Ionization energy: group trend

Ionization energy refers to the energy that's required to remove an electron from a neutral atom. So if we look down here, this A represents a neutral atom, meaning equal numbers of protons and electrons. And since the positively charged nucleus is going to attract those negatively charged electrons, it's going to take energy to pull an electron away from that attractive force of the nucleus. And so that's your ionization energy. If you take away an electron, you no longer have equal numbers of protons and electrons. You'd have one more proton than you do electrons. And so you get a plus 1 charge here. So you form an ion. And so ionization energy is always going to be positive. So it always takes energy to pull an electron away. So positive value for ionization energy. And our units are kilojoules per mole. And in this video, we're only going to be talking about the first ionization energy. So IE 1, like that. Let's look at some actual ionization energies for elements in group one. And so we can see here some elements in group one. And so for hydrogen, it would take 1,312 kilojoules per mole of energy to pull an electron away from hydrogen. For lithium, it would take about 520 kilojoules per mole to take an electron away. And we can see as we go down here, the number decreases. So sodium would be 496. Potassium would be 419. So there's a clear trend. As we go down a group in the periodic table, there is a definite decrease in the ionization energy. So it must be easier to pull an electron away. So let's see if we can figure out the reason why. And we're going to study in detail here these two elements. So hydrogen and lithium. So let's go ahead and look at these diagrams here. We're going to fill them in for hydrogen and lithium. And so for our first diagram, we will put hydrogen. So hydrogen has an atomic number of one. So there's one proton in the nucleus. So a plus 1 charge in the nucleus. And in a neutral atom, there's one electron. So we can go ahead and draw in hydrogen's one electron right here, like that. The electron configuration would be 1s1. So that one electron is in an s orbital in the first energy level. So this negatively charged electron feels an attraction for this positively charged nucleus. And so to pull it away, you must add energy. So if you add 1,312 kilojoules per mole of energy, you can pull that electron away. And if you do that, you'd be left with just a positive one charge in the nucleus and no electrons around it. And so you no longer have a neutral atom. You have an ion. You have H plus, because you have a positive charge of one in the nucleus and zero electrons. So H plus. So that's the concept of ionization energy here. Let's look at lithium. So down here, we'll draw lithium. Lithium has an atomic number of three, so three protons in the nucleus. And in a neutral atom, three electrons. So the electron configuration is 1s2, 2s1. So there are two electrons in the first energy level and they're in an s orbital. So I'm going to go ahead and draw those in here. So these two electrons I just drew represent the two electrons in the first energy level. In the second energy level, there's one more electron. So I'm going to put that electron down here like that. So for lithium, if we were to take an electron away, the one that's most likely to leave would be this outermost electron here, the one in the 2s orbital. So if you apply 520 kilojoules per mole of energy, you can pull away that electron. And so if you did that, you'd be left with a plus 3 charge in the nucleus. And you would still have your electrons in the 1s orbital, so I'm going to go ahead and draw those in there, but you've taken away that outer electron. And so therefore, you'd have a lithium cation here. You'd have Li plus 1, because you have three positive charges in the nucleus and only two electrons now. So 3 minus 2 gives you plus 1. The electron configuration for the lithium cation would therefore be 1s2 because we pulled away that outer electron in the 2s orbital. So this is the picture for the ionization of hydrogen and lithium. And we're going to examine some of the factors that affect the ionization energy. And so first we'll talk about nuclear charge. So let me go ahead and write nuclear charge here. So the idea of nuclear charge is the more positive charges you have in your nucleus, the more of an attractive force the electron would feel. And so therefore, the harder it would be to pull that electron away. So in general, you could think about increased nuclear charge. That would want to increase the ionization energy. Because again, there's a greater attractive force for the electrons. So let's look at these two situations, and let's think about hydrogen first. So hydrogen has a plus 1 charge in the nucleus. And this one electron here would be pulled to the nucleus by that positive charge. If we look at lithium, plus 3 in the nucleus. So that's a greater nuclear charge. So just thinking about nuclear charge alone, you would think, oh, well this electron might be pulled in even more than with hydrogen, because plus 3 is greater than plus 1. And so just thinking about nuclear charge for these two things, that would seem to indicate that lithium's outer electron would have a greater attractive force for the nucleus. So therefore, you might think it might take more energy to pull that electron away. So just thinking about nuclear charge, we might think an increase in the ionization energy. Next, let's talk about electron shielding. So electron shielding, or you could also call it electronic screening. So the idea of electron shielding is the inner shell electrons are going to shield the outer electrons from the positive charge of the nucleus. And let's look at lithium for an example of that. So we have these two inner shell electrons are going to repel the outer shell electrons. So this electron in blue is going to repel this electron in green, and this electron in blue is going to repel this electron in green. And so they're going to shield that outer electron in green from that positive 3 charge, because electrons repel other electrons. Like charges repel other like charges. And so that's the idea of electron shielding or electron screening. And so thinking about just this factor, for lithium, these two inner shell electrons are going to shield that outer shell electron. There's going to be a force in the opposite direction, if you will. And so that means that it would be easier to take that outer electron away due to the repulsive force of those electrons. And so if we just think about electron shielding or electron screening by itself, it would be easier to take away lithium's outer electron due to the shielding effect. And so therefore, you would need less energy. So a decrease in the ionization energy if we're just thinking about this factor. Now, nuclear charge and electron shielding go hand in hand. And one way to relate those would be to think about what's called the "effective nuclear charge." So I'm going to go ahead and write the effective nuclear charge, so Z eff, is equal to the nuclear charge, which is Z, minus the effect of the shielding electrons. And so this is one way to think about it. This is a very simplistic way of doing the math here. So let's look at hydrogen first and calculate the effective nuclear charge that this electron experiences. Well, there's a plus 1 charge in the nucleus. So that's the nuclear charge, Z. And there are zero shielding electrons. So 1 minus 0 is, of course, plus 1. So this outer electron experiences an effective nuclear charge of plus 1. For lithium, there are three protons in the nucleus. So Z would be plus 3. And there are two shielding electrons, these two inner shell electrons here. So it would be plus 3 minus 2. So the effective nuclear charge would be a plus 1. So if you think about it, the effective nuclear charge that hydrogen's electron feels is about the same as lithium's outer electron, because they both have an effective nuclear charge of plus 1. So the fact that lithium has this electron shielding, or electron screening, that kind of cancels out this effect of the nuclear charge. And so these two things kind of cancel out. Now, of course, this is a very, very simplistic way of calculating the effect of nuclear charge. In reality, for lithium, if you do it the more complicated way, you actually get a value of approximately 1.3. So we can say that lithium's effective nuclear charge is close to positive 1, even though it's a little bit more accurate to say it's around 1.3. And so for our purposes, the electron shielding for lithium cancels out that increased nuclear charge. And so we have to look at the last factor to understand this trend. And the last factor is the distance of that outer electron from the nucleus. So let's think about that. So for hydrogen, this electron is pretty close to the nucleus. And the closer it is, the more of an attractive force it has for the nucleus. So once again, in physics, Coulomb's law, it's distance dependent. The closer you are, the more of an attractive force you will feel. So that electron feels a very strong attractive force, so it's hard to pull an electron away. For lithium, this outer shell electron is, on average, a further distance away from the nucleus, and so therefore, doesn't have as much of an attractive pull towards the nucleus. There's not as great of an attractive force, so it's easier to pull that outer electron away. If it's easier to pull that outer electron away, that, of course, would mean a decrease in the ionization energy. So because of distance, we can say that it's easier to pull that outer electron away from lithium because it's further away from the nucleus. And so thinking about all three factors at once, the nuclear charge and the electronic shielding effect sort of cancel each other out. And so we can just think about the distance factor to explain the trend that we see in groups for ionization energy.