In this chapter, we're going to examine the electronic structure of the atom. How does the molecules interact with light, absorbing some wavelengths and reflecting others? And this is what um produces the colors that we see around us every day. So, molecules can interact with many forms of radiation, including visible light, which is the colors we see, ultraviolet light, x-rays, radio waves, there's the whole electromagnetic magnetic spectrum, which is shown here. Spectroscopy studies how substance absorb and emit the radiation. It's allowing us what to understand what's happening with that electronic structure of the atom itself. So we need to kind of talk about this and why we care. So why do we care about it? Why do we care about spectra, energy, frequency, wavelength? Oh, the quant quantum mechanical model. Let's talk about light. Light is energy. And when we pass light through a prism, we can look at the energy in the form of a spectrum or a range of colors. And that's what we see happening here. White light is being passed through the prism. And what's coming out the other side is this range of colors. So things like a light bulb, which are white light, give off a continuous spectrum. All the colors are light, are smoothly blended. When we look at light from a gas like hydrogen or helium, we get something really different. Just a few bright lines of color. This is called a line spectrum. We'll see that on another slide in just a sec. Let's talk through here. We've got your electromagnetic spectrum. An electromagnetic spectrum is just showing you your electromagnetic radiation. Electromagnetic radiation is a form of energy that travels through space at the speed of light. It has oscillating electric and magnetic fields. And if you zoom in here, you can see we've got our gamma rays, our x-rays, our UV rays. So here, gamma rays, x-rays, UV rays, visible light. This is where we see all of our colors. Everything we see is in this small range right here. It's just expanded out here so you can see all the colors of the rainbow. Our IR spectra or infrared rays, microwaves, radio and TV, and then our long radio waves. And so this is your electroic spectrum. You should understand where the different pieces fall, where they're compared to each other. You should know that radio waves have long wavelengths but low energy, low frequency. Gamma rays have very short wavelengths but high energy, high frequency. So lambda is wavelength. Lambda is what we use to describe the wavelength. Okay? And because it is a length, its units will be some type of distance. So like meters, nanometers, centimeters, some type of distance. And frequency is called new. It looks like a V, but it's actually this like curved V kind of like this. kind of like this. That's way too large of a font today, but I or thick of a font. Kind of like this. It's called new. It's a Greek letter, but it looks like a V. Okay, depending on what font you use on your computer, it looks like a V. But a frequency is measured in hertz. So one hertz, one, it's one cycle per second or one per second or seconds to the minus one. So again, just reminding you of what waves look like. Your wave length is your length between the two peaks of your wave. The longer that is, the lower the energy is. The shorter that is, the higher the energy and the higher the frequency. And one cycle um cycles is how much can it cycle through? How many cycles you have per second is your frequency. So really short wavelengths have high frequency, low wavelength, high energy. You do need to um you do need to know plank's constant and the speed of light. So you need to memorize these. Okay, you do not need to memorize the speed of sound. E of a photon, the energy of a photon is the energy of one photon of light. And so a photon is the amount of energy that's released or absorbed when electron is either excited, so absorbed energy, or goes back down releases its energy and goes back down to its ground state. So emits. So photon is H new sorry I forgot I had that function on. H new place constant times the frequency is the energy of a photon. We will talk about the equation in just a minute but you do need to memorize place constant. Place constant is that lowerase H and its value is 6.626 * 10 - 34 seconds and C lowerase C is the speed of light and it's 2.998 * 10 8 m/s. And so what this is trying to show here, part of what this picture is trying to show here is this whole sound versus light thing. If you look here, this is why you always see lightning before you hear the thunder. The thunder is due to that lightning. It's the it's the sound associated with that lightning strike. But your speed of light 3 * 10 8 m/s compared to speed of sound 340 m/s. Speed of light's just a lot faster. You know, if you've got 3 * 10 eth, you've got meters/s compared to 340 m/s for sound. That's why you always see the lightning before you ever hear the thunder. But they do go hand in hand. Okay, kind of going back to that spectrum thing. So again, a light bulb is white light and it gives off a continuous spectrum. And that's what you see down here is this continuous spectrum. All the colors of the light smoothly blended together. When we look at something from a gas, so here we see helium, we see berium, we see what we call a discrete spectrum. It's just a few bright lines of color. It's also called a line spectrum. It's discreet. There's very specific lines. Okay? So that's why it's called a line spectrum. And it's like your barcode or your fingerprint for that element is how we can identify the element. So this is how like physicists can look at the stars and tell you the composition of the star even though it's you know light years away from us. We can look at the lights coming off of it and identify what element is there based on the um line spectrum coming off of that star. These lines happen though because atoms have electrons that absorb and release energy. When you give an atom energy in the form of heat, electricity, whatever you may do, the electrons in that atom get excited and jump up to a higher energy level. And that's what this is trying to show here. The electrons being pro to a higher energy level. The electrons can't stay up there, though. They fall back down. And when they do, they release that exact same amount of energy that they've absorbed as energy again, but in the form of light. And it's energy is equal to H new place constant times the frequency of the light of the energy they had absorbed. So again H new is called a photon cuz it's a small packet of energy and we'll define that again on a future slide. But you can see here the absorption spectrum versus the emission spectrum down here. And so the absorption spectrum, you see you've got some black lines. That's where the light is being absorbed by that species. The emission spectrum, those lines show up. Energy isn't random. It's quantized. Electrons can only jump between specific energy levels. So the light they give off has very specific amounts of energy. And that's why we don't see the full rainbow, just lines. So we can describe light three ways. By wavelength, how long the wave is. by frequency, how fast it's oscillating, how many cycles per second, or by energy, how powerful the light is. And that brings us to our fundamental equations. When you do these calculations, you're figuring out how much energy an electron released when it changed levels. That gives us a window into the structure of the atom, something that we can't see directly. So these electron or these equations turn light into a tool for understanding atoms. So those colors that we saw in that spectrum above, they're not just light. They're kind of the receipt from the electron telling us what wavelength, what frequency, what energy was required so that we could actually read it. Let's talk through our equations here. We've got the speed of light and this is equal to the wavelength times the frequency. We can rearrange this equation. Wavelength is equal to speed of light over frequency. So therefore I see that my wavelength is inversely proportional to frequency. It's again speed of light is the constant here. What that means is that if I have a longer wavelength, I have a shorter frequency. And that's what I saw in the electromagnetic spectrum as well. Longer wavelength, the long waves, the longer that wavelength, the less cycles I'm going to have per second. It's going to be less frequency. Like it's not as strong of a frequency. And we've got frequency equal to speed of light over lambda as well. As long as you memorize one of these, you can rearrange. So memorize one of these and you can rearrange to the other one. Okay? It's just algebra at that point. But you need to know one of them. We also need to know plank's constant or plank's law. Plank's law tells us the energy is equal to h new. Again, energy of what's being released is equal to the um plank's constant times the frequency of that particle. So energy and frequency are directly proportional. So a um high energy high frequency has short wavelengths. Low energy low frequency has long wavelengths. And you can see here we can just substitute this in. So here we're going to just um for frequency we're going to substitute in get that on for frequency we substitute in speed of light over lambda and that's how we get your E= HT over lambda. So truthfully I have this equation memorized and I have well one of these equations memorized doesn't matter which one and I can derive this one but you need to be able to use all of these equations. Okay, so again, you're just substituting in for frequency, and that's how you're getting this equation down here. Let's do an example with it. What is the wavelength of a radio signal operating at a frequency of 90.1 megahertz? What is the energy of this radio signal expressed in kJ per moles? So, there's actually two questions here. The first one is just asking for wavelength, and it's giving me a frequency of 90.1 MHz. Cool. I know that my speed of light is equal to my wavelength time my frequency. I'm trying to find wavelength. So I'm going to re rearrange the equation. Wavelength will be equal to my speed of light divided by my frequency. Speed of light I have memorized. 2.998 * 10 8. That is a positive 8. It's a very big number. M/s. Um some students have this memorized as 3.0. That's fine unless it limits your sigfigs. So, use whatever is not going to limit your sigfigs. Every soft an example where you need four sigfigs in it. So, that's why I use 2.998. This is divided by my um frequency. Notice I have 90.1, but it's megahertz. So, I need to convert that to hertz. So, mega is 10 6. So, 10 6 hertz for every 1 megahertz. Can't forget our conversions there. Remember what a hertz is? Is is a um one hertz is one cycle per second. So seconds to the minus one. So this simplifies my units. I'll do I'll show the calculation and I'll show the units in a sec. This gives me 3.3 m as my answer here. Okay. Now my mehertz have canceled out. How did I get to just meters? I've got meters/s /t. But a hertz is really a second to the minus one. So this is like a one over seconds that well there. So I've got second denominator seconds in the denominator leaving meters in my numerator. And so that's how I got to just meters for the calculation here. Part two of the question is saying what is the energy of this radio signal expressed in KJ per mole. So let's figure it out. I know the energy of a photon is equal to H new length constant I have to know 6.626 626 10 - 34 Jill seconds and my frequency here again 90.1 MHz. So 90.1 MHz* 10 6 hertz over 1 MHz. You don't have to do them all in one calculation. You can do it separately. I just don't feel like doing it separately. I feel like writing it out right here. This gives me a numerical value here of 5.97* 10 - 26 Jew per photon. But again, I don't want jewels per photon. I want kJ per mole. So I'm going to go ahead and convert that. I want number of KJ per mole here. I have 5.97 10 the -26 Jew for every one photon. Let's convert to kilogjles first. 1 kJ 1,00 juwles. Now I know Avagadro's number. I know that 6.022 22 10 the 23rd photons is one mole of photons I get 3.60 105 kJ per mole so my wavelength here 3.3 m pretty low and my energy 3.65 65 kJ per mole. Also pretty low or pretty long wavelength which means a pretty low energy.