Atomic Energy Levels

- [Instructor] Here's a very simplified model of an atom. The nucleus at the center of the atom is where the protons and neutrons live, but they're kind of boring, because for the most part they just sit there. The real star of the show is the electron. The electron gets to do all the interesting stuff, like move around, jump around, bind with other atoms. These dashed lines represent the different energy levels the electron can have while in the atom. We like representing these energy levels with an energy level diagram. The energy level diagram gives us a way to show what energy the electron has without having to draw an atom with a bunch of circles all the time. Let's say our pretend atom has electron energy levels of zero eV, four eV, six eV, and seven eV. Note that moving left or right on an energy level diagram doesn't actually represent anything meaningful, so technically there is no x-axis on an energy level diagram, but we draw it there anyway because it makes it look nice. All that matters is what energy level or rung on the ladder the electron is at. Note that the electron for our hypothetical atom here can only exist with zero eV, four, six, or seven eV. The electron just cannot exist between energy levels. It's always got to be right on one of the energy levels. Okay, so let's say our electron starts off on the zero eV energy level. It's good to note that the lowest energy level an electron can have in an atom is called the ground state. So how could our electron get from the ground state to any of the higher energy levels? Well, for the electron to get to a higher energy level, we've got to give the electron more energy, and we know how to give an electron more energy. You just shoot light at it. If a photon of the right energy can strike an electron, the electron will absorb all the photon's energy and jump to a higher energy level. The electron in this ground state needs four eV to jump to the next energy level. That means if a photon that had an energy of four eV came in and struck the electron, the electron would absorb the energy of the photon, causing the photon to disappear, and that electron would jump up to the next energy level. We call the first energy level after the ground state the first excited state. Once the electron's at the higher energy level, it won't stay there long. Electrons, if given the chance, will fall towards the lowest energy level they can. So our electron will fall back down to the ground state and give up four eV of energy. The way an electron can give up energy is by emitting a photon. So after falling back down to the ground state, this electron would emit a four eV photon. Electrons don't have to just jump one energy level at a time though. If the electron in our ground state were to absorb a six eV photon, the electron could jump all the way up to the six eV energy level. Now that the electron's at a higher energy level, it's gonna try to fall back down, but there's a couple ways it could fall back down in this case. The electron could fall down to the ground state all in one shot, giving up a six eV photon in the process, but since the electron started at the six eV energy level, it could've also fallen first to the four eV energy level, emitting a two eV photon in the process. It's a two eV photon because the electron dropped two electron volts in energy, and now that the electron's at the four eV energy level, it'll fall back down to the ground state, emitting a four eV photon in the process. So electrons will sometimes drop multiple energy levels at a time, and sometimes they'll choose to take individual steps, but regardless, the energy of the photon is always equal to the difference in electron energy levels. What if our electron's in the ground state and we send a five eV photon at it? If the electron were to absorb all of the energy of the five eV photon, it would now have five electron volts, but that's not an allowed energy level, so the electron can't absorb this photon, and the photon will pass straight through the atom. Keep in mind, the electron in the atom has to absorb all of the photon's energy or none of it. It can't just absorb part of it. Alright, so now we could figure out every possible photon this atom could absorb. If the electron's in the ground state, it could absorb a four eV photon, or a six eV photon, or a seven eV photon. If the electron's at the second energy level, also called the first excited state, the electron could absorb a two eV photon or a three eV photon. And if the electron were at the third energy level, or the second excited state, the electron could absorb a one eV photon. Those are the only photons that this atom will be seen to absorb. 2.5eV photons will pass straight through, five eV photons will pass straight through, 6.3eV photons will pas straight through. What this means is that if you were to shine light that consisted of all possible wavelengths through a gas that was composed of our pretend atoms, all the wavelengths would not make it through. Some of the wavelengths would get absorbed, then scattered away in random directions. This would manifest itself as dark lines in the spectrum, missing wavelengths or missing energy levels that correspond to the energies of photons that our electron can absorb. This is like a fingerprint for an atom, and it's called that atom's absorption spectrum. If you were to ever see this progression of dark lines in these exact positions, you would know that the gas you were looking at was composed at least partly of our hypothetical atom. This also allows astronomers to determine what stuff in our universe is made out of, even though we can't get close enough to collect a sample. All we have to do is collect light from a distant star or quasar that shines through the stuff we're interested in, then just determine which wavelengths or energies got taken out. The details are a little messier than that, but this provides astronomers with maybe the most important tool at their disposal. Now the absorption spectrum are all of the wavelengths or energies that an atom will absorb from light that passes through it. You could also ask about the emission spectrum. The emission spectrum are all of the wavelengths or energies that an atom will emit due to electrons falling down in energy levels. You could go through all the possibilities of an electron falling down again, but you'd realize you're gonna get the exact same energies for the emission spectrum that you got for the absorption spectrum. So instead of letting light pass through a gas composed of your hypothetical atoms, let's say you made a container that had the gas of your hypothetical atoms, and you ran an electric current through it, exciting those electrons to higher energy levels and letting them fall back down to lower energy levels. This is what happens in neon lights, or if you're in science class it's what happens in gas discharge tubes. So for the emission spectrum, instead of seeing the whole electromagnetic spectrum with a few lines missing, you're going to only see a handful of lines that correspond to the energies of those photons that that atom will emit. Okay I've gotta be honest about something. If any physicists are watching this video, they're cringing because the energies that electrons will have in an atom are not positive. The energies an electron can have in an atom are actually all negative values. This is because the electron's bound to the atom. Anything that's bound to something else will have total energies that are negative. This is analogous to a ball stuck at the bottom of a ditch. If the ball's not moving it has no kinetic energy, and if we assume that ground level is the H equals zero position, then this ball's gonna have a negative gravitational potential energy. Since this ball has a negative total energy, it's stuck and bound to the ditch. If someone could give this ball enough energy so that it would have positive total energy, the ball could leave the ditch. It would not be bound anymore. So to make our hypothetical atom a little more realistic, let's subtract 10eV from each energy level. This doesn't really change anything. In order for the electron to get from the -10eV ground state to the -6eV first excited state, it's still gonna take a four eV photon. People do get confused with the negative signs though, so be careful. In order to find the energy of the photon that was absorbed or emitted, you always take the higher energy level and subtract from it the lower energy level. So in this case, we would take -6eV, and subtract from it -10eV, which tells us that it would take a four eV photon to bump an electron up to that energy level, and the electron would emit a four eV photon if it dropped back down from that level. Something else that's unrealistic about our hypothetical atom is that real atoms wouldn't just stop at -3eV for the highest energy level. Real atoms have energy levels that get closer and closer together as you approach a zero eV. What happens when an electron gets more than zero eV energy? Well if an electron has more than zero energy, that means it's got positive energy. And if it's got positive energy, it's not bound to the atom anymore. It'll be free to leave, it'll be gone, and we'll say that we've ionized the atom by removing an electron. So for example, say the electron started at the -4eV energy level and it absorbed a seven eV photon, that electron would have a total energy of positive three eV, and so it would be gone from the atom. (upbeat music)