Program 28 - "Empty Atoms"

 

MusicAh, I don't know what to do.Two thousand years I've been looking for these.Two thousand years!When I finally find them, they're empty.Empty atoms.What good are empty atoms?What am I going to do with empty atoms?What good are empty atoms to anybody?I don't understand.Two thousand years...MusicSilico: "We are back with Science 122, The Nature of Physical Science.This is the telecourse that leaves you with that empty feeling.This is Program 28, Lesson 4.6, Empty Atoms."Before we're done with this program, we will have studiedthe relationship between electricity and magnetism,the composition of atoms, and the early attemptsat understanding their structure.We will see how atoms can be studied by shooting bullets at them.And how they behave quite different than what we expect,sometimes behaving as waves, and other times behaving as particles.

 

The photoelectric effect will show us that their particlebehavior is consistent and will lead us to the understandingof the atom as a quantitized system.The relationship between waves and particles will be extendedfrom light to matter in general as we engage in a paradigm clash,the resolution of which, will allow a deeper understandingof atoms and their properties and the role of electronsin chemical bonding and the macroscopic properties of matter.Here are the objectives for today's lesson.These objectives are also in the Study Guide at the beginning of the lesson.Before you begin to study the lesson, take a few minutesto read the objectives and the study questions for this lesson.Look for key words and ideas as you read.Use the Study Guide and follow it as you watch the program.Be sure to read these objectivesin the Study Guide and refer to them as you study the lesson.Focussing on the learning objectives will help youto study and to understand the important concepts.Compare the objectives with the study questions for the lessonto be sure you have the concepts under control.

 

Well, here we are with Program 28.This material in this program today represents a radicaldeparture from the physics we've come to know and love.We included it in the program becausehistorically this is exactly what happened.There was a radical departure from Newtonian physics thatoccurred around the beginning of the 20th century.Historically, it's important in our modern understandingof matter, including everything from chemical bondingto lasers and everything in between.So, we won't have to go through all the paradigm shatteringtrauma in this class which accompanied the acceptanceof these ideas into the scientific community.There are still, in fact, many people within the scientificcommunity who do not accept this quantum theory and stuffas final truth about the small world inside the atom.But, it's fairly well established and it certainly helps usto understand a lot of things that we use in our modern world.So what happened was that around the turn of the century,in the 1890s, basically, the structure of the atom wasinvestigated using radioacivitity, which was discovered in 1898,and, new kinds of matter were discovered at the small scale.These were the subatomic particles, the proton and electron.

 

The neutron wasn't discovered until the 1930s.It was also discovered that light has not only wave likeproperties, and behaves like a wave, for example, in thingslike diffraction, but it also has particle-like properties.So this wave/particle duality was another one of those Millerlight search controversies that people finally cameto reconcile to the wave and the particle nature of light.So, all of this together, leads to understanding of the atomicspectra which we talked about in the last program,and the chemical properties of the elements whichwe'll talk about in the next program.So this material is really thetie-in between understandingatoms, not just as sort of these fuzzy things that go aroundbumping into each other like in kinetic theory or reactingwith each other chemically like in the atomic theory,but things which have structure.And it turns out that the structure, specificallythe electrons surrounding the atoms,is responsible for almost all of the properties of matterwhich we observe on the large scale.So one of the things we need to understand is howto get magnetism from electricity.

 

Now this is a very simple connection and was discoveredalmost accidently by Hans Ursted, a school teacher in Holland,who was trying to prove that there was no relationship.So, let me show you a couple of things.I have some things on the table here, and let's see if we can geta close up of this, we'll see what I have.First of all, I have a magnet.Secondly, you'll see that the magnet affects this, this pieceof iron, which is actually a vertical compass.It measures the vertical deflection of the earth'smagnetic field, but it also is attracted by magnet.I also have a jar of paper clips.You can see that an ordinary magnet simply attractsthe paper clips and magnetizes each of them in turn.So, the rest of this now is the length betweenelectricity and magnetism.I'll use those again in a minute.So what I have here is a coil of wire.It's simply a bunch of wire wrapped around a hollow cylinder.

 

Inside I have some bars of iron, because the barsof iron increase the strength of the magnetismand make the effect look a little better.In fact, here I have a power supply which does nothing morethan send electricity through this coil and generate the magnetism.So, you'll notice here that the magnet deflects thisand whenever there's no magnet around it, this is pretty stationary.So watch what happens when I flip the current on, to the coil.See how it affects the compass, turning itoff...turning it on...affects the compass.Not only that, but it affects the magnet.In fact, if I put the magnet in here, and turn this on,you see that it exerts a force on the magnet.So, it has no effect on the magnet when it's just sittingstationary, but turning it on causes this to exert a force on the magnet.In fact, it's enough to lift the magnet up and down.It will do the same thing with the paper clips.

 

If I put the paper clips out here, this should be prettyinteresting, let's see what happens.I turn this on.Watch what happens.All the paper clips get stuck to the bottom of the magnet,and turning the switch off and on, lifts the paper clips upand down, each time, turning the magnetic field on and off.So, the idea here is that there's some relationshipbetween electricity and magnetism, and electricityis simply moving electric charges.So, the movement of electric charges somehowgenerates a magnetic field which affects iron objectsand other objects that are attracted by magnets.So we can also get electricity from magnets,as well as getting magnetism from electricity.I've put a meter on here, and we've used a meterbefore to show that the presence of electricity or the existenceof electricity flowing in the circuit.So, what I want to do is to take these two magnets and showyou what happens when I run them back and forth in the coil.So let's go to a closeup and see what we can get here.

 

Notice, if I put the magnets inside here, that as long as they'rejust sitting there, stationary, nothing happens.But what happens if I move them back and forth?You see that on the meter there's a jump of the needle indicatingthat there's a current flowing through the meter.Not only that, but if I put the magnets in the other side,you notice that the opposite thing happens.In other words, putting them in one side is like pulling it out of the other side.So, again, we don't have to go through all of the detailsof what's going on here, except to note that there's a relationshipbetween electricity and magnetism, and when oneof them moves, it causes the other...A moving magnet inside the coil causes electric current.

 

A moving current around the outside of the coil causesmagnetism, and it's this connection between electricityand magnetism that helps us understand the nature of lightwhich will eventually help us to understand the nature of the inside of the atom.The first thing we have to look at in terms of lookingat the structure of the atom is the discovery of cathode rays.It's kind of an interesting story.In 1875, a glassblower named Heinrich Geissler inventeda high vacuum pump, a pump which he could use to causea high vacuum, meaning a very low air pressure inside a tube.He evacuated the glass tube.A little later, a man named Plucker, sealed wiresinto the end of this Geissler tube and connected it to a battery.He discovered that a current would flow through this tube,even though there was no substance inside it.

 

Now, ordinarily, a substance is required to conduct electricity.So, this, by the way, was the forerunner of things likefluorescent lights and TV tubes, and even the neon lights.A little bit later on, a man named, Crookes, used an induction coilto produce cathode rays in what's now called a Crookes tube.I have an example of these here.This is a Crookes tube.Notice that its an evacuated tube.This one has the fluorescent screen inside it.It's got metal electrodes at the end.The induction coil is induction coil, we call a Tessler coil,which uses ordinary house current and changes it into high voltage.So, let's fire these things up and see what they do.I have in front of me now what's called a Crookes tube.

 

Crookes was a glassblower who in the 1870s was blowing glassand playing around with taking the air out with the vacuumpump and passing electricity through to see what happens.What happens is something very different.First of all, let me turn the test coil way up and you'llsee several things happening.First of all you see the green.The green is actually a fluorescent screen,much like the screen in your television.And we turn this up, more and more you see a blueglow from the left hand side of the tube.The blue glow is the actual cathode rays.You see, it's sort of here on the left hand side of the tube.The blue glow is what's known as cathode rays because theycome from the cathode of the tube.

 

Now, Crookes didn't have a test coil like this, but he used thehigh voltage electricity he generated in his laboratory.So, here's the weird thing.I have this fluorescent piece in here because the fluorescentpiece is a way of demonstrating what happens to this beamof cathode rays when in the presence of a magnet.So, I'm going to turn this down a little bit.I think to keep the intensity, there we go.So what happens when I put the magnet near it?Notice that the presence of the magnet bends the rays.In this case they're bending, the magnet's bending themdownward, away from the magnet.If I turn the magnet upside down, now they're bentupwards toward the magnet.Notice that the bending doesn't take place near wherethe magnet is, it takes place on the other end of the tube.

 

I should point out to you, those of you who are watchingtelevision right now, that this is exactly what happens in your television screen.That there's an electromagnet inside there that's able to movethe electron beam back and forth to spray a picture on the frontof your television screen on the fluorescent tube.The big question here, though, is what is the nature of thesecathode rays and where do they come from?I want to point out again that there's a vacuum in the tube.There's no air inside here.So, what exactly is this that's passing from one end of the tube to another?The answer is, they were called cathode rays and to see whatthey're actually called and what they're actually made out of,requires a little bit further investigation.So those are cathode rays in the Crookes tube.

 

One of the things that Crookes also observed was that the raystravel in straight lines as they go through the tube,unless they're being bent by the magnet, and also that they cast a shadow.You can put something inside the tube and you can seethe shadow that's cast by them.So, the presence of these cathode rays, then, caused manyquestions, and also prompted very much further study.For example, the cathode rays produced by differentsubstances have similar properties.

 

Now, keep in mind that, when I say differentsubstances, there's nothing inside the tube.The tube is a vacuum.But, if you use different metals for the electrodes,the cathode rays have the similar properties.So, here's some of the questions that come up:What's the nature of these rays?Are they waves like light, or are they some sortof particles, pieces of the atom?It was determined that they carry negative charge, negative electric charge.This you can tell by the way it's deflected by which poleof the magnet causes repulsion and attraction and so forth.But, those questions are kind of trivial really.The main question is, where do these things come from?There's nothing inside the tube.That means that they have to come either from the glass or from the metal.There's no substance inside the tube, and not only that,but its continuous supply of electrical energy producesan unlimited supply of cathode rays.As long as you keep the current flowing, the cathode rays keep coming.Where do they come from, where do they go?And, here's the biggest problem.How do the similar substance, different substances,I should say, produce the same kinds of rays.This must mean that somehow there's something similarinside all these different metals that has exactlythe same properties that can be released.Well, the answer to this question came with the discovery of the electron.

 

So, let's turn our attention now to the discovery of that subatomicparticle that we now know as the electron.The discovery of the cathode rays set off a whole cascadeof events which culminated with an upheaval in the scienceof physics which lasted for 30 years of so.We don't have time to detail all of that.It's a fascinating story.A couple of good books on that.One of these is by George Gamoff called, "Thirty Years That Shook Physics.Tells about the introduction of the quantum theory.But for our purposes we just want to relate thisto the idea of the pieces of atoms.So, the next step in this comes with a man namedWilliam Thomson who is credited with the discovery of the electron.What Thomson did was to take the rays in the Crookes tube,the cathode rays and recognized that they were deflected notonly by a magnetic field, but also by an electric field.In other words, if you put two charged electrical plates,or two electrical charges around them, you can also use that to bend them.Thomson also confirmed that this beam carried a negative electrical charge.

 

Now some people thought that this was the negative fluid of Ben Franklin.Other people thought it was something else.In fact, Thomson suggested that it was pieces of the atom thatwere broken off by the electrical energy.Thomson was able to show that the rays were made outof particles rather than a continuous fluid or waves like light.He did this by a rather ingenious experiment.Now I can't go into the details of this experiment because I don'tthink you'd want me to show you the mathematics that'sinvolved here, but it has to do with the fact that knowingthe formula for calculating the force due to an electric fieldand knowing a similar one for the force due to a magnet field,Thomson was able to measure the deflection of the beamby adjusting electrical field and magnetic field so theycounterbalanced each other.In doing this, now this interesting, what he was ableto do, was not to measure either the charge or the massof this particle, but he was able to measure the ratio of the charge to the mass.

 

Now the ratio of the charge to the mass is simply a number thatrepresents in an equation, the ratio "e" over "m," "e" beingthe charge on the electron, "m" being the mass of the electron.Now you can guess that the mass of the electron is really quitesmall, and so is its electric charge,and Thomson was unable to measure either one.What he was able to do was to determine that there'sa number, the number is 1.76 times 10 to the eleventh coulombs per kilogram.Coulomb is an electric charge, kilogram is a mass.Now, you don't have to know this number, and you don't even haveto be aware of the concept of the charge to mass ratio,but we need to understand that if something has a particularcharge to mass ratio, it means that it is a particle and not a stream of waves.Something can't have an individual mass and anindividual charge, unless it's a "thing" itself.

 

 

 

So Thomson had showed that this was a particle which he called the electron.The word came from the Greek word for amber, "electros,"and the word, "o-n," is something that's always been used for a particle.So, Thomson went on to note that these must be something thatwere broken off of the individual atoms becausethey're the same for all different substances.In fact, all the cathode rays that form from all the differentmetals, not only have the same properties otherwise,they all have the same charge to mass ratio.So, the next step in this comes with the determinationof the charge on the electron which, of course, once you knowthe charge to mass ratio, and you can measure the charge,then you can measure the mass of the electron.The real discrimination of the electron as a particle havinga discrete charge and mass came from a unique experimentand an ingenious experiment done by Robert Millikan.

 

Millikan used a series of experiments between 1909and 1916 to balance the electrical and gravitationalforce on small charged oil drops.Now this is a very ingenious experiment, and it's such a simple experiment.That's why I want to take a minute to show you how this works.What he did was to use an atomizer, just an ordinaryperfume atomizer, and put this, using this spraysmall drops of oil into a dark box.The dark box had a light source so that you could see the oil drops illuminated.Sort of like the way you can see fog in your car headlights.He had two electrical charged plates, positively chargedon the top and negatively charged on the bottom.And he could control the intensity of this electric charge.So what he would do would be to squirt the atomizer and thenturn up the electric charge on the plates, look through thetelescope until he found an oil drop that was exactly suspended in midair.

 

Now the oil drop is suspended by what forces?And this is why I wanted to talk about this for a minute.Because here we have a combinationof electrical force and gravitational force.The oil drop is suspended according to Newton's first law.If it's suspended and not moving, therefore, the forces on it are balanced.So, what are the forces?Well, there's a downward force of gravity on the oil drop thatwould tend to pull it downward, but at the same time,it's negatively charge, and so, it's pulled upwardby the positively charged electrical plate.So, knowing the amount of charge on the plates, Millikan couldcalculate the electrical force on this oil drop and comparethat with the gravitational force.Now you can say, "Well, sure, he could calculate the force on it,but he doesn't know how many electrons are on that particular oil drop."In fact, every time he did this, the oil drops were slightly different sizes.So, the result of this is very interesting, because Millikanwas able to figure out the charge on the electron.The way he did that was very ingenious, and I can give youan example of this by using the concept of lumps of sugar in a cup of coffee.Suppose that you did not know how much sugar there was in a lump of sugar.Now this is an analogy so you have to stretch the imagination a little bit.One way you could figure that out would be...oh, let me just put it this way.Suppose that you had many cups of coffee, all of which had,had some amount of sugar dissolved in it.

 

Now, if the amount of sugar dissolved in the coffee wasvariable, in other words you just poured it out of the box,you wouldn't expect any relationshipbetween the amount of sugar in one cup and the amount of sugar in another cup.But, if the sugar comes in lumps, each lump has the same size,then if you look at the total amount of sugar in each cupof coffee, the total amount should be some multiple of one lump.That make sense?So if you analyze, you have all these cups of coffee thatsomebody's put some amount of sugar into, and you analyze,you take the coffee away and analyze how much sugar is in them.If all the sugar is in some multiple of the same basicnumber, then you would assume that, that basic numberrepresents the smallest unit of sugar.In other words, the size of one lump.So this is basically what Millikan did.

 

I should also point out that when you calculate the chargeon the electron, then knowing Thomson's charge to massratio, you automatically also measure the mass of the electron.So, in a similar way to the way Cavendish measured the massof the earth indirectly by balancing forces, so Millikanweighed electrons, in a similar way by balancingelectrical forces and gravitational forces.It turns out, by the way, that the mass of the electron is very, very small.It's about 9 times 10 to the minus 31 kilograms,and if you're not mathematically inclined, that would be a zeroand a decimal point and 30 zeros and then finally the number 9.This turns out to be about 1/2000 of the mass of a hydrogen atom.And we'll see how that's determined a little bit later on.

 

I should also point out that because of the ingenuityof this experiment, and because of the importance of it,Millikan won a Nobel Prize for this.So, it just goes to show you, you don't need elaborate equipmentnor great ideas to win a Nobel Prize.This is one of the simplest, but yet, most elegantexperiments in the history of science.So I said earlier that there was a cascade of events that happened.That cascade began with the discovery of the Crookes tube;went on to Thomson and the electron; to Millikan and the mass of the electron.But, back at the turn of the century, to back up a little bit,was the discovery of x-rays by a man named Roentgen.Now this is an interesting story because it wasentirely an accidental discovery.Roentgen was studying the cathode rays in a Crookestube, and he had his Crookes tube covered with black paper.He noticed when he turned the lights off in the room thathe had some fluorescent material on the bench over here besidehim, and when the lights were turned out, when the Crookestube was turned on, this fluorescent material glowed across the room.

 

He concluded, somehow, that the light came from the Crookes tube.But he was able to discover that the cathode rays do not traveloutside the tube for very long distances.In other words, you can, there are ways to test this.And there was no source of ultraviolet radiation,which also causes fluorescence anywhere in the lab.So, he called these,simply, x-rays.The word, "x" for unknown.He published his results, and this led to immediate medical applications.In fact, one of the first pictures ever published of an x-ray wasa photograph of a person's hand through x-rays.So, he established the source and the nature of the x-rays.And he knew that they originated somehow at the endof the Crookes tube where the cathode rays strike,not the end that the cathode rays come from, but the end wherethe cathode rays run into the other end of the tube.

 

He also determined that they were not deflected by electricfield or magnetic field, so that these particularrays were not charged particles.He recognized that they had wave like properties.They can be polarized, diffracted, reflected and refracted likewaves, and that their frequency is considerably higher and theirwave length considerably shorter than ultraviolet light.So here we have another form of something coming outof the atom, or that's related to the Crookes tube, unknownx-rays.The x-rays are really only important to us because it wasthe discovery of x-rays that also cascaded theninto the discovery and the explanation for radioactivity.

 

The discovery of radioactivity was oneof those fortuitous accidents.It was one of those things that, like many of the discoveriesin science, was entirely unexpected and entirely unexplainable at the time.It was discovered accidently by a man names Becquerel who wascurious about this fluorescence coming from the x-rays,caused the x-rays, that Roentgen had discovered.Becquerel was aware that certain natural crystals, like uraniumores and calcite will fluoresce or glow when illuminatedby ultraviolet light, and alsoby x-rays.He also knew that uranium ores would darken photographicfilm when it was exposed to light.

 

He discovered by accident one night that light was notnecessary, that the uranium ore would darken the photographicfilm even in the absence of light.He did this by accidently leaving a piece of uranium orein his drawer in his studio, in his laboratory, I should say,and with the piece of photographic film.He found the photographic film and didn't know whether it hadbeen exposed or not, so decided to process and see what was on it,and he found the image of a key that had been in the drawerwith the uranium ore and the photographic film.So, he did all kinds of different things.He discovered other properties.For example, he discovered that uranium salts will continueto emit these rays for an indefinite period of time.And he discovered that they'll radiate whether or not they'rein crystalline form or in compounds or in solutions.In fact, chemically processing the uraniumdoesn't have any effect on it at all.And that they radiate in proportion to the uraniumcontent, and the more uranium that's there, the more rays they have.The significance of this was overshadowed in its time by the discovery of x-rays.

 

Now, Marie and Pierre Curie get credit for most of the workwith radioactivity because Marie was a graduate student workingunder Becquerel, and he turned over this whole thing to her,pretty much losing interest in it.Further studies by Ernest Rutherford, who we'll comeback to and look at a little bit later,showed that this radioactivity had three different components.And he used, basically, the electric and magnetic fields,the same kinds of things that Thomson had donewith the cathode rays to determine the properties of these.He called these two of the kinds of rays, alpha and beta,the first two letters of the Greek alphabet.He discovered that alpha particles are heavy and they carrypositive charge, and they're stopped by thick paper.In other words, they don't have much penetrating power.And that they have the same charge to mass ratio as a stream of helium ions.In other words, they are particles,fairly massive, carrying a plus two electric charge.The beta particles, on the other hand, are light weight.They carry negative charge.They're stopped by thin pieces of metal.And here's the interesting part, the important part.These beta particles are exactly the same charge to mass ratioas the cathode rays that were produced in Crookes tube.

 

Now, the problem, of course, is obvious.On one hand you have these things being created in the Crookes tube.On the other hand you have them being spontaneouslygiven off by radioactive decay.By the way, a third componentof the radioactivity was discovered later by Rutherford.These turned out to be more like x-rays.They're waves instead of particles.But here's the nature of the problem.Number 1, where do these things come from inside the atom?How is the atom arranged?How are the charges arranged inside the atom?And Number 2, which turns out to be probably a more seriousproblem and one that it took Einstein to figure out,is where does the energy of these particles come from?Remember, conservation of energy?Here you have these particles.They have mass.They're rushing out of the, out of these decaying atoms at highrate of speed, so they have kinetic energy.Where does the energy come from?Is this a new source of energy.Does it violate conservation of energy?We'll have to wait a little bit later to find out the answer to that one.So, the first model of the atom is called various things,depending on whether you live in England or the United States.

 

In England it's called the plum pudding model.Here in the United States we tend to call it the fruitcake model.Here's the problem.It's apparent that the atom contains both positiveand negative pieces, because in radioactive decay,positive pieces like helium nuclei come outand negative pieces like the cathode rays come out.So, it's also apparent that the electrons can be knocked outof the cathode ray tube, and the pieces of atoms areejected in radio active decay.So, all this together means that the positive and negativecharges must somehow be together in the atom.Now this is difficult, right?Because positive and negative charges do tend to attract each other.So, the question is, how are these positive and negative charges arranged?The chemical model tells us nothing about the charges.In fact, at this point in history, there was no concept at allof any connection between chemistry and electricity,except, in Faraday's account.

 

Thermodynamic models, the kinetic theory of gasesdoesn't tell us anything about this.So, the simplest model which was put forth by Thomson iswhat we might call this fruitcake model.This we have a simple structure with electrons imbeddedin a positive atom, much like pieces of fruit in a fruitcake.The electrons can be kicked out according to this model by electrical energy.So, it's sort of like the electrical energy comesalong and kicks an electron out.The electron goes flying away; becomes a cathode ray.And also under radioactive decay, for some reason,as yet unexplained at this time in history,the electrons simply go flying away on their own.The problem is that this does not explain the atomic spectra thatthe individual spectrum of individual elements,and it also does not explain the chemical properties of the elements.So, the fruitcake model is a good point of departure,but it's not a very good model, as models go.The next step in determining the structure of the atom and howthese positive and negative charges were arrangedin the atom came with Ernest Rutherford.

 

Rutherford was a New Zealander who was working in England.Rutherford has several distinctions here.He was actually the first of what we might call today the big scientists.I don't mean he was 6, 9 and weighed 400 pounds.I mean that he was one of the first people to run a big sciencelab where he didn't do all the work himself.He had a whole bunch of assistants and lots of grantmoney and everything to come in to work on things.So, what he did basically, was to decide that he could useradioactivity to examine the structure of the atom.This is very much like, well, it's sort of a crude approach,when you think about, it's very much like, if you wantedto know what was in a tin can, one way you could do would beto shoot holes in it with a gun, and look at how the holeson one side where the bullet goes in and comparewith the back side where the bullets come out.And you'd notice, for example, if there was a rock suspendedin the middle of the can, that where ever there was a rock,the bullet would enter the front, but not come out the back.So, if you took enough shots at the can, you'd find that thepattern of holes in the can would reflect the shape of somethingimpenetrable inside, if it was in there.This is Rutherford's model.

 

So, what he did was to use alpha particles to shoot bullets at gold atoms.He did this because gold is the most massive and, I should say,the most dense substance known, so the atoms in gold,Rutherford reasoned, should be massive and close together.He observed that the alpha particles passed right through.I have to show you this setup here.What he did was to take an alpha particle source, like a pieceof uranium, put it inside a lead tube, so that the alphaparticles, remember the alpha particles are those radioactive particles which have a charge to mass ratio like those of helium atoms.So the alpha particles would come straight out of the tube.He put a piece of gold foil and surrounded itwith a scintillation screen which is like a fluorescent tube likethe one you saw, fluorescent plate, I should say,like the one you saw on the Crookes tube.What he expected to have happen was observe somesort of scattering so that the alpha particles would collidewith the atom in here and be deflected much likea bullet would ricochet off a rock.

 

He expected to find most of the countson the scintillation screen over here.Instead, what he found was that most of the alpha particlespassed completely through the gold foil without touching anything at all.In other words, they were not deflected at all.In other words, the atom is mostly empty.Occasionally he found that one was scattered to the side a little bit.And one of the great moments in science came when Rutherfordwas having a cup of coffee, actually.His assistants were watching the scintillation screen and theycame running down the hallway of the research lab, yellingfor Rutherford to come to the lab because they had discovered ascintillation on the back part of the screen.And nobody else, of course, in the lab had any idea what was going on.

 

So, Rutherford comes running down the hallway to find ascattering way back here on the back part of the screenindicating that one of those alpha particles had hit somethingvery hard inside the atom, and was deflected almost straight backwards.So, whereas most of them were reflected to the side,many of them were deflected backwards.So, Rutherford then was able to calculate the relativesize of what he called the nucleus of the atom,simply by looking at the percentage of those particleswhich were scattered backwards as comparedto those which passed through.It's sort of like saying if you're shooting at the tin canand it has a rock inside it, and you look at the bulletsand you shoot 1000 bullets and only one of them hitssomething, then that gives you an idea that the thing that it hitis only 1/1000 of the size of the thing you were shooting at.So this is what Rutherford calculated.He calculated the nucleus of the atom to be about1/1000 the size of the atom itself.

 

Now what this means, of course, is that the atom is mostly empty space.And from this model, Rutherford put togetherwhat we now call the nuclear model of the atom.The nuclear model simply is that most of the mass of the atomis collected at the center and contains the positive charges.Why positive charges?Because the alpha particles which were scatteredwere positive, and positive repels positive.So, if you have a positive nucleus and a positive particle comingat it, the two are going to tend to repel each other, and when theyhit head on, they'll move backwards.If it's an electron or if it was negatively charged,the positive alpha particles would be attracted to it and would stick to it.So, what does all this mean?It means that if the nucleus of the electron or the atom ispositive, then the negative charges much be in orbit.Here we have Kepler's model of the solar system,the Copernican model of the solar system with the nucleusat the center and the electrons moving around it in atomicorbits that resemble the planetary orbits with lotsof space between the electrons and the nucleus.

 

Now I want to point out that there's a couple of things wrong with this model.And this is the controversy that caused the necessityfor further investigation into the structure of the atom.Here's the problem.When you have a nucleus and you have an electron in the circularorbit around it, you may remember that, from Newton'slaws, that something that's moving in a circular orbit is accelerated.Remember, centripetal acceleration.Newton used this to prove the theory of gravity.From the theory of electromagnetism,which had been worked out in the mid 1800s, it became clearthat whenever you have an electric charge like an electronthat's accelerated, it should radiate light and lose energy.And so classical theory, the theory of light, electricity,light and magnetism, predicted that if you had an electronin orbit like this, it would gradually lose energyand gradually spiral into the nucleus, becoming stuckto the nucleus, and so that the atom would become unstable.And the classical theory predicted that an atomshould have a very short lifetime.That's about one billionth of a second it would take for each atom to decay.So, here's the problem.

 

The theory says that atoms ought to do one thing,but atoms actually do something else.So, how do you put it all together?What's the answer to this?The next piece in this puzzle of trying to put togetherthe structure of the atom comes from a rather unlikely place.It actually comes from a graduate student named Max Planckwho was studying something that seemed to be entirely unrelated at the time.He was studying the radiation given off by a hot object.Remember the fact that hot objects radiate?Well, there's a problem here.The problem, I won't go into great detail, but it had to do with thefact that when something is glowing, energy is exchanged.The problem had to do with what's called blackbodyradiation, and Planck was looking theoretically at a box whichwas heated to a certain temperature, and he waslooking at the energy exchanged between thewalls of the box and the light that's given off.So, you've got to understand here that within the closed box lightis given off from one side and it's absorbed on the other side,and there's sort of a constant exchange.

 

At a given temperature there's an equilibrium herebetween radiation absorbed on one side of the boxand radiation given off on the other side.But here's the problem.That the classical theory, again the same theory thathe predicted that the electron ought to spiral into the nucleusof the atom, predicted that as time passed in this warm box,that the frequency of the radiation ought to get,ought to change color, and the radiation ought tobecome bluer and bluer and bluer.This was referred to by physicists of the time as the ultraviolet catastrophe.Because, eventually the radiation would become so blue that itwould pass out of the visible spectrum and become ultraviolet.Now again, this is theoretically what the theory said oughtto happen, and, of course, this doesn't really happen whenyou look at the radiation inside the box.Part of the problem with the theory was that in orderfor this to happen, it would violate conservation of energy.So, Planck was a graduate student, as I mentioned.He was working on this as part of his Ph.D. thesis,and he couldn't solve the problem.So, he decided to invent a fudge factor which would solve the problem for him.What he did was to make a simple assumption.And then again, this was intended simply as a mathematical toolwhich would mess the theory with the observationand explain part of the discrepancy here.

 

So, here's the assumption Planck made.He said, "Suppose, just suppose, that energy can only beexchanged in proportion to the frequency of the radiation."So, if the energy can only be exchanged in proportionto the frequency of the radiation, that means that the colorof the radiation determines how much energy can be absorbed.He came up with a number, which is today called "Planck'sconstant," which relates the energy of a particular amountof, packet of radiation, to its color.And the significance of this as we'll see in the next topicin this program is that it ascribes particle like properties to radiation.And what it means is that the higher the frequencyof the energy, the higher the exchange particle.Now, maybe I should say it this way.The higher the frequency of the radiation, in other words,the bluer the color, the larger the energy packet that has to be exchanged.

 

Now again, I don't expect you to understand this in the samedetail that a nuclear physicist would, we're not nuclear physicists here.The point is that Planck makes this assumption which saysthat energy can be exchanged only in a certain quantum or a certain size of energy.And what he sees now, is that the observed spectrum of this hotobject is a balance on one hand, because on one hand you have alarge number of low energy quanta, each with a small amount of energy.But on the other hand, you have a small number of high energyquanta, each with a large number of energy--a large amount of energy.The best analogy I can give for this is, supposed that you havea business where you make change.But suppose that you have a rule where you only willaccept nothing smaller than $20 bills.So, somebody comes in to buy something and it costs $5,and so you only accept $20 bills, so what's going to happen?Well, somebody comes in to buy something for $5,but they have to give you $20 for the $5 object.Can't you see that you're going to get richer and richer?And they're going to get poorer and poorer?So, you'll find that over time you'll have very few peoplestopping at that store, even though the amountof money exchanged is fairly large.On the other hand, if you have a store that takes $1 bills,you'll have a large number of people shopping there,but the total amount of transactions won't be very much.

 

So the balance between the two stores would be a balancebetween a few high energies and a large number of small energiesso that the average is sort of a peak in the middle, whichrepresents the light given off at the frequency of the averagekinetic energy of those atoms that are vibrating.I know this quantum theory doesn't seem to make muchsense, but keep in mind that Planck put this forward simplyas a way to get himself out of trouble, and it was accepted.His Ph.D. thesis was accepted, and as we'll see, it was Einsteinwho really caused the trouble with Planck's quantum hypothesis.So the next piece of the puzzle now has to do with anotherphenomenon discovered around the same time as Thomsondiscovered the electron, which is known as the photoelectric effect.

 

Now, again, we don't have to know the details of all of this,but it's interesting to see what the photoelectric effect is,and how Einstein's solution caused a major uproar in physics.So here's the photoelectric effect.It was observed that under certain conditions light caneject electrons from the surface of a metal.In other words, if shine light onto the surface of a metal,sometimes, electrons will be given off.Much in the same way that they're given off from the cathode ray tube.It turns out that the energy, the kinetic energy, of the electronsdepends upon the frequency of the incident light and the type of metal.In other words, it depends on the color of the light.So, below a certain frequency, that is, light less than acertain color in the spectrum, will eject no electrons.And above that cutoff frequency, electrons are ejected and theyall have the same amount...well, they don't have the sameamount of energy, but they have a limited maximum energy.What this means is that as you increase the intensityof the light, the number of ejected electrons increases,but their maximum energy isn't effected.What's this got to do with anything?What does this mean?Well, let's look for a minute.

 

In classical theory the energy of waves is proportional notto the intensity, but to the amplitude of the waves.If you look at waves crashing on a shoreline, the taller the wavesare, the higher the waves are, the more energy they have.So, if you notice in a typical wave, if you have a rocksitting on the shore and that rock is going to be picked upby a wave, it's the height of the wave that determines whetherthe rock gets picked up or not, not the wave lengthor the frequency of the waves.So, the question becomes, how can an electron sitting hereon the piece of metal absorb just the right amount of energyregardless of the intensity of the light?In other words, why should increasing the intensityof the light allow the electron to be kicked out,whereas increasing the color doesn't?In other words, how can the wave of light store up just exactlythe right amount of energy until the right amount of energy hasbeen absorbed by the electrons so that it can take it out.You see what's happening here is that people were tryingto apply too closely the idea of Newtonian mechanics.And what's needed here is some other explanation.Well, the photoelectric effect notwithstanding, even if youdon't understand it, the idea is that somehow there'ssomething wrong with the old classical wave theory.

 

Now it was our friend Einstein who gave a nice simple answer to this.Einstein simply went back and, by the way, Einstein was awardedthe Nobel Prize for this, not for relativity or for Brownianmotion, both of which he came up with in the same year,but simply went back to Planck's hypothesis and said that theenergy of the light is proportional to its frequency, and that eachmaterial has a given energy barrier to overcome.In other words, it's sort of like the electrons are stuckinto the metal, and you have to kick them with a certainamount of energy, and once you do, then they come out freely.So, the light with more energy than this amount necessaryto pluck the electrons out ejects the electrons.And it turns out that when do an experiment to check this out,you find that this is exactly what happens.That the light exchanges energy with the electrons muchthe same way that it exchanges energy with the particlesin the box in Planck's quantum hypothesis.So, what Einstein had done was to generalize Planck's quantumto all types of electromagnetic radiation.And, showed that light has wave properties sometimes,but when it exchanges energy with other things, it behaves like a particle.The solution to this problem of the structure of the atom camefrom one of the most brilliant physicists of the 20th century.His name was Neils Bohr.

 

Bohr was famous, not only for this description of the atom,but for engaging in wonderful debates with Einstein,with whom he had many disagreements about certain things.You can imagine that to debate with Einsteinrequires a fairly good level of intelligence.In fact, he used to send Einstein home from these debates,trying to think about what Bohr had come with and tryingto refute it., and many of which Einstein could not do.So, Bohr solved the problem of the nuclear atom, and he assumed,and this is a wonderful use of creativity and creative thinking in science.He assumed that there must be some new principle at workthat we're not aware of, since we observed that atoms are mostly stable.In other words, our observations do not matchour theories, so the theory must be wrong.We're not going to throw out all of Newtonianmechanics, so there must be some new principle.So what he did was suppose that the momentum of the electronin its orbit is quantitized the same way that energy is.You remember momentum from way back earlier in the programs.And that he suggested that the orbits of the electron arestable only for certain values of momentum.In other words, the electron can't just have any orbit, not like theplanets, but can only exist with certain levels of momentum,and he used Planck's constant as the quantum of momentum,figuring that it worked for energy, why not work for momentum.

 

Interestingly enough, now he did simple calculations, very simple.I don't want to show you these but they're complicated onlybecause they contain a lot of terms in the equation,but the calculations are very simple.He did the calculations to determine the radiusof the hydrogen atom, to determine how big it oughtto be and the results agreed almost exactlywith the measured size of the hydrogen atom whichhad been done by other means before.He also then did simple calculations to determine theenergies of these allowed quantum states assumingthat the momentum was quantisized.And he showed then that the difference in energy levelscorresponds to the wave lengths of the hydrogen spectrum.In other words, the energy levels as well as momentum are alsoquantitized in the atom, and that the difference in the energylevels corresponds to the wave lengths of the hydrogen spectrum.In fact, he went on to derive the Rydberg formula.And I can show you how this works on a graphic.

 

The Balmer series, you may remember, was figured out by Balmer.These were the four bright lines in the hydrogen spectrum.This equation is the Balmer equation.And you may remember from the last program that the valuesof "N" here took on the values 3, 4, 5 and 6.What Bohr was able to show was that the energies whichcorrespond to the third, fourth, fifth and sixth levelsof quantitization within the atom represent the energytransitions that will give you the hydrogen spectrum.Here's what I mean by that.Now, these numbers refer to energy levels.The easiest way to visualize this at this point is simply to thinkof these as distances away from the nucleus of the atom.So that the "N' equals one level is closest; "N" equals two level isfurther away; the "N" equals three is further away, and so on.You also notice that the energy levels get little shorter each time.If you wanted to think of this in any reasonable sort of way,think of it as like a stadium with this as the playing fieldand this being the bleachers where the widthof the bleachers gets less and less each time, and their heightgets less and less as you go up toward the top of the stadium.

 

So, what Bohr was able to show was that if you lookat the energy transitions from energy level 6 whichis the outer one to energy level 2, which is the inner one,that corresponds exactly to the blue line in the hydrogen spectrum.In other words, looking at the energy differencebetween the two levels, multiplying that energydifference by Planck's constant, gives exactly the frequencyof that light that's used in the Rydberg formula.You notice here that all of these numbers in the Rydberg formulastart with the number 2, and they involve the numbers 3, 4, 5 and 6.So, what Bohr was able to show was that the Balmer seriesis the transitions that take place from higher levels,3, 4, 5 and 6, down to level 2.That's why the 2 appears here.You also remember from last program that Rydberg had goneon to show that this number could be 2, 3, 4, 5 or 6.It wasn't limited to 2.So, what happens then is that the other lines that show upin the hydrogen spectrum represent transitionsfrom higher levels down to other levels other than 2.For example, when the number in the Rydberg formula is a 1,that represents what we now call the Lyman series whichrepresents transitions from higher levels down to the "N" equals 1 level.And other things, like, for example, the Paschen seriesrepresent the cases where this number 3, which representall of the transitions from energy levels down to level 3.

 

Now, the beauty of this is that it not only explains the structureof the atom, but it also explains the hydrogen spectrum;the use of the concept of electrons; it uses the ideaof nucleus of the atoms; it ties in with Planck's theoryof radiation; it ties in with Einstein's explanation of the photoelectric effect.In other words, what we got here is a model which ties togethermany of these unexplained things that had been discoveredin the previous 15 years before Bohr came about this model.So the next stage in this mystery of putting the piece of the atomtogether comes from another young graduate studentwho was working on a Ph.D. thesis for which he was awarded the Nobel Prize.

 

Now it's pretty nice to be a graduate student and beawarded a Nobel Prize for your Ph.D. thesis.That sort of sets the stage for your career.The man's name was Louis DeBroglie.He was a Frenchman.He asked a simple, but creative question that had to dowith Bohr's explanation for the energy levels in the atom.He simply asked, if light waves can have particle likeproperties, is it possible that particles like electronscan also have wave like properties?In other words, is there a symmetry involved here.And what DeBroglie did for his thesis was to calculate thewave length of a beam of electrons.

 

A wave length of a beam of electrons.What a concept!So, what he did here was to come up with a formula, and again,I don't want to derive how the formula was, how he cameabout the formula, but notice what it involves.It involves the concept of wave length, but it also involves thisnumber called Planck's constant which is related to the energy of the light.Notice that the energy of the light is Planck's constant times thefrequency, whereas the momentum of the light isrelated to Planck's constant and the wave length.Remember, in earlier programs, that energy and momentumwere very closely related to each other.So, the important thing here is that the beam of electrons hasa wave length which involves its momentum and Planck's constant.

 

So, what DeBroglie found then was that if you take this as aquantitized momentum, remember that Bohr had started outwith the concept of quantitized momentum and put thisrelationship back into Bohr's equations, that you find thatthe electron orbits are quantitized because the orbits are in resonance.Now to find out what we mean by resonance, I have to goto the ELMO and show you something.So, here's a, the nucleus of the atom that's positively charged,and here's the orbit of an electron.Now I'm taking circular orbits here, and it turns out thatit's really more complicated than this, but how would youdetermine which orbits are allowed?Well, remember that each electron has associated with ita wave length which depends upon its momentum.So, suppose that you consider a wave length.I'm going to draw down here a wave.Here's a wave.

 

A wave has certain wave length which represents the distancebetween the crest and the trough of the wave.What happens if you try to put a wave like this into a circle?Well, let's see.I can't draw this perfectly well, but notice if I try to make awave in a circle, that if I have the wave lengthwrong, it doesn't line up at the same place.Here I happen to draw a fairly nice wave.So, notice that the wave length here on the circleis proportions of the arc of a circle.So, what's all this mean?What DeBroglie had discovered was that the only orbits whichare allowed for the electron in the atom are those which thecircumference of the orbit is an integral number of wave lengths.Notice the use of the word, an integral number of wave lengths.The word, integer.Remember Pythagoras?Talked about things being integral?You see why it's an integral number of wave lengths don't you?Let me go over here and we'll see one more example.So, here's another atom.Here's the positive nucleus.Here's an orbit.Suppose that I try to put a number of wave lengths in here that's not integral.Then the electrons simply can't have a stable orbit becauseit basically interferes with itself and it doesn't allowit to have an orbit in that particular place.

 

So, the idea of the quantitized orbits has to do with thisquantification of the momentum.So, what's interesting about this now is that within a fewmonths after DeBroglie came out with this idea, it was shownthat a beam of electrons produces a diffractionpattern, much like a beam of light does.Remember diffraction?The diffraction grading and how it spreads out and how we usedthis to discover the hydrogen spectrum?We now see that a beam of electrons will do the same thing.By the way, just as a closing on this particular topic,it's that property of electrons that allows us to use theelectrons in electron microscope to see these beautiful imagesthat you see sometimes of the eyes of fliesand the small crystals and that sort of thing.The reason is that electrons have a smaller wave length thanlight for a given energy, so the smaller wave length allows usto see smaller things without destroying themwith that amount of energy.This whole thing, from Thomson's discovery of the electronto DeBroglie's explanation of matter waves, encompass the time of 17 years.

 

This was a major paradigm transition, major paradigm clash.And what we have here is on one hand you have the classicalphysics of Newton, and the idea of light as a wave.On the other hand you have this new physics which involveselectrons and energy coming out of the atom and energytransitions and quantification and all this stuff.It was a real hard time for physics.In fact, much controversy followed, considering thisreconciliation of this wave particle duality over the next 30 years or so.So it turns out now that today we understand that quantummechanics is the science of the very small and that whenwe look at things on the very small scale, things behave quite differently.It doesn't invalidate the Newton world view, it simply causes usto reformulate it a little bit at the smaller levels.What it has done, is to lead to deeper understandingof the chemical properties and also to the structure of the atom itself.So, it's to those chemical properties that we want to turn.And in our next program, we'll do that and we'll take a look nowat how the Bohr atom relates back to the idea of atoms aschemical entities when we come back and try to explain chemical bonding.So what have we really learned in this program?I know it was confusing, and there was a lot of things goingon here, but it's all important stuff, because it's going to helpus explain chemical bonding and the chemical propertiesof the elements, and this is really the connectionbetween physics and chemistry.So, what have we really done?

 

In this program we looked at the discovery of the election,and then we've seen how radioactivity ties inwith the idea of pieces of atoms because one typeof radioactivity was the same stuff as the cathoderays which turned out to be electrons.Then we looked at Planck's quantum theory which heintroduced almost against his will to explainsomething else which had to do with light.Then we looked at the photoelectric effect whichhas relationship between light and electrons.And then we put this all together with the Bohr atom.

 

In the meantime, of course, was the discovery that the atom'smostly empty space which necessitated Bohr comingback and looking Planck's hypothesis and quantitizing momentum.Then we come back and look at DeBroglie who notes that thereason things are quantitized is because matter behaves likewaves and electrons are actually waves.So, all of this now will set us up for the next program which willlook at chemical periodicity and chemical bonding.So, I hope you can follow this a little bit, even if it is confusing.Check the textbook and I think it will begin to make some more sense for you.Well, that's all.That's it for Program 28, so remember, when it comes to science, get physical.Bye.So, did you enjoy this program?Silico: "That was really confusing.Do I have to know this for the exam?Are my electrons grantitized?Why are you looking at me like that?"Music