First and second ionization energy

In the previous videos we've talked about only the first ionization energy. In this video, we're going to compare the first and the second ionization energies, and we're going to use lithium as our example. So in the previous video, we already know that lithium has an atomic number of 3, so there are three protons in the nucleus. In a neutral atom of lithium, the number of electrons equals the number of protons, and so we know there are three electrons in lithium here. The electron configuration is 1s2 2s1. So we have two electrons in the 1s orbital so we can go ahead and put those two electrons in the 1s orbital like that. And then we have one more electron, and that electron's going to go into the 2s orbital like this. And so that would be a very simple picture of the neutral lithium atom. If we apply enough energy, we can actually pull away this outer electron here. So we can pull away that electron, and we call this the first ionization energy. And to pull away that electron takes approximately 520 kilojoules per mole. And so once we've pulled that electron away, we no longer have a neutral lithium atom, right? We would have a lithium ion because we would still have three positive charges in the nucleus, but we have only two negative charges now. We only have two electrons because we pulled one away. So 3 minus 2 gives us plus 1. So this is the lithium plus 1 cation. And the electron configuration would just be 1s2 because we lost the electron in the 2s orbital. And so we could keep going. We could apply some more energy and pull away another electron. So let's say that we pull away this electron this time. OK, so we're taking a second electron away, and so we wouldn't call this ionization energy 1. We would therefore call this ionization energy 2 because this is to take away the second electron. And this value turns out to be approximately 7,298 kilojoules per mole. And so if we take away that second electron, once again we still have three positive charges in the nucleus, but we have only one negative charge now. There's only one electron so this is no longer the lithium plus 1 cation. This is the lithium plus 2 cation because 3 minus 1 is plus 2. So this is lithium plus 2 here, and the electron configuration would be only one electron in a 1s orbital, so 1s1. So we can see that there is a big difference between the first ionization energy and the second ionization energy, so 520 versus 7,298. So let's see if we can explain the reasoning for this extremely large difference in ionization energies. And we're going to use the three factors that we've talked about in the previous videos. So the first factor we discussed was nuclear charge, which refers to the number of protons in the nucleus. So if we look at the neutral lithium atom, three positive charges in the nucleus. That positive charge is what's going to attract this electron in magenta here. And if we look at the lithium plus 1 cation, similar situation. We still have three protons in the nucleus, and so that positive charge is what's going to be attracting this electron as well. And so because of the same number of protons, we have to think more about effective nuclear charge, as opposed to how many protons there are in the nucleus. And before we do that, we have to consider the effect of electron shielding. So let's talk about electron shielding next. So electron shielding, also called electron screening, so electron shielding slash screening. So when we think about electron shielding, we're thinking about the inner orbital electrons here. So going back to the neutral lithium atom, these two inner shell electrons right here are going to repel this outer shell electron. So this one is going to repel this one as well. And so we can think about it as they screen the electron in magenta from feeling the full force of the positive 3 charge in the nucleus because electrons repel other electrons. And so the way to calculate the effect of nuclear charge-- so we've done this in the previous videos as well-- the simple way of calculating effective nuclear charge is take the number of protons, so plus 3, and from that you subtract the number of shielding electrons. So in this case, it would be these two electrons in the 1s orbital. So 3 minus 2 gives us an effective nuclear charge of plus 1. And so the electron in magenta isn't feeling a nuclear charge of plus 3. It's really only feeling an effective nuclear charge close to positive 1 because the actual value is approximately 1.3 when you do the more complicated calculations. And so the effect of electron shielding is to decrease the overall nuclear charge that this electron magenta feels. And so when we move over here to this electron, so I'm talking about this electron in magenta for the lithium plus 1 cation, it's not the same situation, right? There's not much electron shielding. This electron over here might repel it a little bit, but there are no inner shell electrons repelling this electron in magenta. And because of that, the electron in magenta is going to feel this positive 3 charge, much more of the full positive 3 charge of the nucleus. And so therefore, there's going to be a much greater attractive force holding this electron in magenta to this nucleus. And therefore, you have to apply more energy to pull that electron away. So the effect of electron shielding tells you the second electron is much harder to remove than the first, and so we see a large increase in ionization energy from the first ionization energy to the second ionization energy. The last factor that we discussed was distance, so the distance of those electrons in magenta from the nucleus. So on the left, once again going back to the neutral lithium atom, this electron is in the second energy level. So it's further away than this electron. This electron is in the first energy level, in the 1s2, so this distance here is smaller than the distance on the left. And so since the distance is smaller, this electron in magenta feels more of an attractive force from the nucleus. Once again, that's Coulomb's law. And so therefore, there's an increased attractive force. Therefore, you take more energy to pull that electron away. So it takes much more energy to pull the second electron away than the first, and so that's why we see an increase in ionization energy. So distance says the fact that this electron is closer means it takes more energy to pull it away, and that's another reason why this number for the second ionization energy is so much larger than the first. So it takes a heck of lot more energy to pull away your second electron. And that explains why we see lithium forming a plus 1 cation, because it doesn't take anywhere near as much energy to pull away one electron as it does to take away two to form a lithium 2 plus. And so this is one way to tell what kind of an ion will form. Look at the ionization energies, and when you see a huge jump, that clues you in as to which ions are easier to form.