Atomic spectra | Physics | Khan Academy

We can look at stars or nebulas 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? We 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 going to look at the simplest one: the hydrogen atom. Inside the hydrogen atom, we know there is one proton and one electron, and 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 are quantum objects that have both particle and wave properties. One of the wave properties is that waves are spread out; they're not at one particular location, but they are spread out, which means electrons are also spread out. We call that an electron cloud.

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: it's kind of like a sphere. It's not that the electron is orbiting over here. No, no, no. This U 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, and the question is, what happens to it?

Well, if there's enough energy, then the electron can absorb it and just escape the atom. In that case, the electron just escapes it and you are left with one single proton over here. Okay, but what if you don't give it that much energy? What 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. 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. This ball is analogous to the electron over here, just like how this ball is sitting inside a well.

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 sitting inside a well. The 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 a potential well in general, but the idea is the same: to escape that well, we have to supply it enough energy, right?

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? We might think nothing's going to happen if I supply a little bit of energy; the ball is going to come back down, right? Well, 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.

Now, if you supplied this much energy, the ball can actually go and sit at level 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. Guess 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 it can occupy. If you supply just enough energy, it can jump to higher levels, and when it does that, the electron cloud will change its shape.

Let 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. You can kind of see, just like how the ball is now farther away 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 it turns out, and unlike what we see over here, there are other shapes that the electrons can take at this new energy level. For 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 the shapes and all of that. It just happens to be true that there are multiple shapes it can take, but most importantly, what's crucial is that right now this electron is at a higher energy level, the second energy level that's available.

If I supplied 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 shapes. It's pretty cool! But this is the model that we have today; this is the quantum mechanical model of atoms. 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 the electron is orbiting. This whole cloud itself represents an electron, and we call that the orbitals.

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 is telling is at what energy level these orbitals are. All the orbitals at a particular quantum number will always have the same energy level. Okay? And, 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 you can supply the energy.

It's just that if you supply the right amount of energy, electrons can jump to higher energy levels. But 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.

So again, what I've drawn over here, look, this represents the first energy level that's available for the electron. It doesn't mean that the electrons are 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. The third energy level is even bigger; it's even farther away, and so on and so forth. Again, these are the principal quantum numbers which represent 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 there are infinite energy levels that you can have. You can kind of imagine putting an infinite amount of steps over here, and you can do that if you keep on decreasing the step size. You can sort of, like, 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.

We can show this using 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, eighth, ninth, and eventually, you have the infinite energy level. Now, 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 keeping the step size reduced.

In a similar way, you can think that there are infinite levels that we can put from here to here. You can kind of imagine when you are 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 high energy level? Well, 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? Our 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 it can jump directly from 3 to 1, or it is possible that it can jump from 3 to 2, and then 2 to 1. Anything is possible!

Okay, and when it does so, when it jumps from a higher level to a lower level, the electron has lost some energy. Where does energy go? Energy must go somewhere; energy conservation, that is! 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.

Now, it turns out for hydrogen, if you actually do the calculation, the difference between the energy levels for level three and level two corresponds to red color of light. You can remember that the energy of a photon is correlated with its frequency or its wavelength. More 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 will happen if the electron jumps from 4 to 2? Well, you can kind of imagine 4 to 2 is a bigger jump, which means more energy lost, so the energy of the photon would be higher. The frequency, therefore, would be higher than the red color. It turns out it will lie somewhere in the blue color. If the jump is from 5 to 2 and 6 to 2, it will be even more towards, you know, violet, indigo, and then from 7 to 2, and so on. It becomes ultraviolet; we will not be able to see it.

Okay, what about other jumps? For example, if you have, say, a jump from 2 to 1? 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 will not be able to see. In fact, except for these four transitions for hydrogen, all the other jumps will either be in the ultraviolet region (too high frequency for us to see) or they'll be too small, too low frequency, like the energy difference over here, like 4 to 3 or 5 to 4 or 6 to 3. They'll be so small that again the frequency will be too low for us to see.

For hydrogen, it's only these four jumps that are visible to us. This means if you were to take a hydrogen gas and then heat it up, because there are so many atoms, there will 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. The hydrogen gas will glow! But 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. It will look somewhat like this, and we will call this the atomic spectrum or the hydrogen spectrum.

What's cool about the atomic spectrum is that every element will have its own energy level. That means every element will give out this very specific colors of light, very specific wavelengths of light. So these wavelengths are specific to hydrogen. Helium, for example, will give very different wavelengths of light. Let me show you what helium looks like. It looks like this. These wavelengths of light are the characteristic of helium.

This means an atomic spectrum is like a signature of that element. So tomorrow, if we have an unknown gas and we want to figure out what it's made of, we'll just heat it up and look at its spectrum. If that spectrum looks like this, we can do is we can say, “Hey, look, look, these are the lines that only come from hydrogen, so there must be hydrogen from it.” 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.

By looking at the brightness, we can also figure out which one is more abundant. For example, over here, you can see the hydrogen lines are brighter, so you can say there's more hydrogen compared to helium. This is called spectral analysis.

By the way, this kind of spectrum is called an emission spectrum because it's a spectrum that we get because those specific colors are emitted by the atoms. But you may be wondering, “Is there any other kind of spectrum?” Yes, if you were to look at the spectrum that you get from, say, the Sun, you will not see this. Instead, what you'll find is you will see continuous color, and some of the lines will be absorbed.

In fact, those specific lines that we just threw over here in the emission spectrum, those lines will actually be absorbed, and there will be other elements in that spectrum; therefore, there will be other lines as well. But the lines will seem absorbed; some colors will be absorbed, and that we call the absorption spectrum. That's what we will 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—right? Very hot! Such hot dense objects 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?

However, 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? It'll only absorb those wavelengths of light whose photons have just enough energy to give them these transitions. This means in the visible section they will absorb these specific colors of light. Similarly, if there's helium, carbon, all of that, again, they will absorb their characteristic colors.

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? Yes, 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 directions. They will be emitted back in other directions, but they'll be emitted in all the other directions, so mostly in this direction those colors will be missing. 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. This is how we figure out the elements present inside the atmosphere of different exoplanets, for example.

So whether you'll get an absorption spectrum or an emission spectrum really actually depends upon your viewing angle. But regardless, the analysis stays the same. Okay, now here's a cool summary that I found on the web telescope's page over here.

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 nebula or the outer layers, then they will absorb, and what you will now see is the absorption spectrum. But if your viewing 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.