The Science of Everything Podcast - Episode 8: The Atom

Episode Date: November 21, 2010

An examination of the atom, beginning with the origin of the concept in ancient Greece, and its subsequent development as a truly scientific idea in the 19th century. I explain the various important contributions made to the field by Thomson, Rutherford, Planck, Einstein and de Broglie, and the resultant evolution of our models of the atom. If you enjoyed the podcast please consider supporting the show by making a paypal donation or becoming a patreon supporter. https://www.patreon.com/jamesfodor https://www.paypal.me/ScienceofEverything

and welcome to the Science of Everything podcast. I'm your host, James Fodor. In this podcast, I discuss a wide variety of topics in the natural and social sciences, exploring the many fascinating scientific discoveries that can help us to better understand the world around us. In this eighth episode, the topic will be the atom. And so in this episode, I'm going to look at the basic concept of what is an atom, and then go through the history of the term, and more specifically a look at the different models of the atom that have been used

and changed throughout the mostly 19th and 20th centuries as new scientific discoveries have been made. So to start off with, what is an atom? Well, basically an atom is just the smallest unit into which any substance can be decomposed or broken down into whilst still retaining its chemical properties. So each different element can be, like, for example, iron, tin, silver, gold, etc., can be broken down into smaller and smaller pieces until you get to an atom. Once you get to an atom of gold or silver, of oxygen, or whatever, you cannot break it down any further without destroying the unique chemical properties of that atom.

The term atom was originated in ancient Greek philosophy, where it was used to describe the smallest bit of matter, or the smallest piece of matter that could be conceived of. The word actually derives from the Greek word atomos, which means indivisible. So the concept was that this was kind of the smallest piece of matter you could imagine, and that it was indivisible, you couldn't divide it anymore. We now know today that that's actually false. atoms are not the smallest bit of matter, and atoms can be further divided, but it's just kind of a fluke of history that we came to have a word to describe atoms,

which means indivisible, which is not actually true, and you'll see that as I described the history of our understanding of the atom. So anyway, the idea of an atom came up in ancient Greek philosophy and was sort of thrown around and discussed. Some people believed in it, some people didn't. By the early scientific revolution in the 17th and 18th centuries, most scientists did believe in the concept of atoms, though at this stage there was little empirical support for the idea. Empirical support for the atom will not come until the 19th century, and I will talk about that momentarily.

First, though, I just want to give you an idea of how big an atom actually is. Now, I'm sure you all know that atoms are very small, but it's hard to really get to really get a little. a grasp of just how small these things are. So I've converted the relative sizes of a few different things to objects that you might be a little bit more familiar to you. Okay, so if we take the distance from the North Pole to the South Pole, which is 20,000 kilometers, so that's halfway around the Earth's circumference, let's suppose that that is as big as your fingernail, which is approximately one centimeter across. So your fingernail is expanded to the distance from the to the South Pole. If we do that, then the size of a single cell, a single animal cell,

compared to your fingernail, is the same or equivalent to the size of a medium-sized city, about 20 kilometers, relative to the distance between the north to the south pole. So if your fingernail was as big as the earth, basically, a cell, a single cell would be the size of a city. So, how big is an atom? Well, on this scale, an atom would be about the size of a basketball, about 20 centimeters across. So if our fingernail was the size of the earth, or the size of the distance from the north to the south poles, an atom would be, on that scale, only the size of a basketball compared to the size of the earth. You can see that that is very small, a basketball compared to the earth. That is just incredibly tiny. And if we're

looking at the nucleus of the atom, which is the small part of, the dense part of the atom in the center, which contains most of the mass of an atom, the nucleus on this scale would be about the size of a very small grain of sand, less than a millimeter across. So just to recap, if your fingernail was expanded to the size of the earth, an atom would be about the size of a basketball, and the nucleus of the atom would be about the size of a grain of sand. So that perhaps gives you some idea of how small atoms really are. They're not just small, they are really tiny. They are really tiny. Okay, so now let's move on to the more modern history of atoms, beginning with the discoveries that supported the existence of atoms in the 19th century. In 1803, English natural

philosopher called John Dalton used the concept of atoms to explain why elements always react in ratios of exact whole numbers. And so to explain this empirical result, which had been shown by a number of experiments in the 18th century, he proposed that each element consisted of atoms of a single unique type, and that these atoms could join together to form chemical compounds in specific ratios. For example, we know now that two hydrogen atoms and one oxygen atom make up a molecule of water. So as a result of these theories, Delton is considered to be the originator of monatomic theory, and this was one of the first key evidences that atoms really do. exist. Another line of reasoning to support the atomic theory was began in 1827 when botanist Robert

Brown used a microscope to look at dust grains floating in water and observed that they seem to move about erratically, randomly, just jiggling from side to side. This phenomenon became known as Brownian motion, and it seemed to support the idea that there was some kind of force being exerted upon these grains of dust by atoms. And indeed, this is a theory. that was put forth by Albert Einstein in the famous paper in 1905, where he explained Brownian motion in terms of the water molecules continuously knocking the grains of dust about, so that when more water molecules hit one side of the grain of dust, it moved. It was pushed in one direction, and if more water molecules just happened by chance to hit the other side, it jiggled in another direction. And so the collision of water molecules or atoms with the grains of dust is what caused the erratic motion. And this was further support for the atomic theory of matter, because before this time there were some who thought that matter was continuous, sort of like a line, so that you could divide matter up into any arbitrarily small division

that you wanted, as opposed to atomic theory, which held that matter was discrete, and that there was a limit to how finally you could divide it. However, the work of Delton and later Einstein clearly provided support for the idea that atoms existed and their format was discrete and not continuous. Now, in the late 19th century, there were further important discoveries made which provided new insights into the nature of these atoms, which had just been discovered, as I just discussed, and one of these was the cathode ray tube. Now, what is a cathode ray tube? Well, basically, a cathode ray tube is just an evacuated glass tube, so evacuated meaning most of the air is pumped out, with two electrodes at one end.

So, in the late 19th century, a man named Thompson took these fancy new inventions, these cathode ray tubes, and produced some very interesting results on them. He found that when a certain amount of air was removed from the tube, sparks began to move. began to jump between the two electrodes, and when even more air was removed, the sparks disappeared, but instead a green glow was visible at the opposite end of the tube to the one where the electrodes are placed. And it was found that this was always opposite, particularly this green glow always appeared opposite the negative electrode. And further, that a metal object placed in the middle of the tube cast a shadow on the glow that appeared at the other end. It was also found that magnets placed in the middle of the tube deflected this glow, which were referred to with cathode rays, the supposed rays that were generating

this green glow, thereby demonstrating that whatever was causing the glow must be charged particles because they were affected by a magnet. When an electric field, as opposed to a magnet, magnetic field was applied across the tube, the direction in which the glow, and therefore the rays, was deflected by the electric field, demonstrated that the, whatever was causing it, had to be negatively charged. So now we know that they are not only charged particles, but they have to be negatively charged. But what the heck were they? No one knew what these things were. However, Thompson examined the amount of deflection from his electric field, and doing so was able to calculate

the mass charge ratio, so the ratio of the mass of these particles to their electric charge of whatever it was that was causing this funny glow. And it was found that this number was about 2,000 times smaller than the mass to charge ratio of the hydrogen ion, which was essentially the smallest atom. Now, by assuming that the charge of both the hydrogen atom and this new particle were the same, Thompson determined that cathode rays must have a much smaller mass

than the hydrogen atom, about 2,000 times smaller. And if these new particles had a mass of only 1,000th of a hydrogen atom, that meant that the atom had probably been split. And Thompson's supposition that the charge of this particle must be the same as that of a hydrogen ion, which is just a proton, was confirmed by Robert Milliken in 1910, in an experiment where he showed that electric charges of, always come in whole number multiples of a given base, and that therefore these new particles

that Thompson had discovered would have to have the same charge as a hydrogen atom, and then hydrogen ion, excuse me, and therefore based on the amount of deflection that they showed when placed in an electric field, they must have a mass only one two thousandth of that of the hydrogen ion. And so it was conclusively proven that the atom indeed had been split. And if you hadn't guessed by now, these new particles that Thompson had discovered were in fact electrons, negatively charged, whereas protons are positively charged. Okay, so as a result of these experiments, Thompson developed the first model of the atom, which is now referred to as the plum pudding model. In this model, these negatively charged electrons were spread throughout some positively charged material which formed the rest of the atom. So basically, according to his model, an atom was like a pudding.

Most of it was positively charged, but there were these tiny negatively charged electrons dotted throughout, and so the atom's whole was neutral. Had no charge. And he also theorized that the number of electrons and their precise arrangement determined the element and therefore the exact properties of the atom. And these properties were well known because they'd been explained by Mendelief, who had constructed the famous periodic table a few decades previously in around the 1860s, 1870s. So it was known that different atoms had different properties,

and Thompson suggested that this was based upon the, as I said, number and arrangement of the electrons in this kind of pudding substance of positive charge. There are a variety of things that this model could not explain, which I won't go into right now, what we'll talk about later, and we now know that this plum-putting model of atom is quite incorrect. So I'm just bringing it up now for historical interest. Don't think that it actually reflects what an atom is, because it's quite inaccurate. Okay, so stepping forward in time, we have a new physicist called Rutherford,

and he worked in the early 20th century. Now Rutherford did experiments firing alpha particles, which he used because they were about the size of an atom, an alpha particle we now know is two protons and two neutrons, and carries a net charge of positive two, though at the time he didn't know that. He just thought that they were kind of basically helium atoms, smallish atoms.

So anyway, he was firing these alpha particles at a thin sheet of gold foil, and by doing so, he hoped to determine the size and shape and structure of atoms. Now, according to Thompson's model, the positive material in the atom was too spread, out to make much of a difference, to interfere with anything, and therefore he expected the particles to pass straight through the gold foil.

His astonishment, however, well, most of the particles did pass straight through as he had expected, but to his astonishment, some of them were def-some of the alpha particles were deflected right back at him, and he compared this to 19-inch shells, as in artillery shells, being reflected off of tissue paper. It just didn't make sense to him. The alpha particles, according to the current theory should have, because of their kinetic energy and their size, should not be affected at all by the tiny, thin strip of gold foil. And so what on earth was going on here? So on the basis of this experiment, Rutherford hypothesized that all of the positive charge of an atom

must be concentrated at a tiny spot in the centre. And this would explain his results, because most elf particles passed straight through the tinfoil because the atoms in the alpha particle, the nucleus of the alpha particles and the nucleus of the gold atoms missed each other because they were very small and so most of the atom was just empty space

and so most of the time the alpha particles just sailed right through. But occasionally an alpha particle nucleus would come very close to or actually strike a gold atom nucleus and when that happened there was a significant amount of mass that was involved, relatively speaking, and so the alpha particle rebounded. And so Rutherford calculated, using data from his experiments,

that on this model the size of the nucleus would have to be 100,000 times smaller than the size of the atom, which means that atoms were mostly empty space. And this comes back to the size of the nucleus that I mentioned earlier, that if the nucleus, sorry, if the atom was the size of a basketball, the nucleus would be the size of a tiny speck of sand. It's just, and remember that that nucleus comprises the overwhelming majority of the mass of the atoms. So, virtually all of atoms are just comprised of empty space, which is something that Thompson, when he originally discovered, the electron, had never imagined. And so, on the basis of this discovery, Rutherford proposed a new, model of the atom. You could think of this as atom 2.0. This was the solar system model.

He proposed that electrons orbited about a positively charged nucleus in a similar way to which the planets orbit about the sun in the solar system. So you know that the planets go about the orbit around the sun in elliptical orbits. And the reason that they stay in those orbits is because although they are attracted to the sun by the force of gravity, they also have perpendicular velocity to the Sun, so they're kind of moving away relative to the Sun. And these two forces cancel out, resulting in a perpetual, close-to-circular motion around the Sun. And I refer you back to my first podcast on explaining gravity for a bit more of an explanation on how these orbits work. But basically, Rutherford proposed that the same basic thing happened in atoms.

The nucleus was positively charged, and electrons were negatively charged. So you would expect the electrons to be attracted to the nucleus. But the reason that didn't happen is because they were constantly, is because the electrons had a perpendicular velocity, and so we're kind of trapped in an orbit about the positively charged nucleus. And this is the model of the atom that you may have learned back in high school or in a similar situation, because it's still frequently taught today,

even though we, as I'll explain later, it's not quite correct. However, there was one fatal problem with Rutherford's model of the atom. Specifically, according to Maxwell's equations, which describe the electromagnetic force, when you accelerate a charged particle, and of course an electron is a charged particle, it should emit light or electromagnetic radiation. Now, as an electron was orbiting around the proton as Rutherford had hypothesized, it did, it would have to be being accelerated by the proton. Now, normally we think of acceleration as a change in velocity, a change in speed, but actually you can, acceleration refers also to a

change in direction of the direction of travel of something. So as a result of the attractive force between the proton and the electron, the direction of travel of the electron is constantly being changed, and that's why it's constantly going in a circle about the nucleus. Otherwise, it would just keep going in a straight line and would fly off into space. So the fact that the electron is orbiting the nucleus clearly demonstrates that it is being continuously accelerated by the nucleus. But as Maxwell's equations show, when you accelerate a charged particle, it should, in fact it must emit electromagnetic radiation. But if electrons were constantly emitting electromagnetic radiation, they would also be constantly emitting energy. And therefore, they would constantly be

losing energy, which would mean that they would constantly be slowing down as they traveled about the atom. And this would be demonstrated by the electrons gradually spiraling into the neutral, to the nucleus, as they lost energy and therefore traveled slower and so gradually captured, if you like, by the protons in the nucleus. And according to this model, calculations were done that showed that as a result of this process, atoms should collapse in about a billionth of a second. And clearly atoms did not collapse in one billionth of a second, so something had to be wrong with the model. And Rutherford just basically said, in a rather hand-hand-waving fashion, that, well, maxes, Maxwell's equations did not apply to the subatomic level and didn't really explain why. And so this was a big mark against Rutherford's model, or at least in the eyes of many scientists,

an indication that our understanding of the atom at that time was far from complete, and indeed it was not complete. And there was yet another problem with Rutherford's model, and indeed with other models of physics at the time. So this problem was not unique to Rutherford's model of the atom, it was a broad problem, and it's called the black body paradox, the black body radiation paradox. Now, to explain this problem, we just need to step back a bit and talk about what black body radiation is. All objects glow by emitting

electromagnetic radiation, which is light. The hotter an object is, the more radiation it emits, and therefore the brighter it glows. Now this might sound a little bit counterintuitive, but just think about a piece of metal. If you put a piece of metal in the fire, gradually it starts to glow and then it starts to glow brighter and brighter and brighter as you heat it up further. The sun glows extraordinarily bright, partly because it is really hot, and therefore emits a lot of EM radiation just by black body radiation. Humans also emit black body radiation, although the reason you don't see other people glowing is because humans are relatively cool, and therefore most of the radiation we emit is in the

infrared spectrum, which is light that we can't see. But if you've ever seen those, seen the dark goggles or infrared cameras or whatever, where people appear as kind of red and purple splodges, which walk around, that's detecting the black body radiation that human bodies give off as a result of our temperature. And so, not only does...

So as an object heats up, it emits more radiation, so it glows brighter, but it also emits a larger fraction of its radiation in higher frequencies. Higher frequencies of light correspond to higher energy, more energy in each photon light. Now, experiments by the late 19th century had shown that this black body radiation, the distribution of frequencies of light emitted by black bodies,

was the same for all objects and that were at the same temperature. So whether you were a pig, a blade of grass, a rock, or anything, you would have the same black body radiation spectrum as long as you were at the same temperature. It didn't matter what material you were made of or anything as long as you were at the same temperature. But as temperature was increased, the distribution would change, so you would emit more light,

and more of that light would be at a higher frequency. Okay, so that's the basic idea of black body radiation. So you might ask, well, what's the paradox? This all seems to make sense. Well, back in the late 19th century, physicists could not really explain why, obviously it made sense that more radiation would be emitted as you increased temperature, but what they couldn't explain was why the frequency of radiation increased as the temperature increased. Nor could they explain why there was a peak of intensity of radiation at a specific wavelengths,

which then declined for shorter and longer wavelengths. In fact, according to the theories of the time, the intensity of emitted light should have increased exponentially so that effectively a black body should, according to their equations, have been emitting an infinite amount of wavelengths of high frequency. So basically the black body radiations that were shown to occur from experimental data did not, were inconsistent with those predicted by theory, and they could not explain the difference. Particularly, they couldn't explain why there was a relationship between the temperature of an object and the frequency of radiation that emitted.

And this black body paradox was a huge problem in physics in the late 19th century. Until, in 1900, along came Max Planck, a person of whom you may have heard. So in 1900, he was able to solve the black body radiation paradox by using a mathematical technique where he assumed that radiation or energy was quantized into tiny chunks rather than being continuous as previously thought. So if you remember, in the start of this lecture, I started this podcast, I talked about how atoms, the discovery of atoms showed that matter was quantized rather than continuous. There was a limit to how far you could go and breaking it down until you reached a basic core

entity which couldn't be broken down any further. Max Planck proposed that energy was the same way, that there was a limit to how far you could break energy down, that it was therefore quantized into small chunks, into small units, and it was not continuous. In fact, this was in such sharp disagreement with the consensus of the time, because it had long been thought that light energy was continuous, was a wave. this was the consensus for so long that Max Planck did not actually propose that light really was quantized, he just sort of said,

well, this is a useful mathematical technique that we can apply to solve the blackbody radiation paradox, but, you know, we don't have to take it too seriously. Ironically, that was also the same sort of justification that was put forth by Copernicus when he proposed his hideocentric model of the solar system. But that's a separate issue. Max's theory required that

so-called atomic oscillators could only vibrate at certain discrete energies which would mean that they would only emit light in tiny discrete bundles which he called quanta and these atomic oscillators it doesn't really matter what they were but they were supposed to be the things that were emitting light

so the idea was that these atomic oscillators which were in some way related to atoms emitted the light, the frequency at which the atomic oscillators vibrated, determined the frequency of the light that they emitted, and also the fact that the atomic oscillators could only vibrate at certain discrete energies, so, you know, maybe a wavelength of one or two, but not 1.5, so the wavelength of these atomic oscillators was quantized, meant that therefore the wavelength of the light or energy emitted by the atomic oscillators

also had to be quantized at these particular discrete energies. So, you know, you could have light with a wavelength of one or two, but not one and a half. And also, according to Planx-Max Planx equation, higher frequencies of radiation meant more energetic quanta. So higher frequencies translates to more energy. And this is a principle that was prior to this time not known or not understood. And so this new idea of atomic oscillators with quantized vibrations and therefore quantized emissions of, in the frequency of life that they emitted, and also with higher frequencies,

translating to more energy, if you put it all into the equations that did all the math, it solved the problem. And I won't go into all the details of that now because I don't really understand it myself, and it's rather complicated. The point is that by making this assumption of quantization of energy and quantization of vibrations,

Max Planck was able to solve this black body radiation paradox. However, there was another problem of physics, around the late 19th century. So we'll come back to the Max Planck's solution a little bit later. This other problem was called the photoelectric effect problem. Basically, and this one's a little bit simpler to understand than black body radiation, the photoelectric effect referred to the observation that when you shined light on certain polished metal surfaces, electrons were ejected from the metal atoms. Now this isn't perhaps that surprising. What was more surprising was the way it happened. It was found

that the maximum possible energy of the emitted electrons depended on the color of the light, while the rate of the ejection of the electrons was determined by the intensity of the light. However, changing the intensity of the light did not change the maximum allowable energy of the electrons.

And this didn't seem to make any sense, because according to the continuous theory of light, the continuous theory of energy at the time, the more light you shine on it, so the more intense the light became, you should get more energetic electrons being ejected. Not just more electrons, but more energetic electrons as well. But that was not actually what happened. Also, it was thought that the longer you shine the light on the surface, the more radiation and the more energy would be absorbed. And so the more energy the emitted

electrons would have. But this also was found not to be the case. As soon as you started shining the light on the metal surface, electrons of the maximum allowable energy would, start being reflected off, ejected off, and no matter how long you continue shining the light on, the energy of those electrons would not change. It would just be dependent upon the colour of the light. And this did not make any sense. This photoelectric effect paradox continued to plague physics until in 1905 Albert Einstein published another paper in which he drew upon the work of Max Planck to explain this photoelectric effect. Basically, he, by assuming that light itself was quantized,

that there were only certain wavelengths of energy that light could take, he was able to explain the photoelectric effect. So he borrowed this idea of quantization from plank and applied it to the photoelectric effect. Basically, the idea was that light itself was quantized and the units of light, the units that carried this quantized energy were called photons.

And whenever a photon struck an electron, so whenever a photon of light hit the metal surface and struck an electron, it gave up its entire energy to that electron. Now this explains why there was a strict maximum energy limit of the emitted electrons, because they could not obtain any more energy than that carried by a single incident photon. So, you know, an electron couldn't hang around and soak up the energy of several, photons before being emitted, as had been thought previously. It was a one-shot deal. You got the energy, and each electron got the energy of one incident proton, and that was it.

So that explained why there was a limit to the maximum energy. It also explained why emission could occur so quickly, because you only needed one collision. So as soon as the light starts hitting, you get a collision, and the electrons start being ejected out. You don't need any time for the energy to be soaked up in any way, because that's not what happens. Also, Einstein borrowed Plank's idea that the frequency of light was related to the energy of that light in order to explain why the colour of light seemed to matter, because he proposed that higher frequency light, which translates into different colour of light, the frequency and colour of light are closely related, they're basically the same thing. For example, red light has a lower

frequency than blue light. This difference in frequency between colours of light explained why the colour of light mattered in determining the maximum allowable energy of the electron because the higher energy of the light, the higher the energy of the electrons that it could emit. It also explained why the colour did not affect the number of electrons being emitted, because even if you have really high-energy photons being incident on the surface of the metal, you still only have the same number of photons. So you can't increase the rate of electron emission. The only way you can increase the rate of electron emission is to increase the intensity of the light.

so put more photons on it. So more photons incident on the metal means more electrons coming off the metal, but the only way to increase the energy of those electrons is to use a higher frequency of light, or higher intensity of radiation. So there was this separation between the intensity of the light, which was corresponding to the number of photons, and the energy of the light, which corresponded to the frequency of the photons. And so using this principle of quantization of energy borrowed from Max Planck,

Albert Einstein was able to explain, in a very persuasive way, the photoelectric effect. Now, you might be wondering what all of this stuff about black bodies and photoelectric effects has to do with atoms, apart from the fact that they seem to relate to small particles. Well, basically, both the black body radiation paradox and the photoelectric effect problem and Max Planx and Albert Einstein solutions to them seem to conclusively demonstrate that energy and energy was quantized like matter and so that it could not take on any old value you wanted

but could only take on certain specific values and that also energy was divided into discrete units called photons and this is very important for the later development of atomic theory So now let's move back into atomic theory by looking at the discovery of electron shells. Now, before we explain the genesis of electron shells, I first need to explain one last problem with the one last problem of 19th century physics, which contributed to the development of atomic theories.

We know it today. And this was the atomic spectrum problem. Basically, it had been found that whenever, you run an electric current through a gas or burn an element or in any other way sort of put energy into a particular type of, into a particular element, it emitted light in a specific characteristic color. And when you, when this light was put through a prism, it was found that it produced a pattern of discrete colored lines at specific frequencies. And these, so these frequencies of light that were emitted were found to be unique to each element and always the same for that element. And so we could actually use these unique emission spectrum, as they were called, to identify which element it was that was being burned or excited by electricity or whatever it was. So this was very interesting, these atomic spectra, but scientists in the 19th century had no idea why they occurred. There was no explanations to why some frequencies of light were emitted, and some weren't. And so this was the atomic

spectrum problem. Now, in 1913, a physicist by the name of Bohr developed a new atomic model, so this is atom 3.0, by incorporating Planck's discrete energies and Einstein's photons, so Planx and Einstein's quantization theories, into Rutherford's solar system model of the atom. So here we've got Bohr pulling together Planx, Einstein's, and Rutherford's models all into a single new model of the atom, as I'm calling it Atom 3.0. Now his new model was based upon several postures. First, he proposed that the angular momentum of electrons, orbiting about the nucleus, was quantized according to a particular equation. So this meant that electrons could only have angular momentum of taking particular values, not any old value that you liked, which classical theory would have would have held.

Now, the angular momentum of electron, by the way, is just a measure of energy related to the motion of an element, and elevation. electron, but particularly its motion in a circle, so angular relating to a circle, angular momentum is its motion in a circle, so it's kind of like the motion it has owing to its circular motion, the energy it has owing to its circular motion. Now, because the angular momentum of an electron depends upon an electron's mass, an electron's velocity, and also its distance from whatever it's traveling around, a restriction on angular momentum also places restrictions. on possible values of velocity and radius. Because all electrons have the same mass, so that one doesn't change.

So the point is, if you restrict the number of possible angular momentum values, you also restrict the possible velocities and distances away from the nucleus that the electrons can be. Now, because there also must be a stable relationship between velocity and radius, just like there is a, in Kepler's planetary laws, there is a relationship between distance from the sun and the velocity at which you travel. They're also, in order for electrons to maintain a stable orbit about the nucleus, there had to be a relationship between the velocity

at which the electrons were traveling and the distance they were from the nucleus. Basically, the closer they were to the nucleus, the faster they had to be traveling to stay in that sort of stable orbit, otherwise they would either fly off or spiral in. So V and R, velocity and radius, are related to each other. So basically, this is important because it means if you restrict angular momentum, you also restrict possible values of R, possible values of the radius of the orbits of electrons around the nuclei. So restricting angular momentum means that you can only have specific restricted distances of orbits of electrons around the nucleus. And therefore, the value of that electron's potential energy was,

dependent upon its distance from the nucleus, because of course as the electron and protons in the nucleus are attracted to each other, so if you like, in order to move the electron to a higher orbit, you needed to exert energy. You need to pull it away, if you like. So the further the electron was away from the nucleus, the more potential energy it had. Kind of like if you raise an object off the ground, it has more gravitational potential energy. In this case, if you move an electron further away from the nucleus, it has more electric potential energy. And so the quantization of angular momentum also translates into a quantization of the total energy of that electron. And so therefore, just by quantizing angular momentum, we get a discrete set of allowable energies for electrons around an atom. So why does this matter? Well, this matters because it could explain atomic spectra. Bors' idea was that when an elect if electrons absorbed or emitted exactly the right amount of energy, they could jump from one orbit to another. And so if they absorb some energy, say from a photon,

they could move up to a higher energy level, a higher orbital level, which was further away from the nucleus, and then if they emitted that energy back out again as a photon, they would jump down to a lower orbit, closer to the nucleus. And because these orbits, these electron orbits were only, at certain distances away from the nucleus, only certain amounts of energy could be emitted or absorbed at any given time, and therefore each element would emit light only at certain distinct frequencies. And this explained the unique atomic emission spectra of every element. I should say that every element had a unique spectrum because the exact energy levels would differ depending on exactly how many protons the atom had, how many electrons there were and stuff like that. interactions of these things produced slightly different energy levels for each atom, for each element, excuse me, and therefore each element had its own unique emission

spectra, which was explained in this way by Bohr's model. Boar also postulated that when an electron was in one of the allowed orbits, it did not radiate any energy, and he just argued that, well, Maxwell's equations, which said that it should emit energy, did not apply to the subatomic realm. And so using these three postulates, the postulate of quantization of angular momentum, the postulate of electrons jumping between one allowed orbit and another, and emitting radiation in the process, and the third postulate of no emission of radiation while an electron is within an orbit. Bohr was able to explain atomic emission spectra, and the paradox from Rutherford's model

that atoms should be unstable and collapsed in a fraction of a second. So this was a big step forward in atomic theory. Now this model of the atom, Boar's model, or Atom 3.0, is a reasonably good model. It explains quite a lot, and it's still widely taught, for example, in high schools to this day, but it does have its limitations. Most of all, it incorporated classical and quantum mechanical ideas, for example the idea of quantization in a rather haphazard manner, without any real explanation as to why it was being done. apart from in order to fit the data. For example, electrons were supposed to orbit the nucleus because of the electromagnetic force

in accordance with Maxwell's equations, but then Bor just threw away Maxwell's equations when these equations predicted that the electrons should constantly emit radiation and therefore should spiral into the nucleus. There were also additional subtleties to the spectral lines, which I won't go into now, but suffice it to say there were these subtleties

to the spectral lines which Boer's model could not explain. And these and various other problems led later physicists to develop fully quantum mechanical models of the atom, which are far more satisfactory, and now provide the best models for understanding the atom today. However, it seems that I have run up against the time barrier, and so I will continue this discussion about the current models of the atom, next week, along with, I think, an introduction to some basic principles of quantum mechanics, which are in fact necessary to understand monotomic theories. So hopefully you learn something interesting from this show.

And if you enjoy the podcast, please help to spread the word by posting a review on iTunes. I don't think I have any yet, or anywhere else you may feel so inclined to do so, or by sharing the podcast with a friend. If you have any questions, comments, suggestions, or anything else you'd like to say, please feel free to contact me. My email address is FODs12, that's FODS-12, at gmail.com. You can also find detailed show notes for this podcast and leave comments at my website, which is Scienceof Everything.webs.com. Thanks for listening, and I'll talk to you next week.