Atomic spectra

0:00- [Instructor] We can look at stars or nebulae, or even planets which are very, very far away, and estimate what composes them, what are the elements that are there inside of them? But how do we do that? How can we sit here on Earth, and figure out what elements are present inside, say, the atmosphere of an exoplanet?

0:19We do that by using the atomic spectra and spectral analysis. But what exactly are these things? Well, let's find out. Let's start by looking at the model of an atom, and we're gonna look at the simplest one, the hydrogen atom. Inside the hydrogen atom, we know there is one proton and one electron.

0:34And in most popular depictions, we show the electron circling around the proton, right? But that's not the right model, because electrons are not tiny balls of matter that go around like this, like the planets. Instead, they're quantum objects that have both particle and wave properties.

0:51And one of the wave properties is that waves are spread out, they're not at one particular location, but they're spread out, which means electrons are also spread out. We call that as an electron cloud. And these electron clouds can have different shapes. For example, if you consider the hydrogen at its lowest energy level, then the shape of the electron happens to look somewhat like this.

1:14It's kind of like a sphere. And it's not that the electron is orbiting over here. No, no, no, this cloud that I've drawn over here itself represents the electron. Now here's the main question for us. What happens to this atom if we supply it some energy? When you supply some energy, the electron absorbs the energy.

1:32And the question is, what happens to it? Well, if there is enough energy, then the electron can absorb it and just escape the atom. In that case, the electron just escapes it, and you just are left with a single proton over here. Okay, but what if you don't give it that much energy?

1:45What if you give it a little bit of energy, not enough energy to escape it, but just a little bit of energy. Then what happens? Ooh, now some interesting things can happen. And to understand that, let's take an analogy over here. My favorite analogy is thinking about a well in which you have a ball over here.

1:59This ball is analogous to the electron over here, just like how this ball is sitting inside a well. And if we want that ball to escape that well, we have to supply energy to it, enough energy. In a similar way, this electron is also sit, this electron cloud is also sitting inside a well.

2:16The difference is here you have a physical well that is caused due to gravity. Here, it's a different kind of well, it's a well that is caused due to electric forces. We call this as a potential well, in general, but the idea is the same. To escape that well, we have to supply it enough energy.

2:30And now the big question was what if you don't supply that much energy? What if you supply a little bit of energy? Then what's going to happen? Well, we might think nothing's going to happen. If I supplied a little bit of energy, well, it's gonna come back down, right?

2:40Well, it turns out that the potential well over here is not like this. Instead, the potential well can be thought of to look somewhat like this. What we see is that there are different levels at which the ball can be sitting. Right now, it is at its lowest level, which we'll number as one.

2:54Now if we supply it this much energy, the ball can actually go and sit at two. That's possible, there's another energy level at which the ball can sit. If you supplied even more energy, the ball can sit at a slightly higher energy level, and so on and so forth.

3:08Guess what, the same is the case with our electrons. Right now, this electron is at its lowest level, but there are other higher levels that can occupy. If supply just enough energy, it can jump to higher levels. And when it does that, the electron cloud will change its shape.

3:24Let me just give you an example of that. So if we supply just enough energy so that the electron can jump to, let's say, the next level like this, then the shape of the electron will change. The new shape would look somewhat like this. This is at energy level two, the next available energy level.

3:41And you can kind of see just like how the ball is now farther away from the earth, from the ground, because it has higher energy, similarly, you can kind of see that the electron cloud is sort of bigger because it has more energy, right? But turns out, and unlike what we see over here, there are other shapes that the electrons can take at this new energy level.

4:01For example, another shape that the electron cloud can take looks somewhat like this. It's pretty cool, right? Don't worry too much about how we get this shape and all of that, it just happens to be true that there are multiple shapes at which it can take, but what's important is that right now, this electron is at a higher energy level, the second energy level that's available.

4:18And if I supply even more energy, again, just enough energy to get to the next level, well, the shape will again change, it'll become even bigger. And at this level, it can have even more shifts. It's pretty cool. But this is the model that we have today. This is the quantum mechanical model of atoms.

4:34And just to give some technical names over here, these different shapes that we talked about, we call them the orbitals. Notice, it's not an orbit. It's not that electron is orbiting, this whole cloud itself represents an electron, and we call that the orbitals.

4:50And these energy levels, well, we give a name to them as well. We call that the principal quantum number. A fancy name, but all it's telling us is at what energy level these orbitals are, right? All the orbitals at a particular quantum number will always have the same energy level, okay?

5:08And of course, if you're wondering how do we supply that energy? Well, there are multiple ways to do that. By collision, by heating the atoms, or even by radiating some light on it, there are multiple ways in which we can supply the energy. It's just that if you supply the right amount of energy, electrons can jump to higher energy levels.

5:23But for our purposes, the shapes, the orbitals are not really important. What's important are these different energy levels, and understanding what happens when electrons jump from one to another, right? So for that, let's just get rid of the shapes, and use circles to represent the different energy levels.

5:38So again, what I've drawn over here, look, this represents the first energy level that's available for the electron. Doesn't mean that the electrons orbiting over here, okay? Then you have the second energy level, just like what we saw in the orbital, the second energy level is bigger.

5:50The third energy level is even bigger, it's even farther away, and so on and so forth. And again, these are the principal quantum numbers, which represents the energy levels. But how many such energy levels do we have? That's a good question. Well, it turns out that I have only drawn four, but it turns out that there are infinite energy levels that you can have.

6:08You can kind of imagine putting infinite amount of steps over here. And then you can do that. If you keep on decreasing the step size, you can sort of like, you can imagine that you can keep on squeezing out lots, and lots, and lots, and lots of steps. That's basically how the energy levels are.

6:21And we can show this using a diagram, an energy level diagram, which kind of looks like this. So look, this is the first energy level, second energy level, third energy level, fourth energy level, fifth, sixth, seventh, eight, ninth. And eventually you have the infinite energy level.

6:36Now it doesn't mean it takes infinite energy to go over here. No, no, no, look, look, it takes a finite amount of energy to go from here to here, but I have put infinite steps in between by reducing the step size. In a similar way, you can think that there are infinite levels that we can put from here to here.

6:52You can kind of imagine when you're very far away from the proton, you are pretty much at the infinite energy level. So you don't need infinite energy to actually go over here, okay? Anyways, now comes the question what happens when electrons jump to a higher energy level?

7:05Well, first of all, we call this the ground state, and we call these other higher energy levels the excited state. So let's say we heat up an atom, and the electron jumps from the ground state to the third level, the excited state over here, okay? What happens to it?

7:19It turns out electrons cannot stay in the excited state for long because they're very unstable. And so they will immediately try to jump back to any lower available energy level. So it's possible that can jump directly from three to one, or it is possible that it can jump from three to two, and then two to one.

7:33Anything is possible, okay? And when it does so, when it jumps from a higher level to lower level, electron has lost some energy. Where does the energy go? Energy must go somewhere, energy conservation. That energy goes out as a photon of light. So for example, if the electron jumps from level three to level two, it releases a photon of light, and that photon will have the same energy as the difference between these two energies.

7:58Now it turns out for hydrogen, if you actually do the calculation, the difference between the energy levels for level three and level two, that energy corresponds to red color of light. You can remember that the energy of a photon is correlated with its frequency or its wavelength.

8:14More the energy of the photon, more is its frequency, or shorter is the wavelength. For this particular energy difference, the wavelength or the frequency happens to be in the red color. Similarly, what would happen if the electron jumped from four to two? Well, you can kind of imagine, four to two is a bigger jump, which means more energy lost, so the energy of the photon will be higher.

8:37The frequency therefore would be higher than the red color. It turns out it'll lie somewhere in the blue color. And if the jump is from five to two, and six to two, it'll be even more towards, you know, violet, indigo. And then from seven to two and so on, it becomes ultraviolet, we'll not be able to see it.

8:55Okay, what about other jumps? For example, you have, say, jump from two to one. Well, it turns out that this energy jump is so big, and I've probably not drawn it accurately, but it turns out to be so big that even that lies in the ultraviolet region, which we'll not be able to see it.

9:07In fact, except for these four for hydrogen, except for these four jumps, all the other jumps will either be in the ultraviolet region, too high frequency for us to see, or it'll be too small, too low frequency, like the energy difference over here, like four to three, or five to four, or six to three.

9:23They'll be so small that it'll be, again, the frequency will be too low for us to see. So when it comes to hydrogen, it's only these four jumps that are visible to us. That means these are the only four colors that hydrogen light will emit in the visible region.

9:37So this means if you were to take a hydrogen gas and then hit it up, that because there are so many atoms, there'll be so many electron transitions continuously happening, almost all the possible jumps that you can think of will happen, and therefore light will come out, and the hydrogen gas will glow.

9:52But in the visible section, the light will only be composed of these four specific wavelengths. So we will see a light that is a combination of these four wavelengths. And if we then use, say, a prism, or something like a diffraction grating, which can separate those particular wavelengths, then you can see these four individual wavelengths separately, and it will look somewhat like this.

10:15And we will call this the atomic spectrum, or the hydrogen spectrum. And what's cool about the atomic spectrum is that every element will have its own energy level. That means every element will give out very specific colors of light, very specific wavelengths of light.

10:34So these wavelengths are specific to hydrogen. Helium, for example, will give very different wavelengths of light. Let show you what helium looks like. It looks like this. These wavelengths of light are the characteristic of helium. So this means an atomic spectrum is like a signature of that element.

10:55So tomorrow, if we have an unknown gas, and we want to figure out what's made of, we'll just heat it up and look at its spectrum. And if that spectrum looks like this, then what we can do is we can say that, and we can look at these lines and we can say, hey, hey, look, look, these are the element, these are the lines that only come from hydrogen.

11:10So there must be hydrogen from it. And then we can look at these wavelengths and say, hey, these wavelengths only come from helium. No other elements will give me these lines, so there must also be helium in it, and so on and so forth. And by looking at the brightness, we can also figure out which one is more abundant.

11:26So for example, over here you can see the hydrogen lines are brighter, so we can say there's more hydrogen compared to helium. This is called spectral analysis. And by the way, this kind of spectrum is called an emission spectrum, because it's the spectrum that we get, because those specific colors are emitted by the atoms.

11:43But you may be wondering, well, is there any other kind of spectrum? Yes, if you were to look at the spectrum that you get from, say, the Sun, you'll not see this. Instead, what you'll find is you'll see continuous color, and some of the lines will be absorbed.

11:58In fact, those specific lines that we just draw over here in the emission spectrum, those lines will be actually absorbed. And there'll be other elements in that spectrum, and therefore there'll be other lines as well. But the lines will seem absorbed, some colors will be absorbed.

12:12And that we call as an absorption spectrum. That's what we'll get if you look at, say, the spectrum of the Sun. But why do we get that? Why are we getting something like this? Well, let's see. When you're looking at the Sun, for example, the Sun's core is extremely hot, very hot.

12:29And such hot, dense objects, they tend to give out white light. All the colors, they don't do this, they give out just white light, okay? So if you were to just see that particular light through the prism, then we should expect just all the colors of the rainbow, right?

12:47However, the outer layer is much cooler, therefore the atoms over here will absorb light over here. Now if there's hydrogen, for example, which colors of light, which wavelengths of light will it absorb? He'll only absorb those wavelengths of light whose photons have just enough energy to give them these transitions, which means in the visible section, they will absorb these specific colors of light.

13:11And similarly, if there's helium and carbon, all of them, again, they will absorb their characteristic, you know, colors. And that's why those specific colors will be missing, and that's why we will see dark lines over here. But wait a second. Once they absorb them, shouldn't they also again release them?

13:29Yes, they do release those colors, but when you're looking over here, those colors will be absorbed from the outer layer, and then they'll be released in all the other direction. They will be emitted back in the other directions, but they'll be emitted in all the other directions.

13:41So mostly in this direction, those colors will be missing, and that's why you get the absorption spectrum. But the analysis is the same. By looking at which colors are absorbed, which particular wavelengths are absorbed, you can identify which elements are present, say, in the outer atmosphere over here.

13:57This is how we figure out the elements present inside the atmosphere of different exoplanets for example. So whether you get an absorption spectrum or an emission spectrum really actually depends upon your waving angle. But regardless, the analysis stays the same, okay?

14:11Now here's a cool summary that I found on the web telescopes page over here, okay? The summary of everything we saw, the light that we get directly from the hot sources would be continuous spectrum. If there are things that are relatively cooler, gases like say nebulae, or the outer layers, then they will absorb, and what you'll now see is the absorption spectrum.

14:30But if you're waving angle is such that you directly see the light coming from those gases that absorb the light, then you'll be able to see the emission spectrum.