Let's continue our study of the ways in which the electrons are arranged around the nucleus in an atom. You'll recall in the previous studies, we were looking at this data. The ionization energy. This is the energy required to remove an electron from an atom. Remember that we're going to take an atom and try to extract an electron from it. Leaving behind a positive ion and the minimum energy required to do this, we call the ionization energy. So this is a graph of the ionization energies, a function of the atomic number. Remember the atomic number tells us something about the positive charge and the nucleus. So if the atomic number is z and the positive charge and the nucleus is z plus. And here's our nucleus. And now, we'll imagine that we're looking at some electron which is moving outside of the nucleus out here somewhere. Then we're asking the question, how much energy does it take to remove that electron from the atom? To really understand that in detail, we need to understand the energy of the interaction of that electron with the nucleus or the force of attraction of the electron with the nucleus. And that is described by something called Coulomb's Law. Coulomb's Law in our version is going to describe the potential energy for an electron interacting with a nucleus. In general, it actually describes the potential energy of any two charged particles for interacting with each other. So let's say we have two charged particles. One of them has charge q1, and the other one has charge q2. The potential energy of interaction between them is proportional to the product of those two charges. The bigger the charges are the greater the magnitude, the greater be the interaction. It also depends upon the distance between the two charges. As the inverse so that the denominator is what contains the the distance between the two. So again, if I've got some charge here q1 and I have another charge q2 and I'm interested in the interaction between these two. That interaction depends upon the distance between them or 1, 2 and that's Coulomb's law. Since Coulomb's Law is a potential energy, and potential energy might not be as familiar to you, let's go back now and think very carefully about what we mean by a, a potential energy. Recall that potential energy is sort of a relative term. It matters to us whether the energy is greater or smaller relative to some particular location. The question in this case might be, for example, when does the potential energy of interaction between this charge and between this charge actually go to zero? That would be the point at which they are no longer interacting with each other. Presumably that would be the point at which they are so far apart from each other. That in fact their interactions go to zero, and in fact, that turns out to be exactly correct. The potential energy is zero when r1 2, the distance between the two of them, is very large, and that's perfectly sensible. So in each case when we're looking at the potential energy of interacting two particles, we're comparing it to the amount of energy they have when they are very far apart. When do we see attractive forces between the two? Well we would expect that to be when the particles were closer together But also when they are oppositely charged. If we look at this formula again here, that's going to be a negative number when q1 is positive and q2 is negative, or q1 is negative and q2 is positive. Let's imagine for simplicity then, that what we're talking about here is the interaction between a positively charged nucleus, and an electron some distance away, r1 2. Then in fact the potential interaction of energy between those two has to be the charge on the nucleus multiplied by the charge on an electron which is a negative number you'll recall. Because the charge the electron is negatively charged. Divided by the distance between those two. That's going to be a negative number and the negative number is going to be a larger negative number when r1 2 is small and its going to be a larger negative number when the nuclear charge is larger. So clearly, both the nuclear charge and the distance of the electron from the nucleus effect this potential energy. What else? Well, let's see. What about positive interactions? Well, if the two charges are the same, for example, if we're talking about the interaction between two electrons, then they would have the same charge. That means that the product between the two charges is a positive number, and the potential energy is positive, which means it's greater than the potential energy when the two electrons are widely separated. Let's consider this now in the particular context of the ionization energies, since that's the data that we were interested in. And we can conclude two things. One, the electron is attracted to the nucleus because they have opposite charges, the electron has a negative charge, and the nucleus has a positive charge. And the strength of that interaction depends both on the nuclear charge and how far away the electron is from the nucleus. In addition, in all atoms except for hydrogen, there is more than one electron and those electrons are going to repel each other and that's going to effect the energy as well. How does this effect the ionization energy? Well, as follow. The stronger the attraction of the electron to the atom, the greatest the ionization energy. And that attraction is clearly related to how strongly attracted the electron is to the positively charged nucleus. Or the weaker the attraction, or the greater the amount of propulsion from positively charge electrons, the lower will be the ionization energy. So, we can understand ionization energies then by trying to look at the distances of the electrons from each other. The distance of the electrons from the nucleus, as well as the charge on the nucleus. Let's go back and look at our data then. Here's the data again, and we saw a number of really dramatic features, when we looked at the ionization energy as a function of the atomic number. And one of the most pronounced of these is, of course This dramatic rise as we move across the periodic table. Remember the periodic table looks as follows. As we're moving from lithium to beryllium across boron, carbon, all the way to neon. That's what's going on here when we're looking at this rise as we move from lithium to neon. So, the, interactions clearing getting much stronger because the ionization energy is getting much stronger. So the question is, why do we get that rise as we move from say lithium to neon or similarly from sodium to argon? Well going back and looking at our formula here, two things must be true. Z is increasing as we move from lithium across to neon because the atomic number is increasing. The atomic number is the number of positive charges in the nucleus. And that could account then for the decrease in the potential energy of the electrons, provided that r1 2 is not changing. Because if, in fact, r1 2 was getting much larger That could all set the increase in the atomic charge. So is, the r1 2 must be about the same. It must be staying relatively constant with one another. So we can then begin to understand why we get these dramatic rises because we see an increase in the nuclear charge without the distance changing over that course. That gives rise, then, to the concept of a shell. A set of electrons which are a fixed distance away from the nucleus, approximately, even though the nuclear charge may be increasing in the atom. So a shell is a set of electrons. About the same distance away from the nucleus. And we're starting then to get an understanding of the arrangement of the electrons about the nucleus. The next most dramatic thing, though, that we see in these data, is that these trends don't continue. That we actually see as we get past neon, and go on to sodium, This is a dramatic drop. That is despite the fact that the atomic number in neon is 10, and the atomic number is sodium is 11. The increase in nuclear charge, we might have thought, looking at our previous results here, would give rise to a continuing increase in the strength of interaction of the electron to the nucleus. But the opposite is what we actually observe. We look at this data again here, what we clearly see is that sodium has a very low ionization energy. Looking again at our formula here and thinking about the comparison. The only way that that number becomes a smaller number such that the strength of interaction of the electron to the nucleus is smaller, is if r one two must be much larger. This number must be much larger for the electron in sodium compared to neon that's the only possibility. Because the numerator clearly for sodium is larger than it is for neon because their atomic number is larger. So to offset that the denominator must also be larger and what that tells us then. Is that the comparison is that there must be an icnrease in the shell radius. It must be that when we move from neon to sodium, there's a much larger distance in the electrons from the nucleus. But why would that be true? Apparently, it is the case, that although as we move from lithium to sodium, we could continue to put electrons into the same shell. About the same distance away from the nucleus. That must not be true when we get to sodium and onto the next set of electrons. Therefore that shell must have been somehow or another full. It was not possible to put additional electrons into that next shell. Let's then consider one more piece of data that we see and hear. Which has to do with another trend that's observed. For example, the fact that as we move to higher and higher atomic number, we see a decrease in the ionization energy within a particular group. I've drawn here for the noble gases, for example, going from helium to neon to argon. But we actually see that same decrease a we move through the alkaline metals going from lithium to sodium to potassium. What's gong on there? Again, the atomic number is clearly increasing as we are going down in a particular group, say from helium to neon to argon. So again, the only possibility here is that the distance of the electrons from the nucleus must be increasing. So again, we must be going to a larger shell with a larger shell radius. Let's see if we can summarize these conclusions then and figure out what we have learned about the arrangement of the electrons in an atom. We've now created this idea of electron shells. That is it possible for electrons in the same shell to be approximately the same distance away from the nucleus. And if that's the case, then for those electrons that are in the shell with a larger atomic charge, they are going to feel a stronger attraction nucleus, and they are going to feel a stronger ionization energy. And that's what accounts then for this variation that we see as we move within a single shell. Apparently the electrons over here, as we are in the group from lithium up to neon, are all in about the same shell. Well, let's see what else can we conclude? Apparently, as we have seen, a limited number of electrons can fit into a single shell. We just essentially run out of space and at that point the next electrons are going to have to go into another shell a little further away from the nucleus. Now, each subsequent cell is larger than the previous shell as is observed by the fact that the the ionization energies continue to go down. As we move from one shell to the next. Finally, then we're going to describe something that we're going to call the valence electrons. The valence shell is the outermost shell. We call it that because valent means important. So there is a valence to these electrons. There the one that effect the ionization energies in the atoms. Turns out they also effect the bonding of the electrons and so forth as we will see. And the valence shell contains, what we'll call the valence electrons. Let's go back now and ask though, how many electrons are there in the valence shell? How many valence electrons can fit into a particular shell? And the data here actually give us some kind of an indication. Because if we stare for a minute at, say, lithium, in comparison to helium it has a very, very much smaller ionization energy. What does that suggest must be true about the structure of lithium? Let's see if we can draw a picture then. This is lithium, sorry, with a three plus positive charge and recall then, it has three electrons. And apparently, based upon what we observed with hydrogen and helium, there are two electrons in essentially, an inner shell at a smaller distance away from the nucleus. Say an electron here, and an electron here. And the third electron has to go into a new shell, that's apparently farther away from the nucleus. And apparently therefore we can conclude, that lithium has one valence electron. Because the other two electrons are in here, in the inner part in the inner part of the atom so only a single electron is out here. As we move on to the next atom then say, which is beryllium, apparently then we're in the same shell because the ionization energy has gone up. So the distance from the nucleus is about the same. So apparently, beryllium then has two valance electrons, and of course we could go all the way across to say from lithium to neon. And if we count carefully we actually see that there are one, two, three, four, five, six, seven, eight elements. As we moved from lithium to neon. So apparently neon has eight valence electrons. And apparently, however, that's as far as we can go. Because if we contunue to look here, we see that sodium's ionization energy drops dramatically, telling me that if I look at sodium. It must be the case that I've added that electron to the next layer out. Correspondingly then, I can say that sodium has one valance electron in a larger valance shell than any of the electrons of the the elements rather, from lithium going out to neon. Notice if I make a comparison here, lithium and sodium belong to the same group in the periodic table. You can go back and see that in our periodic table. Back over here, lithium and sodium are adjacent to each other. And the data on the left side back over here clearly tell me that lithium and sodium have the same number of valence electrons. Let's summarize all of this then. We've created this idea of a valence shell, where there are electrons in the outermost region of the atom that are most important. And what we've also now discovered, is that elements in the same group had the same number of valence electrons. For example, we compared lithium to sodium. What about all the remaining electrons though. Let's actually see if we can draw a picture of what this tells us that sodium actually looks like. Recall that sodium has atomic number equal to 11. And so the nuclear charge is plus 11. And if we go back and look at our data. And think about what's happened here, going from hydrogen to helium, clearly there was an inner shell that contained two electrons. And then as we move back over here from lithium to neon, we know that we have another shell farther out that apparently contains eight electrons. One, two, three, four, five, six, seven, eight. And the eleventh electron in sodium clearly has to be even further away than that. And that is actually what we'll refer to as the valance electron or the valance shell. By contrast to the valence shell then, what we're going to say is that these electrons in the inner-most region of the atom are what we will refer to as the core and the outermost we are going to refer to as the valence shell. And what we will see progressively over the course of this semester, is that we can understand the chemistry of the atoms by looking at the number of electrons which are in the valence shell and the number of electrons which are in the core. We'll continue to develop that in the next lecture.
