So now we want to take the ideas of Quantum Mechanics, and apply them to Atoms, and see how we can use these ideas to look at atomic fingerprints, and figure out what planets and stars are made of. So let's go back to the basic structure of our atom. Remember, we have this nucleus in the center surrounded by electrons. Now, the Pauli exclusion principle implies that I could only put one electron in any given state, any given description in an atom. So, I can fit just a handful of electrons in inner orbit. And as I go out, I can fit more and more electrons in the atom. And the overall Atomic Structure, is determined by the charge of the nucleus. And this polar exclusion principle, which tells me how I have to fill up this space with electrons, and each atom is going to have its own distinct structure. This is the polar exclusion principle, telling us that I can only fit one electron in each state. So for example, here is a helium atom. A helium atom, in it's lowest state. The n equals 1, the most tightly bound state. There are 2 electrons that we could put into that state. One spinning up, the other spinning down. These, this is the ground state of helium. This is the excited states of helium, and this is the next orbital up, the n equals 2 orbital. And I've got n equals 3, and n equals 4, and higher energy orbitals making up the structure of helium. What happens when light comes in, is light can come along. If it has just the right energy, it could excite this electron from the ground state, to an excited state. That's what happens, when an atom absorbs light. It excites the electron from one state to another, and to do that it has to have just the right energy. Now you don't have to have the perfect energy, to do this because, some atoms are moving. If an atom's moving towards you that red shifts, that blue shifts light, if it's moving away from you it red shifts light. That changes the energy, so in a gas of say, helium, there's a narrow range of energies, we'll call it the line width, that determines whether or not you can excite helium from the ground state to the excited state. So, if I have cold cloud of gas and something hot behind it like a star, light from a star going through a cold cloud, cloud of gas if that light comes in with just the right energy, it's going to be able to excite the helium say in this cloud. From the ground state, to the excited state. That will absorb some of the light from a star. So when we look at the starlight, we will see absorption lines in the spectrum. On the other hand, we will also be able to observe emission from this gas, because this gas is absorbed some of that light. So some of the electrons are in this excited state, and when they decay from the excited state back to the ground state that's emission, that will produce emission lines in the spectrum, so by looking at a spectrum against a bright source so we can see absorption. Our own emission, we can figure out what's going on with the gas. So this plot shows the energy distribution from the Sun, at the Earth's surface. At the top of the Earth's atmosphere, the energy distribution of the Sun is very close to the plank of black body spectrum. A nearly smooth curve with a significant fraction of the energy in the ultraviolet, some in the optical, some in the infrared. As the Sun's radiation starts to propagate towards the Earth's surface, a lot of that radiation in the ultraviolet. Is absorbed by the Ozone layer, decreasing the amount of ultraviolet that reaches the surface. And in the infrared, there are absorption lines from water and carbon dioxide, that produce these features in the spectrum, and you can see at some wavelengths. The Earth's atmosphere is opaque, and the Earth's, the molecules in the Earth's atmosphere absorb all of the radiation, and prevent any from reaching the surface at some of the wavelength bands. And you can see some of the narrower features, some here. Associated with atoms or molecules that absorb a significant fraction of the radiation from the Sun. Each atom or molecule has its own particular finger print, its own particular spectral pattern. That pattern is determined. By the energy levels, that the electrons occupy in the atom. So for example, in hydrogen, we have a series of distinctive lines, associated with transitions between the different energy levels in hydrogen. And if we see in a star or in the laboratory. This pattern of lines that tells us we are looking at hydrogen gas. Helium, has a different pattern. Mercury, yet another pattern. We know, when we look at and say, neon lights or sodium lights. Our eyes could see the characteristic emission lines, associated with sodium or neon. Big atoms like uranium, have very complicated spectrum, because there are many, many different emission lines. And what we can do, when we study the Star. Or the atmosphere of a planet is we can look at the pattern, this for the Sun, of absorption lines in the stellar atmosphere, and that tells us the composition of the Star. Basically spectroscopes. Can fingerprint the property of a Star, or a planet by looking for these features in its atmosphere. And going from the Sun's spectrum, we can determine its composition. Here again is the spectrum of the Earth. If you were, observing the Sun from the Earth's surface, you can notice that there are a bunch of absorption lines. And from that, we can determine, another way, we determine the composition of the Earth's atmosphere. The Earth's atmosphere has Ozone and oxygen, with lines we can see and water lines. And carbon dioxide lines. Now you'll notice in the Earth's spectrum, there are no very strong nitrogen lines, even though nitrogen is the dominant molecule in the Earth's atmosphere. And that's just due to, the atomic energy levels in nitrogen. There happens to be no strong absorption line of nitrogen at visible or near infrared wavelengths. So we don't have a distinction, distinctive nitrogen feature. But we do have these other features, which service as fingerprints that would tell, that tell us the composition of Earth's atmosphere. Or potentially the composition of other atmospheres of other planets when we observe them. The Earth's atmosphere I should note depends on time. If we looked at the early Earth, and we'll come back to this when we look at the Earth's evolutionary history in just a couple lectures, the early Earth's atmosphere didn't have any oxygen in it. The dominant features we have seen in the earlier, is water and methane. No oxygen. So, by looking at the spectrum of a planet or the spectrum of a Star, we can finger print it. We can figure out what is its composition. Is we can find the distinctive features of each atom and molecule, associated with the energy levels, of that atom and molecule. Here for example are the lines associated with carbon dioxide, and this is what we'd see if we were looking at a planet with a carbon dioxide atmosphere. This plot shows the range of spectra, associated with different types of stars. Looking at this plot, we're going from low mass stars, these M and K red dwarf stars, up in increasing mass towards massive O, B, and A type stars. We call that a sequence in mass, along the main sequence, is sequence in temperature. So these stars are very hot, these O stars are so hot, that they have ionized most of the atoms in their atmosphere, so they have a relatively featureless spectrum. These A and B stars, have lots of excited and iron, and some ionized hydrogen in there atmosphere. They have very strong lines associated with hydrogen. As we move towards these cooler stars, we get towards F and G stars. They have weaker hydrogen features. And some atomic features in their spectrum. And as we move down towards K and particularly M stars, these M stars get so cool, that molecules are able to form in their atmosphere. And we've seen in the M star here. Many absorption lines, associated with the many energy levels in the molecules. So by looking at this spectrum, we can measure the temperature, and the composition, of all these different types of stars. And each star has its own distinctive fingerprint, that lets us determine its composition and its basic properties. Here the spectrum of very low mass stars, brown dwarf stars, and you'll notice these large numbers, of molecular lines associated with the brown dwarf stars. So, now that we've a measured spectrum, you can see that each atom, each molecule, has its own distinctive fingerprint. One of the things we can do as astronomers, is we can look for these fingerprints, these distinctive lines associated with. Atoms like hydrogen, and helium, and carbon, not just in stars in our galaxy, but in other galaxies. So let me, leave you for a moment to think about this question. how we can use this, to test with the laws of nature, vary across space and time. So think about that and we'll come back in a moment.