here and welcome to chapter 2. so in this chapter we're going to be talking about the nature of light and we're going to be looking at the bohr model of the atom we're going to be taking a deep dive into the wave nature of matter then we're going to flesh out what quantum mechanics is and how the atom plays a role here and lastly we're going to finish up by looking at the shapes of the atomic orbitals so let's get started shortly after the discovery of the electron in 1897 early 20th century scientists began investigating these particles and they took a deep dive into the absolutely small world or the quantum world of matter and scientists leading the way included albert einstein niels bohr louis de broglie max planck as well as many many others and their investigative work laid the foundation of our current understanding of matter and its behavior in the subatomic or absolutely small level among the things that they discovered is that absolutely small matter those subatomic particles protons neutrons and electrons behaved much differently than matter of the macroscopic world so up until the turn of the last century up until the discovery of the electron most of how it was that we interpreted the world was based upon the physics of isaac newton so he was the one who taught us that the apple falls from the tree and that we have the ability to predict how projectiles go through the air so and speed and velocity so he gave us these things but these things described what big objects objects that were made up of many molecules or many atoms how they behaved and so once they started looking at the electrons they discovered some very unusual things that they had not predicted and one of the things that they found is that subatomic particles appeared to exist in two conditions one was matter because these subatomic particles in fact do have mass and they do occupy space but perhaps more interesting is that they can also behave as wave as previously discussed electrons are incredibly small the number of electrons in a single speck of dust is greater than the number of people who have ever lived on the planet earth and despite the invention of the electron microscope observing electrons directly is impossible we're able to predict their behavior based upon their effects not by looking at what they do so why are we so concerned about the electron well it's because much of the behavior of atoms is determined by the electron so what does the quantum mechanical model tell us about the atom's electrons why are we even looking at this well quantum mechanics explains the manner in which electrons exist and behave in atoms and perhaps more interestingly it is the light wave the energy nature not the particulate or the matter characteristics of the electron that dictate or explains the chemical and physical properties of matter now that means that the electron then can no longer be viewed as a small piece of matter orbiting around the nucleus of an atom but that it exists more as a cloud of probable positions and we have to take a look at the wave nature of the electron in order to further explain these things so light is a form of magnetic radiation and it is composed of perpendicular oscillating waves one for the electric field and one for the magnetic field and an electric field is a region where an electrically charged particle experiences a force and a magnetic field is a region where a magnetized particle experiences a force so hence the word electro magnetic now all electromagnetic waves move through space at the same constant speed which is the speed of light and it has a value of 3 times 10 to the 8th meters per second that's going to be a value that you need to write down on your cheat sheet and make sure that you know what it is because we're going to be using it in a lot of different formulas and here's a nice image representing oscillation and if you think of the direction of travel as this straight line the oscillation of the two waves will either be around the line moving either above and below it as in the red wave line or from side to side as with the blue wave line we say that light comes in waves so what are the characteristics of these waves how can we describe them well two characteristics are amplitude and wavelength so what is amplitude well let's bring up a picture and take a look so we can say that amplitude is the height of the wave we can say that it is the distance from node to crest or node to trough so i guess what is a node well a node is this region right here where our wave intersects the line so from node to crest or from node to trough so it's that point furthest away from the line that our wave is going so that's the amplitude the amplitude is a measure of light intensity so amplitude tells us whether we're looking at a bright light or whether we're looking at a dim light now what is wavelength well wavelength is measured as the measure of the distance covered by the wave so given um the distance of our line we could say that a wave goes from here and it goes up and down and then back up so this distance right here would be the measure of our wavelength so we can say it's the distance from crest to the next crest or the distance from one trough to the next or the distance between nodes so i gave you the distance between nodes it could be the distance between the crest it could be the distance between the troughs but it however it is you measure you're going to measure it at the same point that the cycle is in so here this the cycle is starting in an up fashion and it doesn't start going up and crossing that line until it reaches right here so that's what that means so as previously stated amplitude represents how bright or how dim the light is and here you can see that represented in this graphic the the smaller amplitude wavelength wave has is the dim light and the larger amplitude would be the bright light so what does the wave length tell us well it tells us the color of the light so what do you notice about these wavelengths well you might notice that the longer wavelength is red and the less long or shorter wavelength is yellow and the shortest wavelength at least in this picture is blue so what the artist is attempting to convey is that different wavelengths represent different colors and that's true in life so what is the relationship between amplitude and wavelength then well actually none wavelength and amplitude are independent properties which means that one doesn't really influence the other you can't make a prediction based upon one given the other so this means that you can have a bright red light or you can have a dim red light and the same holds true for each color i mentioned color in the previous slide so what is color well color the color of light is determined by its frequency or by its wavelength and white light is a mixture of all the colors in the visible light spectrum so it includes all the spectrums of red of orange yellow green blue indigo and violet now we see here in this graphics a picture of a prism and it has white light going in and it has all of these different colored lights coming out of it the reason why is because the light gets diffracted as it moves through this medium the medium of the prism and then it comes out on the other side in a way that we can see each color distinctly but each one of those is contained in the white light which is why we're able to separate them now when an object absorbs some of the wavelengths of white light and reflects the others it's going to appear as though it has a color the observed color is predominantly the colors that are being reflected back so how does that work so let's say that we were looking at an apple so what's going to happen here well the white light is going to hit the apple and all the spectrum except one red is going to be absorbed by the apple and red will be reflected and that reflected light wave is going to penetrate through our pupil and hit a specialized cluster of cells in the back of our eyes known as the retina and then that is going to create a neurological event and it's going to cause that neurological impulse to travel through our brains all the way to the back way back here to the visual cortex at which point our brain will sort out all those impulses and say oh look it's red that's how we perceive color which is rather amazing when you think about it what if instead of a red apple we had a green one can you tell me what's going to happen here well everything except the green light will be absorbed the green light will be reflected it's going to penetrate the eye hit the retinal cells create a neurological impulse which is going to travel to the posterior part of the occiput of the brain and our brain will sort it out and say oh green okay so we've talked about two characteristics of light we've talked about wavelength and we've talked about amplitude another characteristic is frequency so this is the number of waves that pass a point in a given period of time usually it's measured in seconds because these guys are traveling pretty fast and the units used to measure frequency are the hertz or is the hertz and it's named after heinrich rudolph hertz of hamburg germany he was a physicist who made many discoveries regarding electromagnetism so that's what the hertz is someone's name so the unit of hertz is equal to 1s in seconds to the negative one now what does that mean well you might remember that anything written with a negative exponent can be written like this it can be one over that value so in our case it's 1 over 1 s to the power of 1. and i've left that exponent there so you kind of see how the that transition went now what could we add to the denominator to help us make sense of all this what is it that we're looking at that's happening in this one second well it is one cycle it is the one cycle of a wavelength in one second that gives us the measurement of hertz so because hertz is basically one cycle of our wavelength per second so let's bring up a wave how about this one right here now this is a relatively low energy wave so let's say somewhere in the red color range and if we bring up a timeline and there's our one second we can now see that this wave conducts a complete cycle that is it goes from up to down to back up that starting point in one second so we could say then that this wave has a frequency of one cycle per second or one hertz what about this wave well it goes from up to down to up that's one cycle and then down to up again and that's two cycles has two cycles in one second so what's the frequency of this wave well it's going to be equal to two hertz because it undergoes two cycles in that one second and what about this wave well this one goes down to up to down there's one and then up to down there's two and then it goes just to up before we hit that one second mark and that's only half a cycle so all done in one second we're going to have two and a half cycles which is two and a half hertz previously when we were looking at amplitude and wavelength i asked if there was a relationship between the two it could you determine something about amplitude if you knew something about wavelength and the answer is no these are values that exist independent of each other so then i guess we can ask ourselves is that the same case for wavelength and frequency and the answer is no there is a relationship between wavelength and frequency and the relationship between wavelength and frequency is one that is inversely proportional so what do i mean by that well let's bring up a timeline and our second mark and let's drop in our red wave so i'm going to measure from crest to crest and we're going to call this wavelength i'm not going to assign a value i'm just going to show you a distance so this is going to be our wavelength now previously we determined that this frequency was one cycle per second so we could say that it is one hertz which is one cycle per second now let's compare this to our blue light and let's take a measurement of its wavelength and we're going to drop it over here and you might remember that we said this was two and a half hertz its frequency was two and a half hertz so by looking at the information that we just put here to the right of both of our wavelengths we can determine then that when we have a long wavelength we have a low frequency and that's demonstrated by our red light wave what about our blue light wave well we have a short wavelength but yet we have a high frequency so this is demonstrating that when you have a large value of one you're going to have a small value of the other and vice versa this is the nature of inversely proportional relationships now can we encapsulate this with some sort of a mathematical formula indeed we can and it's going to look like this now you might remember that we said frequency has this symbol right here this is nu it's the greek symbol nu and it's equal to the speed of light which we represent as c over lambda which is the value of our wavelength so here's the thing with me and formulas if there's a formula that shows up in the chapter and particularly if you're doing homework utilizing this formula you can expect that formula is going to show up on an exam or a quiz maybe both so that's a little bit about how i test so this is a nice diagram of the electromagnetic spectrum so let's start by looking at the color red and if we look at red right here we can see that it has this 750 what is that 750 well that's telling us the wavelength wavelength is represented by the symbol lambda and we measure the wavelength in nanometers really really really tiny so relatively speaking that 750 nanometers is a rather large wave when you compare it to the other end of the spectrum which is violet violet's wave is 400 and is 400 nanometers which is almost half of what we have with red but if we look at the titles of um on this picture we can see that we have a long wavelength over here on the left and then over here on the right we have the short wavelength if we go back to the left we see a low frequency which corresponds with a big wavelength and if we look to the right we have a large frequency which corresponds to a short wave length so this is that inversely proportional relationship being demonstrated here on this diagram all right now i would first like to point your attention to these various regions where we have high low energy to high energy and we have these titles of radio microwave infrared visible light ultraviolet x-ray and gamma ray now where are the highest energy waves they're going to be to the right and the gamma waves are the highest energy waves now where might we find gamma rays well a nuclear explosion is known to have gamma rays and certainly those gamma rays are going to do some damage not because of just the force of the explosion but the gamma rays themselves emit these tiny particles that can disrupt our cells structure and function all right what's the next highest energy wave well that would be the x-ray and where do we find those yeah at the doctor's office here's an x-ray one of a nasty fracture in an arm it looks like that hurts so these are x-rays and what do what's next ultraviolet and where we're going to find ultraviolet rays yes our beloved sun so if you are a fair-skinned person such as i am we do love the sun but we have to watch how much we get of the sun exposure because it can cause a burn sunburn right all right so what is it that we notice about these first three waves well they can all do some form of biological damage so these are very powerful waves that can do harm to us and other animals and and plants alright so what's the next set of rays that would be visible light out of the entire electromagnetic spectrum this teeny tiny region is the only set of wavelengths that we can see right here pretty amazing when you think about it like that all right so who's after that that would be infrared now how do we experience infrared as heat we have special scopes that allow us to pick up the signatures heat signatures which is basically reading these infrared light waves so anything that is emitting heat is releasing infrared waves whether it's a mouse or you or your dog or the food that you just ate or a specially designed light source that emits heat for the purposes of emitting heat there are some therapeutic devices that use infrared heat in order to warm the tissues this is all a form of infrared light waves all right what's next microwaves and these are experienced as microwave ovens as well as some other waves but this is our most common experience of it and last but not least is the radio wave which can be experienced in the form of radio as well as some television now i'm going to go off script for a second because look at where cell phones reside they are almost slipping into microwave yeah so i don't know what to tell you i don't talk on my phone a lot i'll tell you that so what happens when you have more than one wave happening well there's a possibility of them interacting and the interaction between waves any wave whether it's a sound wave or a light wave or even an ocean wave the interaction is called interference now there are two types of interference one is constructive interference where the waves will interact in such a fashion that they actually make the wave larger and the other is destructive interference and you guessed it when that we have that type of wave interaction the waves actually cancel each other out and so we can see from the graphics how those two look now when waves encounter an obstacle or an opening in some sort of a barrier they're going to bend around it or go through it and this is called diffraction now think about the waves of an ocean when they these waves encounter let's say a piling at a pier they don't just simply stop if if they encounter that piling they move around it if they were to encounter a crack in a wall those waves would actually move through that little opening so when waves encounter some sort of a barrier and there's a way for them to move through it they will actually bend around it that is a nature of waves now what about this thought traveling particles particles do not diffract now for example if you were to shoot a bb gun the bb is going to travel until it hits something solid or it it exhausts its ability to travel but if this was a a particle beam shooting a bb any bbs that landed right here going to come to a sudden stop any babies that make it through the slit are going to keep going straight you see no bending around that opening or diffraction occurring with particles this only happens with waves so what about two openings these two slits in our barrier well the waves are going to pass through each slit and this will create two sets of waves that now have the possibility of interacting and with wave interaction you can have constructive or destructive interference now what experiments have shown us is that we will get an alternating pattern of light since these are light waves that we're talking about we're going to get an alternating pattern of light and dark indicating that alternating pattern of constructive and destructive interference was created so this is a little bit about how waves behave so among the many things that einstein studied was something known as photoelectric effect now einstein wasn't the only one to make this observation so let's look at what the observation is first the observation is that when light is shined on a metal surface electrons are produced from the surface so the electrons emitted from the metal surface are called photoelectrons and uh this phenomena is called photoelectric effect now because other people had looked at this as well they there was a theory that existed and the theory basically said that if the wavelength of light is made shorter or the light waves intensity is made brighter then more electrons should be ejected so the thought was that the intensity and the energetics of the light wave was what was forcing electrons from the surface of the metal sheet and furthermore the energy of a wave is directly proportional to its amplitude and its frequency remember amplitude is how bright or dim it is and the frequency is the number of cycles given a certain period of time so this is what the classical thought and the classical theory was that depending upon the energetics of the light um you would have this experience happen and that the more intense the light was the more electrons would be scattered so that's classical theory so after einstein had done some of his own work he came to disagree with the classical theory regarding photoelectric effect and he developed something that he called a quantum theory so based upon einstein's work he discovered that there is a minimum frequency of light needed before the electrons could be pried away from the metal and he called this minimum frequency a threshold frequency furthermore einstein contradicted his work contradicted the classical theory because he found that a high frequency light from a dim source caused just as many electrons to be ejected as a bright high frequency light did so einstein's work proved that amplitude had nothing to do with the number of electrons ejected or whether or not electrons were even ejected but it was the frequency of the light that made all the difference because remember amplitude isn't associated or tied to wavelength or frequency but wavelength and frequency have that inverse relationship furthermore einstein went on to explain that light energy was delivered to the atoms in these packets of energy called quanta or photons i typically use the language photons from this point forward so in the classical model the flow of light energy was considered to be like a ribbon it was considered to be like a stream and it just came out in this little you know flowy consistent um volume but einstein said no no no that light is not fluid it doesn't come out and flow like a ribbon would flow it's actually more like oatmeal very lumpy um and in fact the way that the energy comes at physical structures is more like um a spit ball so it's just like pow pow pow pow so it wasn't this lovely uh image that classical the classical theory regarding photoelectric effect would have you think so he this is why it's called the quantum theory is because it has to do with saying that these energy packets were distinct units and they could be um you could give them a quantity you could assign an energy quantity to them and that's what this equation is that we see on this slide this will be an equation that you need to know this is a formula that you need to know so what this formula is telling us is that the energy in a photon of light is equal to planck's constant which is represented by the h times the speed of light divided by the wavelength of that light so two of these values are constants and you can see them right down here and again these will be values that you want to have on your cheat sheet because we'll be using them a lot moving forward now before i i walk away from this i just want to point out that the original equation actually had frequency in it and what we know about frequency is that frequency is equal to the speed of light over lambda which is why we can throw in planck's constant and then come up with the energy of it so there's that so as einstein put this together even more he was examining his findings versus what the classical theory of photoelectric effect said because remember the classic theory basically said that the the higher energy your light source is the more electrons will be emitted but einstein's work proved that that wasn't the case so first of all we have this idea of the threshold frequency which means that you have to have a photon you have to have the light energy meeting the binding energy the energy that holds that photon to that sheet of metal your your light energy has to be at least that in order to pry that electron loose so there's this concept of binding energy that's basically our threshold frequency so those two are more or less analogous numbers it's the same concept is there there has to be a particular frequency of our light in order to help it overcome the binding energy that keeps that electron attached to the sheet of metal and when you have these electrons being irradiated by shorter wavelength photons what do we know about wavelengths that are shorter they're higher energy that when you have more energy being bombarded on that electron part of it's going to go to binding energy but then the rest of it gets absorbed by the electron and as a result you end up with a surplus that's called kinetic energy so think of it this way say like in the morning when you in order for you to get up and get moving you have to eat a pop tart so you eat your one pop tart that's enough to get you out of bed but let's say that you eat two pop tarts what's going to happen with the energy that comes from that second pop tart well that's the thing that's going to get you to run the mile after you get out of bed so we can think of the energy of binding energy being that first pop tart that's the thing that prize you lose but that second pop tart is the thing that's going to give you some energy of motion and that's basically the revolutionary idea that einstein came up with with regard to photoelectric effect all right let me ask you a question a metal will eject electrons from its surface when struck by a yellow light what will happen if the surface is struck with an ultraviolet light hmm well first of all we might want to know where on the big energy scheme of electromagnetism the yellow light lies and where the ultraviolet light lies so you may want to look at that lovely graphic there is a picture of that on your book in your book i don't know what page is on but let's see what the choices are the choices are no electrons will be ejected when it's been hit with the ultraviolet light electrons will be ejected but they'll have the same kinetic energy as those ejected by the yellow light electrons will be ejected and they will have greater kinetic energy than those ejected by yellow light or option number four electrons will be ejected and they will have lower kinetic energy than those ejected by yellow light so what is your answer well it really depends upon where the yellow light lies as far as frequency and the ultraviolet light doesn't it i'm kind of stalling to give you time to pull up the picture well if you look at the graphics of the electromagnetic spectrum because ultraviolet light has greater energy than the yellow light the electrons will be ejected and that that that extra energy from the ultraviolet light will be will be part of the kinetic energy that the electron will experience so it's the one pop tart and two pop tart sort of scenario right here so the yellow light is one pop tart and the ultraviolet light is two pop tarts