This atomic number is then for hydrogen one, for helium two, for lithium three, for calcium 20, for zinc 30, etc. We can confidently predict that in a few cases in which the order of the atomic weights A clashes with the atomic order of the periodic system, the chemical properties are governed by N, while A itself, probably a complicated function of N." This is brilliant.

This is a graduate student in 1913 correcting Mendeleev. So, what are the implications? What are the implications? So, this proton number, we're not going to give it its due. We are going to call it Z, the atomic number.

This is the Social Security number of every atom, the atomic number. So, what's the significance of this paper? First of all, corrected Mendeleev, not to say that Mendeleev was bad. Mendeleev was brilliant in what he did.

But there were a few things that Mendeleev couldn't account for. So, now we know in the post-Moseley world, that periodicity, that is, the periodic variation in properties is not a function of atomic mass.

It's no longer a function of atomic mass as per Mendeleev, but rather a function of the atomic number. OK, and this now resolves the problems with argon, potassium; cobalt, nickel; tellurium, iodine, these three were known.

These three were known. And, Mendeleev kept saying go and measure them again. The atomic masses are wrong. And, he was right in certain instances. They did find a number of incorrect values. But these weren't among that group.

And lastly, a pair that they wouldn't have known: uranium and neptunium are in the wrong order. All right, so you say, OK, well that's cute. But let me show you something else. By understanding that the atomic number is the critical factor in determining where something belongs in the periodic table, he was able to place the lanthanides.

If you look on the periodic tables from the early part of the 20th century, they don't know where to put the lanthanides. They are trivalent, so they tend to put them under aluminum, maybe under scandium.

But they don't know what to do with them. So, with this, he was able to place the lanthanides, and more importantly, he was able to predict that there are 14 of them. There are 14 in all. Now, how do you do that? It's really simple.

Lanthanum was discovered in 1839. Lanthanum was discovered in 1839. It has an atomic mass of 138.91, and there were various other lanthanides that had the discovered. And, I'm going to put in lutecium, which had been discovered only recently in 1907.

And, its atomic mass is 174.97. So what? What can I learn from this about how many elements lie between lanthanum and lutecium? It's anybody's guess. But, with Moseley, Moseley comes along and he says, this isn't the critical figure.

The critical figure is the atomic number. I'm going to tell you because we can do the experiment. And, we can determine that lanthanum has an atomic mass of 57, and lutecium has an atomic mass of 71.

Now, I ask you, how many elements are there? How many elements are there to be discovered? With the atomic number, everything is resolved. In fact, once you know that the atomic number of uranium is 92, you can say with surety that there are 92 naturally occurring elements up to uranium.

They couldn't do this before Moseley. And, he kept going. He didn't stop with this. Who else was in town in 1913 in Manchester? Niels Bohr. So, Moseley looks at these data, and he says, I wonder if I can fit these data to a line? So, he said, well, Bohr is in the building.

I'll go talk to Bohr. And he says, why don't I use a Rydberg-like equation? And this is what he writes. The nu bar varies with the square of the proton number in the following manner: R, the Rydberg constant, one over N final minus one over N initial, each of them squared, times Z squared.

But he knew those lines don't all go through the origin. They don't go through the origin. So, it's Z minus some nonzero constant squared. So, wave number goes as the square of the proton number, but there's a little bit of an offset.

And this is called Moseley's law. This is Moseley's law. So, it's a Rydberg type equation. It's essentially a Bohr adaptation for the x-ray spectra that he had measured. And so, for example, you can have a Lyman-like series.

The Lyman-like series would be two to one, right, N equals two down to N equals one? So that means, that's all of the K alpha. So, the wave number of any K alpha line is equal to, if I plug in one over two squared minus one over one squared, this will come out to give me three quarters times the Rydberg constant times Z minus, pardon me, sigma squared.

Well, he keeps going. Let's see what he does. He goes through, and he rewrote the thing in a slightly different form. But ultimately, if you read the highlighted passage here, hence the frequency nu varies as N minus K squared, and N for calcium is really 20, then K equals one.

He solves for this thing, solves for it. And look at this little sort of very delicate, extremely important statement. But, very typical British understatement: "there's good reason to believe that the x-ray spectra with which we are now dealing come from the innermost ring of electrons" because he knows he's way down inside.

So, sigma equals one, in this case, for K alpha. And, there is a Balmer like series. This is to x-ray what Balmer was to hydrogen. And that would be lines three to two. And, so that would be by definition the L alpha lines.

And that would be one over three squared minus one over two squared, which gives you 536 times R times Z minus sigma squared. And, it turns out that sigma equals 7.4 for L alpha series. So, this is really good.

Now, let's go into the physics. Let's try to understand, what is this sigma? Where does it come from? So, for that, let's look at this little cartoon. Here's my K shell. This is K shell. Here's the L shell.

Here's the M shell. Now, K shell, I've got maximum. I've got two electrons max, filled. OK, L shell I've got eight electrons max. And, out here I've got 18 electrons max. Let's look at, first of all, sigma equals one.

That involves transitions from L down to K. So, for transitions from L down to K, normally I've got two electrons in the N equals one shell. If I'm going to have cascade, one of these is missing. There's a vacancy down here.

So let's go up here. I've got one, two, three, four, five, six, seven, eight. Now the eight of these electrons are feeling the positive attraction of the nucleus mediated by the presence of the one electron.

So, you see plus Z minus one. So, we say that the attractive force of nucleus is mediated. Or, we say the electron screens the attractive force of the nucleus. So, the outer electrons are going to fall down, don't get the full brunt of the positive force of the nucleus.

And, there's only one electron here. So, instead of Z, it's Z minus one. It makes sense. It makes sense. And, how about, let's do the next one. The next one would be from three to two. So, out here, I've got electrons.

If they are going to go from three to two, I need at least one vacancy. I could have a vacancy here. So, there's maybe, instead of eight electrons there is seven. Here, there's either one or two electrons.

Suppose there's two here and there's seven here. That's nine. Suppose it is only one here. Well, one plus seven is eight. But, maybe I've blown both of these out. Maybe I've blown more than one of these out so, you put it all together, and it turns out that the number has to be somewhere on the order of what? Eight, seven, something like that? And, sure enough, the number is 7.4.

So, there is a physical basis for the screening factor. Sigma is termed the screening factor. The screening factor defines a Z effective, not the Z. There's a Z effective. It's what's mediated. And to show you, just to get a sense of how powerful Moseley was, here's the thing.

I told you that I've had it drilled into my head that the lambda of copper K alpha is 1.5418 angstroms. There's not many things I know of five significant figures. I know my Social Security number to nine significant figures.

But I know this one to five significant figures. And, if you use Moseley's law, lambda of copper K alpha for Moseley is 1.546 angstroms. And, the delta here is 0.3%, one third of one percent. There's no question this man should have won the Nobel Prize.

He should have won it right away. But he didn't. Mosley was very politically active. And, he decided when World War I broke out to enlist in the British military. And, Rutherford was furious. Rutherford called the Secretary of War and tried to get Moseley a desk job and keep him in London.

And, Moseley refused. So, he ended up in the military, and one of the major battles of World War I was the Battle of Suvla Bay, which was part of the Gallipoli campaign, which was managed by none other than Winston Churchill.

This cost Churchill his political capital. It took him years to recover from the debacle of the Battle of Gallipoli. The Battle of Suvla Bay took a quarter of a million lives on the Allied side, and about a third of the million lives on the Turkish side, over half a million people killed in that campaign.

And, on August 8, 1915, at the age of 27, Moseley was killed in action. And, they don't give the Nobel Prize posthumously. So, no Nobel for this, one of the most brilliant pieces of work in those early days of the 20th century.

Bohr said that World War I, he called World War I a horrible spectacle inflicting great losses on humanity. But the number one loss to the world was Henry Gwyn Jeffreys Moseley. So, that's why you won't see Moseley's name among the physics Nobelists.

Well, this is brilliant work. Is there any data? What's the data? Well, what should this look like? If we take this set of lines and we make a spectrum, the spectrum will be intensity, right, intensity versus some energy coordinate.

OK, so we should have something that looks like this: K alpha, K beta, and then over here, L alpha, L beta. That's what it should look like. And, so just to be clear, we have an emission spectrum that is quantized.

It's quantized because the energy levels are quantized. So, we have a quantized emission spectrum. That's what we should expect to find. It's a function of the atomic number of the specimen. And, so we say that this spectrum is characteristic of the target, or of the anode.

And, I told you last day, if I walked into a room and I saw an x-ray spectrum, and I saw that this was 1.54 ≈, I go its copper because as Z changes, so does the element. In fact, look at how sensitive this technique is.

It's additive. Look down here at brass. Brass is an alloy of copper and zinc. So, there's the copper lines. And in brass, you see the copper lines, and you see the zinc lines. So, by this technique, I could give you an alloy consisting of three elements.

And, you could see from where those lines are what the elements must be that are present in the alloy. And, the relative intensity of the lines must be related to the relative concentrations of this constituents that are present.

This is so important. It's amazing. All right, so let's look at the data. Here's the data. This is data from molybdenum. Now, remember, this is what we are expecting, and this is what we've got.

So, it's there's something else going on here. It looks as though what we have is a combination of, it looks like we've got a combination of this plus this. So, this here is our characteristic spectrum.

It's as though our characteristic spectrum is imposed upon something else. And this something else is continuous, right? There's no break in this curve. So, this is a continuous spectrum. This is a continuous spectrum.

There are various ways of describing the shape. It's certainly asymmetric. But since we're in New England, we call this whale shaped. It's a whale shaped. And, it's got a very steep, it's got a vertical rise here.

I want you to note the shape. It's not just arbitrarily drawn. It's a steep vertical rise, and then an asymptotic tail, and of course a maximum skewed asymmetrically. So it's not quantized. And, furthermore, if you look at this figure carefully, you'll see that there is a family of these.

There is a family of these, and they are enveloping one another. They envelop one another as shown here so that as the plate voltage increases, the height increases and the minimum wavelength decreases.

So, if this is wavelength increasing from left to right, this means that energy is increasing from right to left, which makes sense. As you go to higher plate voltage, you go to higher energies. But, what's going on here? What's the physics of the spectrum? Oh, by the way, and the highest one, you see the K alpha, K beta designation? If you didn't know what they were, you just took the value of K alpha, it looks like it's around, oh, about three quarters of an angstrom by my eyeballing it.

It looks like it's about three quarters of an angstrom. And, if you take the calculation of Moseley's Law for lambda of molybdenum K alpha. You know that molybdenum is Z equals 42 for Moly. Z equals 42; plug them in and you get 0.72 ≈.

So, that seems to be OK. So, in other words, Moseley is predicting the peaks. And, the peak, by the way, is I'm drawing a straight line like this. But in reality, these peaks have some finite width because real materials are not perfect.

And so, there's going to be some variation in the spacing and the energies. OK, so what's going on here? How can we explain this? What's the underlying physics here? Well, let's take a look. Here's a body centered cubic crystal, as is molybdenum.

So, let's say the plane of the table is the anode. And, the electrons are zooming in from the cathode in the ceiling. So, the electrons are coming down. They're coming down, and smashing into this.

And, something's going on that causes the emission of x-rays in all directions. And, we've just seen, it's OK, you've seen in the central board, there, what those energies should be, the discrete energies.

But let's see what else is going on. Let's zoom in at the free surface of the molybdenum. Here's body centered cubic. And, the electrons are coming in. Let's say electrons coming in from the top, and electrons charge negatively.

And, we know that this is net neutral. But, there is an electron cloud. And so, we've seen Born repulsion in the past. We're going to see it again. The mutual repulsion of the electrons in the molybdenum atom with the incident electron that's just arrived long distance from the cathode is going to cause some repulsion.

And it's going to be a deflection. Another electron might come in a little closer. If it comes in closer, it might be deflected more. Now, when a charged particle changes direction, you know, any particle, forget charged particle, a change in speed or a change in direction represents an acceleration.

But, when a charged particle accelerates, that causes emission of radiation. So, every one of these changes in direction, change of direction we term acceleration. That's point one. And, point two, charge accelerating produces radiation because it's an energy change.

So, what kind of radiation? Every one of these comes off. They give off a photon. And, different deflections mean different energy differences. Modest deflections, modest difference, intense deflection, intense difference.

You might even get one that comes in sort of a la Rutherford that comes in and gets turned around. So, what do we see? That could explain what's going on here, where we have at the one extreme, this is very low.

This is a high wavelength, low energy. So, this is low energy; this is low angle deflection. And, this is the most common. This is the most common angle. And, over here is very high angle, and there aren't many of them.

And we can't predict what this line is. There's no way we can calculate that curve except for one point on it. And, that's the remote possibility that an electron comes in dead-on, stops, is captured by the molybdenum atom, and gives up all of its kinetic energy and converts it to photon energy.

And, that one we can calculate, for that one we know that if we take the energy of the incident electron, the total energy. Total kinetic energy is equal to what? The product of the charge on the electron times the plate voltage.

The charge on the electron is the elementary charge, and convert that into the energy of the emitted photon, which is equal to hc over lambda. If we do that, we can invert this and get the value for this point here, which is lambda of the shortest wavelength, which is the wavelength represented by the conversion of the total kinetic energy of the incident electron, lambda of the shortest wavelength, then, will equal hc over e times V.

And, if you plug in Planck's constant, speed of light, elementary charge, you end up with 12,400 over plate voltage in angstroms. You know I am not fond of the nanometer. I insist on using the angstrom in defiance of Systeme International.

So, it's 12,400 divided by plate voltage. So, you can see that if you have on the order of 10,000 volts, 10,000 V will give you a shortest wavelength of 1.24 angstroms, smack dab in the middle of the x region of the spectrum.

And that's what you're seeing up here. There is another term for this phenomenon of changing directions. And it comes from the idea that we are decelerating the incident electrons, decelerating not by changing velocity, but by changing direction.

And, it's the German term Bremsstrahlung. Brems means to brake as in putting on the brakes of your car. Brems means to brake, and strahl is the word for ray. Strahl means ray. So, this literally means braking radiation.

It's the radiation from the braking of the incident electrons, braking radiation. So, the bremsstrahlung plus the characteristic spectrum give us what we see in the figure up here. Last topic I want to cover is something on instrumentation and safety.

A number of you approached me after the last lecture and asked, with incredulity, how could these people work with these generators exposed to x-rays? These were clear glass tubes emanating in all directions x-rays.

Well, the answer is it was unsafe, and many of them died as a result of the radiation exposure because they didn't know at the time what was going on. So, I want to show you several things that have been done in order to make things a little bit safer, and also to be more efficient.

And, what I'm going to show you is the design by Coolidge in 1913. And Coolidge made the following improvements. And, I think I've got a cartoon up here. This is taken from one of your readings out of the supplement.

This is out of the Stout and Jensen book. So, this is figure 1.5. What I did is I turned it on its side so it would look like all of our gas tubes. Every gas tube I've ever drawn for you has the anode on the right.

So, just to orient it I lay it on its side. And so, the anode is on the right. The cathode is on the left. And now, what I want to do is highlight what the improvements have been. So, the first thing that Coolidge did is he used a bona fide vacuum tube.

He got the gas pressure way, way down. And, this did two things. First of all, there's no glow in the visible. And secondly, it's a much higher efficiency because when you have glow, what it means is that some of those electrons leaving the cathode are not getting to the anode.

They are colliding with gas molecules and consuming their energy. So, by the time they get to the anode, they don't have enough punch to kick out inner shell electrons. So, the vacuum tube is an improvement.

The second thing is hot cathode. What happens with a hot cathode? You know, you have to rip the electrons out of the cathode. And the electrons are bound. So, if you raise the temperature of the cathode, the thermal energy then weakens the bonds.

And so, it takes less Coulombic force to rip the electrons out. Now, how's he going to heat the cathode? Let's think about this. You can't use a torch because you've got a vacuum inside. So, a torch won't work in a vacuum.

So, I wonder, maybe if I passed a current, and sure enough, what he does is he's got a second power supply. You see, here's the anode over here. Here's the cathode, and there's the 30,000, 40,000 volts between the cathode and the anode.

And, the electrons boil off here and zoom from left to right. And, he's got a second little circuit here. You can put more than one electrical signal through an item. So, let's put a second circuit through here.

And, this circuit is a little heater circuit. And, all it does is it makes this cathode filament through joule heating, raise its temperature. And that makes the electrons less tightly bound, so it's easier to boil them off.

So, the hot cathode, by raising temperature, reduces binding of the electrons. And, you're trying to get rid of them. The third thing he did was water cooling. You've got all of these electrons. They've zoomed across at an acceleration voltage of 30, 40, 50,000 volts.

They're crash, crash, crash, crash, hitting that copper or molybdenum anode. Where is that kinetic energy going? Some of it's going into light, and some of it's going into heat. And, the temperature of the anode is rising to the point where you could melt this.

So, what Coolidge did is he put the anode on a hearth, and the hearth is copper.. And underneath, there's water running through copper tubing. So, by water cooling, he's able to keep the anode cool, so, dissipate heat, and the second thing, remember, Roentgen used pulse power.

It was eight times a second: bam, bam, bam, bam. If you've got water cooling, now you can go to continuous power, dissipated heat, and allowed for continuous current flow. If you've got continuous current, that means you've got continuous x-ray emission.

You don't want an x-ray flashbulb. You want an x-ray beam. And, the last thing he did is probably the most important thing is he put lead shielding, which I've indicated in yellow, he put lead shielding and beryllium windows.

Beryllium windows for efficiency, and lead shielding for safety. OK, now let's think about it. Let's think about why we would choose these. Why would you choose lead for the shielding and beryllium for the window? For that, I decided, why don't we go back to our friend the periodic table? Look at where beryllium and lead lie on the periodic table.

Beryllium is the lightest practical element. Hydrogen and helium are gases, and lithium as a metal is unstable in moist air. Beryllium is the first metal that can be used sensibly in our atmosphere.

And, look at lead. Lead is down here. And remember, it's 1913 so forget about the actinides. So, you've got bismuth, polonium, and astatine. So, lead is effectively the heaviest practical element.

Why would you choose this? Why would you choose lead as your shielding? What do we know about the energy levels in lead? First of all, there's lots of them because you have not only K, L, M, and N.

You've got n. You keep going, oh. So, you've got plenty of levels. And, the levels are very closely spaced. So, if you've got lots of energy levels, and they're closely spaced, then that means when an x-ray comes in, you'll have excitation and cascading down into much, much longer wavelengths.

So, because of the extra energy levels, this causes the lead to act as a frequency shifter. So, it moves you out of the x region. You still get radiation, but it's not so toxic. I mean, you have conservation of energy here.

But, I mean, you don't have things coming at you into x region of the spectrum. So, if there were a shortage of lead, or, let's say, for the man or woman who has everything, when he or she goes to the dentist, what would be a really chi-chi material to make the vest out of? Mercury is a liquid at room temperature, bad choice.

Thallium: toxic. How about gold? How about a vest made of gold? It would work. That would be a classy vest. Now, how about up here? Beryllium window: beryllium is the inverse. Beryllium has very few energy levels and they are far apart.

So that we don't want the x-rays absorbed as they are going to the window. So, if you had a window that wasn't crystalline beryllium, you run the risk of losing some of your x-rays. So, your efficiency goes down.

So, you choose a low z element for the window, and the high z element for the shielding for those reasons. It all goes back to the internal structure energy levels. OK, well, let's take a look at another use of x-rays, x-rays in art.

This painting, anybody recognize this one? The Angelus by Jean Francois Millet painted in 1857-1859 on commission for an insurance company in Boston. Millet was very popular with Boston Brahmins because he painted rural life in 19th century France.

This painting was commissioned and hung here in Boston. It's now at the Musee d'Orsay. Salvador Dali had to paint this as part of his art education. He hated this painting, and in 1963, it was hanging in the Louvre.

And he had the painting x-rayed. He said there's something spooky about this painting. Well, Dali had such authority that he could ask for the x-ray, and they x-rayed it. And they discovered that, indeed, the painting had been painted over.

It's not an art forgery. It turns out that this zone down here, the little basket of potatoes was not the basket of potatoes in the original painting. The original painting depicted the casket of a baby.

This is showing the poverty, the futility, of peasant life in France. And, these people are so poor that they just lost their baby. Now, you can imagine that this painting comes to Boston. They unveil it, and they say, my God, we can't hang this in the lobby of an insurance company.

So, my theory is that they sent it back and Millet painted it over, put a basket of potatoes. But, their heads are not bowed in the form of saying a prayer thanking God for this miserable bounty of potatoes.

It doesn't make sense. So, x-rays figured out what was going on. So then, Dali got a chance to paint. And this is his revenge. This is his painting in 1935. This is Dali, and this is his father.

You notice in this case, the man is taller than the woman. Here, the woman is taller than the man. There's all kinds of Freudian stuff going on with where he's got his hat placed, but I don't have enough time to go into that.

So, you can see. While we're talking about Dali, here's the hallucinogenic toreador. And, I want to show you this because it hearkens back to crystal structures. He went out one day in Manhattan to buy some Venus pencils.

They're pencils, but the Venus was the manufacturer. See, I have the Venus de Milo on the pencil box. So, you see a bunch of Venuses facing forward, and some facing back. Can you see the breast here is the nose of the toreador? Here's it's mouth; does that help? OK, those are the gadflies of St.

Narciso, which is I think the patron saint of Catalonia. You see, here's his cape, and there's the bull. And, you can see symmetry planes here. OK, there's the head of the thing, OK. There's the bull, yeah, yeah.

OK, now look, here's the symmetry. See, these Venuses are forward. These Venuses are facing backward. What else do we have? I don't know why it's doing this. OK, now, there's the bull. What's the crystal structure? See, this is the life force leaving the bull.

What's the crystal structure? If you ignore color it's simple cubic. You can even see symmetry here. You see the shadow of the fly? You see these two atoms here, these two atoms here? There's even something.

You see the shadow of the Venus actually looks a little bit like, come on, come on, come on. It looks a little bit like this. He really hated this. OK, we're going to show you one more and go through this.

Ah, this is his tribute to Watson and Crick. Over here, you have the DNA double helix, and what he's portraying here is that now that we have the capacity to understand how life is encoded, replication, and so on, ironically, humanity hasn't figured out how to stop killing itself.

And so, he has this group of people all arranged in cubic arrays with muskets pointing at one another. Again, crystallography, you could say actually this is simple cubic, but if you put somebody inside, it would be body centered cubic.

[LAUGHTER] On the last thing, lithium, why is 7-Up called 7-Up? When it first came out it was called lithiated lemon-lime soda. It contained lithium citrate in large quantities. It was supposed to make you happy.

It was an anti-depressant. And, it turns out that some people have a sodium deficiency. Lithium's a smaller ion. If you're already sodium deficient, lithium gets in there, displaces a sodium; you die.

[LAUGHTER] So, after some tens of people died, they took the lithium out around 1950. So, you don't have lithium in your 7-Up today. I'll see you on Friday.

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