Lecture 2: Classification Schemes for the Elements

Slides (PDF)

Reading: Elemental Bibliography (PDF)

 

A few announcements at the beginning today. This is 3.091. For those of you who are new to the class, welcome. A couple of administrative things. When you joined 3.091, regardless of what registration took place outside, please check in with my office.

I want you to check in with either Hillary or Lori who will assign you to a lecture section. There is a lecture now Monday, Wednesday and Friday at 11:00. There is also a lecture Monday, Wednesday and Friday at 1:00.

And we are trying to level out the populations so that they balance the seating capacity. And also, likewise with the recitations. We have recitations that run all day long Tuesdays and Thursdays.

The earliest one is at 9:00, the latest one is at 4:00. And, again, we are trying to balance the occupancy there so that we have good access to the recitation instructor. So please don't go squatting.

We need to know what the populations are. And that office is just down the hall here in 8-201. There it is. They are supposed to take that light out, but maybe by the end of the semester a miracle will occur.

So why don't you look over here. There is the coordinates 8-201. And talk to Lori or Hillary. There will be a test on Tuesday based on homework one; ten minutes at the beginning of the recitation.

You are allowed to use on the test the official version of the Periodic Table of the Elements which most of you should have by now. There was a shipment that came in partway through the day on Thursday.

If you didn't get a Periodic Table, swing by the office. It is just down the hall from this lecture theater. And you bring the Periodic Table and the Table of Constants and a calculator and something to write with.

That's four items. Show up, sit down, and the first question is does anybody have a pen? We may not have that many pens. So those are the four items. You do not use an aid sheet on the weekly test.

Aid sheet is for the monthly tests, not for the weeklies. I have asked all of my recitation instructors to state office hours. And I, too, will have office hours. So if you want to come and see me Monday 3:30 to 4:30, I am just down the hall.

Come in and see me. If you can't come by at that hour, you can send me email and I will be happy to meet with you. And I mean that. I get to meet a lot of people through the course of teaching, and I recognize a lot of faces.

I can't say I will remember everybody's name, but I will recognize you. And the same thing with the office hours for the TAs. The office hours are a time when they will be seated waiting for visitors.

That means they will not look at their email, they will not take telephone calls. They will be sitting there waiting for visitors. If you cannot make the office hours, again, contact the recitation instructor to make other arrangements.

Yes? STUDENT: Is there a limit to the type of calculator one can use during the test? No, I don't care. The question is there a limit to the kind of calculator? I don't care. You can bring a mainframe in on a truck.

I don't care. [LAUGHTER] It doesn't matter. A big calculator, you know, I am holding you on your honor. I am assuming you haven't loaded the Encyclopedia Britannica into the memory. It is a calculator, so aid in computational efforts.

What else do I have to tell you? The readings. Well, here is the homework. This is what it is based upon. And we were issuing those. When you go to sign into the class you will get a copy of this.

Some people asked me, if they bought the earlier version of the text, you can find the translation to the earlier version of the text on these question numbers. And if you go to the website and look down here, Fall Term '02.

Go to Fall Term '02 and those homeworks are listed bilingually. Last year I listed them, and there were not that many people that had the First Edition of the text. But if you have the first edition of the text, go to Fall Term '02 and it will show you the earlier translations.

In preparation for lectures, I urge you to do some reading. And so up here you look at lecture topics. It is the second button down. And you will get to a page that looks like this. And so, for today, for example, it says Classification Schemes, Mendeleev, Atomic Structure, Readings Chapter 1, Chapter 2, Appendix A.

I don't cover everything in there, but you are not in high school anymore. You are going to read, you are going to learn, you are going to come to lecture, I am going to hit some high points, things that I find particularly interesting, but it is not sort of well, he said we are going to read this but then he didn't talk about it in class.

Well, get over it. [LAUGHTER] Now, when you starting looking for next week, you are going to see reference to a chapter, which is in the core text, and you will also see this LN, LN, LN archives. These are archived lecture notes that were written by my predecessor, Professor Witt.

And if you go back to here and click on Archive Notes, it is the fourth button down that will take you to something that looks like this. And then if you look at Archive Notes number one this is what you will see.

In some instances, these notes are superior to the text. There is a reason for it. 3.091 has a syllabus that is unlike general chemistry taught anywhere else on the planet. That is why you paid so much money to come here.

You didn't pay money to come here to take something that you could get just anywhere. That is the good news. The bad news is there isn't a text that fits this syllabus, so we choose readings from various sources.

And the text that I have chosen is the best of a bad lot. It at least overlaps to a greater extent than most of the other books. And using the text plus these archive notes, I think you will be able to piece together what you need.

And there is a third alternative. I don't know if you know this. Maybe on the campus tour they kept you away from this part of the campus, but if you go over to the east close to the river there is a building called "the library."

And you know what they have in the library? They have books. And if you go into the library you could find books on topics that we are discussing here, and you could read on your own. But I wouldn't dare suggest anything so radical.

Oh, by the way, speaking of text. My office got a call from the purveyors of text, Quantum and The Coop. And I don't work for them, and this purely a courtesy so that they will know what inventory to keep.

Could I have a show of hands of people who are planning to buy the text but haven't done so yet? Would one of the TAs count, because I don't want to. Just hold your hands up. I am going to keep talking.

We just want to get a rough idea so we can tell me they need to have another 20 or they need to have another 100. Two significant digits is good enough. We don't need to know. I think that is everything that I wanted to cover.

Oh, yes. And, of course, the Webcast is available so that if you miss something during lecture, or if you miss lecture altogether you can go to the website, click on Webcast and follow what happened in lecture.

Let's see. Let's get on with the lesson. Last day we started talking about taxonomy and looked at classification schemes starting with Democritus, which was very forward-looking, and then the backtracking of Aristotle.

And I would like to go further. We started with just the seven metals and carbon plus sulfur, it was the point of departure for Democritus. And the Aristotelian view held for a long time, but eventually it started to crumble in the light of more data.

And, again, all of these slides that I am showing all convert to PDF and will be posted at the website. So you can just watch, take notes, but you don't have to copy every last detail down. By the time of the American Revolution these are the elements that were known.

And here we have arsenic, antimony, and bismuth, three delightful that were given us in the 12th, 13th and 14th centuries by the alchemists. In 13th century India, they knew how to isolate metallic zinc.

In fact, there is a pillar there of high purity zinc that stood for the duration. It is almost a thousand years now and it is in high purity. Platinum was unknown until the Spanish came to South America.

It was unknown. It is an American metal. Platinum is an American metal. And, oddly enough, it was given a bad name. Plata is silver. So platina is like a diminutive of silver, but we now know that platinum is far superior to silver.

It is far more noble. It has a higher melting point, a higher chemical inertness, a fantastic metal. An American metal. And then all of a sudden we have discover, discover, discover, discover. What does this mean? Are we saying that until 1774 there was no oxygen because it was discovered then? No.

What does it mean? It means that it was isolated and characterized. Lavoisier characterized oxygen. Cavendish characterized hydrogen. And so now we see the shift from craft to science. Now we have all this data, and this Aristotelian model is looking goofier and goofier.

So we need to have some better explanation. And one of the earliest was that of John Dalton. John Dalton was an Englishman who proposed the following classification of the elements. John Dalton's science was very accurately weighing the elements.

He has arranged the elements here in a column. It is a double column, but it is only made double for convenience. You can see, it starts with hydrogen and goes to mercury in ascending order of atomic mass.

And he was very proficient at measuring atomic mass. And, furthermore, he started to abbreviate. Instead of writing gold he made this symbol. Silver was S with a circle. He could have worked on a ranch out in the West, couldn't he? This looks like branding things, don't they? Well, this is interesting, cute fonts, but in point of fact they were short-lived.

Berzelius, the Swedish chemist suggested that the French might take umbrage at having to use I for iron. He said why don't we choose something neutral? Let's choose Latin, the language of scholarship, and so iron became Fe for ferrum and lead became Pb for plumbum and gold is Au for aurum and so on.

And nobody quibbles because nobody speaks Latin so it is neutral for everybody. John Dalton also talked about other things. He said I am going to propose a model. And this is right out of Chapter 1 of the text, 1803.

These are the planks of his model, that matter is composed of atoms that are indivisible and indestructible. Well, doesn't that sound an awful lot like Democritus? He is taking us back. He is getting us out of that Aristotelian rut and moving us back to something that makes more sense.

All atoms of an element are identical, that's good. Atoms of different elements have different weights and different chemical properties. This is important. The word "property" is really important - to connect the concept of property with something fundamental in the make-up, in the constitution.

What I am doing, listen to me, I'm talking at two levels here. I am talking at the level of this is Dalton's model, but then there is a meta knowledge here of how you develop models in general. If you are trying to model, I don't know, the efficacy of a particular drug, these are the baby-steps that you will go through.

Atoms of different elements combine in simple whole number ratios to form compounds. That is important, that elements, because they are the building blocks, they combine in whole number multiples. If you have a set of blocks, mechanical, physical blocks, and I tell you to build something and I say, oh, by the way, you have to cut the blocks in smaller pieces, you are going to get angry, aren't you? You are going to say, well, I thought these were the blocks.

These are the basic blocks so, therefore, whole number ratios is a consequence of that. And, lastly, this is Democritus that the being is made of particles that are eternal. This is eternity here.

Atoms cannot be created or destroyed. And when a compound is decomposed, the atoms are recovered unchanged. This is good stuff. It was 200 years ago. Just last fall there were some events in the world celebrating the bicentennial of Dalton's scientific achievements.

Oh, by the way, just to let you know, these scientists of that era were polymaths. They were not specialists. I am a specialist of atoms that are left-handed on Thursday afternoons, and don't talk to me about anything else.

These people had broad scientific interests. Dalton did a lot of work on vision. He, like many men, was afflicted with red-green colorblindness. And he developed the understanding of red-green colorblindness, and it is known as Daltonism.

The same man. Other classifications, Dobereiner at Jena talked about triads. People, remember, they were measuring atomic masses. He saw that if you take the atomic mass of chlorine, add it to the atomic mass of iodine, divide by two, you get something that is really close to the atomic mass of bromine.

And he did it for other triads. And he found that the middle member of the triad had an atomic mass that was midway between the atomic masses of the end members. An attempt. You have to give him credit.

Second was Newlands that I will talk about. I like Newlands because he had a musical flair about him. He talked about octaves. He said look at sodium, magnesium, aluminum, silicon, phosphorus, sulfur, chlorine, potassium.

One, two, three, four, five, six, seven, eight. Potassium lies one octave from sodium. He talked about octaves. When he presented his results at the sitting of the Royal Society, he was ridiculed.

He was laughed at. He was derided. Somebody rose and asked him if he had considered putting the elements in alphabetical order. They were very cruel. These people were nasty. They don't welcome innovation.

Science is very hostile to innovation when it challenges existing theory, sort of like management, the same thing. Let's move onto something that really took the giant step ahead, and that was Mendeleev.

And I also want to mention Lothar Meyer in Tubingen who came up with the same classification scheme, but we are going to see in a moment why Meyer is not well celebrated today and the glory to goes to Mendeleev.

1869, Mendeleev, here is a picture of him taken from that period. He was 35 years old at the time he enunciated this. 35, positively brilliant. Here is his paper. It was published in The Journal of Russian Chemical Society, 1869.

And it is really great because he actually goes through the thought process for you and describes -- I need to give you one piece of background. Mendeleev played cards. And he traveled by train. And so to pass the time, he would play solitaire.

He was used to working with cards and putting things in rows and columns by suit. You had to find what is the distinguishing feature? Well, these are all clubs, these are all spades and these are all hearts.

And I get down to a certain card and I am stumped, so I will leave a space waiting for that card to appear on cue. That is the background. Here he is. He has all the information he knows that has been reported on the various elements on file cards.

He even carried them around in his pocket and he would look at them from time to time and try to devise a scheme. Remember the other people, the octaves had been enunciated, the triads had been enunciated.

Here he is in his paper and says at that time I decided that it was advantageous to find a more general system of the elements and here is my attempt. And here he has laid them all out. And he has left blanks here, question marks here and says it is advantageous to put them in rows and to form a table.

And here is the smoking gun sentence right here. It says finally it came to place, according to this concocted system, and I've underlined in red, very many undiscovered members. So what does he do? He knows that he shouldn't put arsenic under -- He shouldn't put arsenic under aluminum.

Arsenic is nothing like aluminum. Arsenic is like phosphorus. He takes those two facts, plus the courage to leave blanks, and this is what he gives us. Lothar Meyer was doing the same thing, but Mendeleev does something more.

He says not only does arsenic belong under phosphorus, I predict that there is an element that lies below aluminum and above indium. And I will go even further and will predict what its atomic mass is.

So he called them eka. Eka comes from Sanskrit meaning one after. So eka-aluminum is one after aluminum. He predicted 68 for the atomic mass. Gallium was subsequently isolated 69.7. Eka-silicon, which we now know to be germanium, 72, 72.6.

He says there is an element under zirconium, and it should be about 180. He said there should be an element under boron. He called it eka-boron, scandium 45, 45.0. It gets better. He goes into excruciating detail.

This is his prediction for silicon. I already showed you the atomic mass. He said I predict its density 5.5. It was measured 5.36. He says it will have a high melting point. Well, that is arbitrary.

It melts at 958. It forms a dioxide, has a high melting point. And he predicts the density of the oxide of the yet undiscovered element. And he gets it right to two significant figures. And then he says the tetrachloride will be volatile, and it will have a density of 1.9.

And subsequently germanium tetrachloride was synthesized and measured to be 1.88. That is why we celebrate Mendeleev. What we are seeing here is a big transition from just experiment and documentation to modern chemistry.

And how does modern chemistry work? Well, first of all, look at the data. We always have to look around us and account for all the evidence. And this is an ethical question, people. Sometimes you get data that throw you off.

And it is so easy to dismiss those data. What you have to do is have the courage to say I have got to account for the bad data, what I think are bad data and the data that helped me build my theory.

So you recognize patterns and then develop a model, and most desirably a quantitative model. A quantitative model that explains the observations, obviously. But what Mendeleev did was he came up with a model that not only explained what we observed.

It made prediction. And it made predictions that can be tested. I would love to make predictions that you cannot test. Well, let's make predictions that can be put to the test. So this is modern chemistry.

I have told you about the table of the elements. Why do we call it the Periodic Table? We'll again go back to the website. Down here is a button called Courseware. If you click on Courseware you will get to this menu, the first of which preferences is Periodic Table.

If you click on Periodic Table, you can get a variety of choices. One of them here I happened to choose is boiling point versus atomic number. Mendeleev is the one who taught us that the properties of the elements are a function of the atomic mass.

So let's get that down. By the way, the Cyrillic to Latin translation has not been agreed upon, so you will see Mendeleev's name spelled many different ways. You will see it spelled like this. You will see it spelled like this, like this and so on.

And so, when you do a search, it is sometimes frustrating. But I will use various forms. Mendeleev wrote the following. He says that the properties of the elements are, or let's say vary, the properties of the elements vary periodically with atomic mass.

We will find out later that is almost correct. There is a slight variant on there. But right now I am going to give it to you as Mendeleev enunciated it. Atomic number, we will learn later, is the improvement.

That is why this says atomic number, but for most intents and purposes we can say this could be atomic mass. What I am looking at here is boiling point as a function of atomic number. And what we see is it is not monotonic.

It is not continuously rising, continuously falling. It seems to rise and then fall. And then it rises and then it falls. And then it rises and then it falls. And it rises and then it falls. And, if you laid this out in a table, as Mendeleev did with his cards, you would find that the local maxima all occur roughly in the same horizontal position from the end points of the rows.

And then there is a trend going from least massive to most massive. So that is where the "periodic" comes from. We have a table of the elements with properties varying periodically with atomic mass, so we compress all of that information and refer to it as the Periodic Table.

Here is atomic radius versus atomic number. You see the radius is high and then it falls. It rises, it falls. It rises, it falls. It rises, it falls. We are going to now go into the atom and try to understand the scientific basis for this observed behavior.

And so here is the Periodic Table in its glory today following on Mendeleev's scheme. The elements have been named up through -- The one that you are getting hasn't got the latest information. This was named over the past summer.

This is element 110 which has been named darmstadtium after Darmstadt. And I will tell you why in a minute. If you do look down at the Periodic Table and get above 109, you will see these strange notations here, Uun, Uuu, Uub.

What is all of this? These are elements that have yet to be isolated. These are elements that are unstable. These are what are known as the superheavies. Elements beyond uranium, these are synthetic.

And where are they made? The manufacturing facility. There are three places on the planet that have the high energy physics equipment in order to make these, and these are the three places. One is Dubna in the former Soviet Union in Russia, one is in Darmstadt in Germany and the third one is in the United States in Berkeley.

These are the three places where they have the accelerators. And the kinds of reactions -- Here is how they were able to make darmstadtium. They take an atom of lead, accelerate it and have it collide with an atom of nickel.

And, if the conditions are right, they will combine, fuse and form darmstadtium plus neutron. So these devices, when I was a youngster, were colloquially known as "atom smashers", because they have the capacity to actually break these and have them reform.

And there are various forces that play in the nucleus that will dictate when this will be stable and when it won't be. They isolated it, but it decays very quickly on the order of microseconds. Lifetime on the order of microseconds.

So, you can imagine, that is why we don't have the boiling point of darmstadtium and its electrical conductivity. They have isolated it enough that they can actually say the bare minimum about it. So we have it.

And then, just so that you will be literate in the rest of the Periodic Table, if you look at the higher ones, this is how you name them. Use these Latin prefixes. 111 would be un plus un plus un. So 115 is ununpentium.

That is why you see these Uup, Uun. My favorite is 111 because that is unununium. I am going to be sad when they finally get a name for it. There they are. And, when they are named, they are named by suggestion by the scientist who have isolated them.

And there is a lot of competition. Obviously, if it is Russian team that isolates the element, they are going to advocate the name of a Russian scientist or a Russian location or whatnot. Obviously, the work that was done to isolate 110 was done in Germany and they proposed the name Darmstadt.

And, hence, it is named darmstadtium. There is a dubnium and there is also a berkelium. And, if you look in the very high numbers, you will see these nomenclatures. There is darmstadtium sitting there.

For reading, if you are really curious about some of this early history, I can recommend this book. It is "Mendeleev's Dream." I read it the summer before last. It has a lot, of course, about Mendeleev.

But what is really interesting is the author assumes that the reader hasn't taken 3.091. And so the first three chapters take you through the history of chemistry starting with Democritus. And it takes you through to the Aristotelian theory.

After you have had these lectures, it will be a joy to read. Now let's go inside the atom to try to understand what is going on. And this is taken from your book, Table 1.3. And so these are the subatomic particles that we have to contend with.

We have the electron. It bears a negative charge and the value of minus 1.6 times 10 to the 19 coulombs. This is the SI unit, the systeme international unit for electric charge. And it has a mass of 9.11 times 10 to the minus 31 kilograms.

The charge compensation comes out of the nucleus with the proton and it is positive 1.6 times 10 to the minus 19 coulombs. But its mass is 1800 times that of the electron. The electron is just a little gnat in comparison to the proton.

And then there is this third species, the neutron, which has no charge. Roughly equal in mass to that of the proton. And so what we do, in order to designate the identity of an atom, is the following.

This is the atomic symbol which was given by Berzelius. This is the Latin one or two letter character. And we began with the proton number. The proton number is in the lower left corner. Z proton number.

Number of protons in the nucleus, this is number of protons in the nucleus, which in the neutral atom is equal to the number of electrons. Now, to get to the number of neutrons, what we do is go up here to the upper left.

And this is called the atomic mass. And it is equal to the sum of the number of protons plus the number of neutrons. So we get at the number of neutrons indirectly because we know the proton number here.

This is sum of protons plus neutrons. And we don't put the mass of the electrons because they are so light in comparison. This will give us the sum that we need. And, at some level, there is some redundancy here.

If we want to write sodium, for example, sodium 23, 11. Well, 11 means it is sodium. If you have 11 protons, it must be sodium. We could get away with just 23 Sodium **23Na**, but if you wanted to be a real smart-aleck you could write sodium like this.

You don't need anything here. Just a suggestion. Now, atoms need not be neutral. They can be charge deficient or charge excessive. And so Michael Faraday coined the term "ion" for atoms of net charge, atoms and other species bearing net charge.

For example, the positive ions, these are electron deficient. We cannot do anything about protons, they are buried in the nucleus, but we can add or subtract electrons. The positive ions are electron deficient, and these are known as cations.

And you can use mnemonics to try to keep these straight. I see the T as sort of a plus sign. It comes from the fact that in an electrochemical cell, the cations are those that are reduced. You know from catastrophe, cata is Greek for down.

Catastrophe is a downturn. So that is the cation. The negative ions, these are electron-rich. They have an excess of electrons. And these are known as anions. It has the n, which might conjure up negative, or anion and minus both have five letters.

I don't know how you want to try to keep those straight, but anyway. Those mnemonics sometimes come in handy. All right. Now the last thing is that because the neutron has no net charge, we can change neutron number.

Neutron has no charge. This means you can vary the neutron number without changing chemical identity, because chemical identity is fixed by the proton. And since we don't have to charge compensate, we can add or subtract neutrons at liberty.

And so you can look, for example, at the Periodic Table. And, if you look up the atomic mass of carbon, you will see that carbon comes at 12.011 for carbon. Well, isn't this against Dalton? This thing is supposed to be a whole number here.

But, if you look more carefully, you will find that this is a blend of three different forms of carbon. We have carbon 12. I will even leave off the 6 because we already know it is carbon. It has to have 6 protons.

So carbon 12. We know that it has the proton number, by definition, is 6. And the neutron number, 6 from 12 is 6. So it has 6 protons and 6 neutrons. And it is the dominant form of carbon. So its abundance in nature is 98.892%.

There is a carbon 13, however. It axiomatically must be 6 protons, and it has 7 neutrons. And this found in an abundance of about 1.108%. And then there are the last four, carbon 14, which is a radioactive form.

And we will talk about that later in 3.091. And its use in radiocarbon dating. And carbon 14, 6 again and it has 8, and it is found in vanishingly small amounts, 10 to the minus 12 or part per trillion.

If you add all these up then you end up with 12.011 as the atomic mass. They all have the same Z, the same proton number, but different A, which means number of neutrons varies. That means they are found on the same place on the Periodic Table.

If they are found on the same place, it is iso-topos. These are called isotopes. Isotopes have the same chemical identity but different nuclear properties. What are the units here? We write 12.011.

It is either grams per mole. And I am not making a mistake here. Most of chemistry has gone SI so every mass should be in kilograms. But occasionally there is this one little remnant of the old CGS system, centimeters-gram-second, and this is one.

This is 12.011 grams per mole or 12.011 atomic mass units, AMU. And the AMU is defined as the mass of one-twelfth of a carbon 12 atom. I talked about this concept of mole here. What is the mole? Mole is a more practical value, something that we can handle tangibly.

And how do we get the value of the mole? The mole is something that was also defined in terms of carbon. And the mole is defined as the mass of, excuse me. It is the amount of carbon 12 weighing exactly 12.000 grams.

You can see the atomic mass unit will be, excuse me. Let me go at it a different way. This will be the definition of the mole as the amount of carbon weighing exactly 12 grams, so I would like to know now how many particles, how many carbons are there in that mole.

And one way we can get to that is by looking at two pieces of data. The first one, again, is by Faraday. Faraday conducted electrolysis of silver. In an aqueous solution, he passes electric current and causes silver ions to deposit and form metallic silver.

And he measures how much charge is required. He has current. We know that charge is equal to the integral of current times the time. And he knows the current, he knows how much time and then he weighs this.

So he is able to weighthe silver and compare it to carbon. And, against that scale, he finds the silver weighs 107 grams versus 12 grams for carbon. That is the ratio. Now, if he only knew what the electron brought him he would be able to divide through and calculate how many species there are in a mole.

And, in order to determine that, we had to wait a few years until 1909. In 1909 Robert Millikan doing experiments at the University of Chicago conducted this interesting effort where he took atomizer, filled it with oil and then squirted fine droplets of oil mist in between two plates that could be electrically charged.

He further charged the droplets by irradiating. Here it is showing x-rays. He used x-rays. He used various forms of high-energy radiation in order to make the droplets bear a charge. Now you have this situation where you have a droplet that is net negative or perhaps net positive.

And it lies suspended between two plates. And I am able to vary the voltage on the plates making this for argument's sake negative and this for argument's sake positive. If there is no charge on the plate, these droplets will simply fall under gravity.

Once the droplets are charged it makes no difference. They will fall regardless of the charge. When the charge is applied, if the upper plate is negative, we would expect that the negative droplet would be repelled at a rate exceeding the gravitational fall.

The positive droplet, its fall will be slowed and could even be made to lift. And so, by playing with a variety of sizes, remember the atomizer is going to give a distribution of droplet sizes, a distribution of voltages, Millikan was able to develop a relationship between the applied charge and the observed velocities of the droplets.

Let's plot droplet velocity as a function of looking at the number that have this velocity with the zero being in the center here. What do you expect is going to happen? If there were no voltage on the plates, we would expect everything to be over here in some negative value falling.

But what he found was a distribution. He found a distribution. And, if you look more closely at the distribution, here is what he found. He found that some droplets had a certain velocity, and then others had a velocity plus some step.

And he couldn't get values of velocity in between certain steps. He reasoned then that the charge, since he could vary voltage continuously but got a discontinuous variation in velocity, his conclusion was that the charge must be discontinuously attached to the droplet.

Out of that he concludes charge must be quantized. Charge is quantized. In other words, it comes in batches of a certain unit. Charge is quantized. And, secondly, he was able to measure the value of the elemental charge.

We use the term element to mean the lowest value. The element is carbon. That is the smallest unit. Chemically this is the smallest unit of charge. And he gave us a value that turns out to be 1.6 times 10 to the minus 19 coulombs in modern times.

And the electron has a negative charge, so we would say the charge on the electron is minus 1.6. But I want you to learn this as e being the elementary charge. E is the finest charge that is available to be attached.

And so now if we take the value of the Faraday, Faraday found that to get 107 grams of silver required 96,485 coulombs. This is on the basis of the integral of the current times the time. And Millikan said that e is equal to 1.6 times 10 to the minus 19 coulombs.

This is coulombs per charge and this is coulombs per mole. If you divide the two of them through you will get 6.02 times 10 to the plus 23 per mole. So this is how much charge there is in a mole of electrons.

This is the number of carbons there is in a mole of carbon. And this is given the value the notation N Avogadro **NAv**. Avogadro's number we call it. Avogadro was a professor of chemistry at the University of Turin who did a lot of work on gas laws, understanding the number of gas particles in a given volume at a given temperature.

Isn't this nice? They name constants after professors. They didn't name it after a baseball player. They named it after a professor. So now we know the Avogadro number and are able to count the quantities accordingly.

What I am going to do next day is go into the larger stoichiometry and understand the principles of mass balance and reactivity. But before you go, hold it, I don't want you racing off. We should be going to 55 minutes after the hour, so I have something to share with you.

I don't know if you heard this morning, but there was news of the discovery of yet one more element. Anybody hear of it? I guess you were busy. I got this off of NPR. It says the discovery of the heaviest element known to science has been reported.

Obviously it has to be heavy. All the light ones have been discovered. The new ones are going to be heavy, so that's great reporting. The element tentatively named administratium. It has been tentatively named administratium.

And this will have to go up before The International Union of Pure and Applied Chemistry before they approve it because they fought over element 106 for the longest time, but I think this will go through fairly quickly.

Maybe not. It has no protons, so therefore, it has no electrons. Because proton number equals electron number, which means if it has no protons its atomic number is zero. So you are learning already.

However, it does have one neutron. It has 125 assistants to the neutron, it has 75 vice neutrons and 111 assistants to the vice neutrons. That gives it a mass number of 312. The 312 particles are held together in a nucleus by a force that involves the continuous exchange of meson-like particles called memo-ons.

These memo-ons just go back and forth. Now, there are no electrons so there can be no electronic mail. We speculate there may be neutronic mail here. But, anyway, let's talk about the properties. Since it has no electrons, it must be chemically inert.

However, it can be detected indirectly because it seems to impede every reaction in which it is present. According to the discovers, the presence of a few nanograms of administratium made one reaction that normally takes less than a second take over four business days.

Oh, there is more. Because it is heavy you expect it is radioactive. It has a half-life of approximately three years at which time it stops decaying. Then it undergoes a reorganization in which the vice neutrons, assistants to the neutron, the assistants to the vice neutrons exchange places.

And there are some early indications that the mass actually increases after each reorganization. Now I will send you on the weekend with a chemistry joke. We have to have a little bit of humor. I need it quiet, though.

It comes right over here. Actually, this one. We have to put the audio visual up. This is the one you need. You need this one right here. Can you see this? OK. Neutron walks into a bar and sits down at the bar.

The bartender looks at him and says I know you. You're a neutron. He says, yeah, yeah, I'm a neutron. Neutron is kind of quiet. Finally, he looks up and says how much for a beer? The bartender says, "for you, no charge." OK.

Get out of here. Have a nice weekend.