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So before we go into our periodic trends, it's important to understand the forces that the proton exerts on an electron. And so let's say you have a nucleus with some amount of protons and some amount of neutrons, and you have electrons moving around the nucleus. And so if we imagine that this is one shell, which holds a maximum of two electrons, and so let's pretend this is one s and you have another sad or another shell that is to us and so on. So it's your another shall just for this example. So let's just call this teepee and it is partially occupied. And so, um, depending on where the electron is, it will experience a different force from the protons in the nucleus. And so it's important to distinguish the nuclear charge of Adam and the effective nuclear charge. And so the nuclear charge of an atom is represented by the letter C, as we've seen from our last topic, when we were talking about the nuclear charge of a hydrogen atom when using the Boer equation. So the effective nuclear charge is represented by Z subscript E f F, which is again the effective nuclear church. And so the difference between the nuclear charge and the effective nuclear charge is that one is independent off the electrons that you're talking about. And the effective nuclear charge is the force that the electrons experience as a result of its position in the atom as well as its neighboring electrons. And so, if we look in our diagram, we see that there are some electrons that are very close to the nucleus, and there are also some electrons that are much farther away from the nucleus. And so the electrons that are much closer to the nucleus will experience more of the truth. Um, nuclear charge, because there are no other electrons and the wife, and so it would be kind of extrapolate this. So this is the nucleus, and this is the electron theologian. Tron feels the force directly from the proton onto the electron, and so this experiences the nuclear touch. But if this is the nucleus, and let's say there are a couple of electrons in the way from the lower attitude orbital's and we're looking at an electron that is farther away from the nucleus, the nucleus will have some kind of force on the's electrons. But the force that the proton exerts on this outermost electron will be different. And so this electron is experiencing the effective nuclear charge as a result of all the other electrons. Sandwich in between that electrons and the nucleus. And so these electrons were actually called. She was in electrons. And the shielding effect is basically when you have electrons that are in between the nucleus and the electrons interest. And so those electrons actually weakened the force of the proton on the electrons in the outermost shells, and so we can actually calculate a numerical value for this. And so if you wanted to calculate the effective nuclear charge, this is equal to the nuclear charge, minus the shielding constant. And the showing constant is a result of the electrons that are in the way, or those that occupied the lower energy orbital's um, when you're trying to understand the effect of nuclear charge, electrons that are farther away around the nucleus, and so there are a couple of rules that will help us calculate the effective nuclear charge, specifically an electron in an atom. And so for sliders rules. There are a couple of things like you need to know. And specifically we can divide rules into two categories, and so you're electrons can occupy the space and US, P. T or F atomic corals. And so there are specific rules. If you're electron is an SP, and there are rules when you're electron is indeed or and so if you have an electron and your s orbital and you want to figure out the effective nuclear charge for that electron, Um, if you're electrons are in the same energy level, that means that the electrons have a shielding numerical value of 0.35 in the same level. And so, for example, if you have an electron inthe e second energy level, um, in the S and P atomic orbital's, that means that all of the electrons in that rink well, I have a feeling value of 0.35 And for electrons that are in an energy level, that is one less than the level of interest and so on, minus one, this has a shooting constant of 0.85. And so, for example, if you have electrons in energy level to when you're observing the effective nuclear charge of electrons in energy level three. That means the electrons and energy level two will have a shielding contribution off 0.85 And lastly, if you're electron is in some kind of lower energy, so basically A and is less than two or lower, that means the shoes in contribution is one. And so, for example, let's say you're observing an electron in the energy level three and you're trying to figure out the shooting constant for the ones in energy level one. And so this is actually two levels route, um, from the level of interest. And so those electrons contribute a value one for the shielding constant. Now for D, enough thes rules are a bit more simple. And so if your Ultron is in the same group, so I want Thio mention that this is different from the first case, because in this case we have the same energy level. But in this case, we're only talking about electrons in the actual T orbital or an F, and so these contribute 0.35 and basically everything else. So laura groups, plus lower energy will contribute one. And so basically any electron that is in another atomic orbital, such as as your P or electrons, that Aaron lower energy levels. Those will contribute a shooting constant of one. And so those are the general rules when you need to figure out the affected nuclear charge, Um and so this will be better demonstrated by a couple of examples. So for our first problem, let's say that we need to figure out the effective nuclear charge for an electron and C three b orbital for CEO. So whenever we figure out the effect of nuclear charge, we always want to make sure that we write the electron configuration first. And then from there, this'll help guide us in terms of figuring out the shilling contribution for each electron in each energy. So, first of all, we know that Corinne is here on the periodic table, and so we can use the periodic table to figure out the electron configuration of, and so first we know that we can feel electrons in the first energy level, so this would be want us to. And then, from there we can fill up the electrons in the two s orbital and the two p six and the three of us to and finally, for the peace. We have five electrons, thio get to glory. And so this would be the electron configuration for inquiry. Um, And so let's write this out. So it's a bit more neat. And so you know the electron configuration ISS want us to do you ask you two p six? Three s two and three p five. And so now that we have the electron collaboration we can use, leaders will to figure out the shooting constant. And then from there, figure out the effective nuclear charge for the electron in three people. And so, um, for the first part, we know that electrons in the same group we'll have a shielding constant of 0.35 Um, specifically because our electron is in the P orbital. That means that we're talking about all of the electrons in the same energy level. And so because we're talking about one electron of the five that we have, we know that these electrons are the ones that are wow, contributing to the shooting. And so we have four from the AP, and we have to for the US in the energy level, three. And so that means that for the same group contribution, we have four time 0.35 plus two times 0.35 And so, if you put this into your calculator, we end up with a value of 2.1. And now we need to look at end minus one, which has a contribution of Sarah 10.85 And so we have eight of these electrons, six from the P and do for the S. So we have six time 0.5 waas, too Time 0.85 And if we put this into our particular, we get a value of 6.8. And lastly, we have n minus two, which has a contribution of one. And we have two electrons and the S orbital. And so this will give us, too. If we add all of our numbers together we get a total showing constant 10.9. And now we can use the equations. He effective is equal to Z minus s. And so we know that the atomic number for chlorine is 17. So this V 17 minus 10.9, which will give you a final answer uh, 6.1. And so this is the effective nuclear charge for an electron in the three B orbital for glory. So now let's thio another example. So for our next problem, let's say you need to figure out the effective nuclear charge for an electron in a three d orbital for the so again, Thio do this problem. You need to first figure out the electron configuration and then order these orbital's in terms of the energy level. And then from there we can figure out the choosing contribution for each electron and then figure out the effective nuclear terms. And so if we look at our periodic table, we can spot sink here and so we can determine the electron configuration for Is it? So we have one. Us too. Certainly make this in a different layer. Eso we have one s two do us to you two p six three us too. Three p six and for us to and three details. So what's interesting when you're using Slater's rule is that you actually have to group the orbital's not by the actual energy, but by the energy levels. And so we're actually going to group this. So it is one as to to us to two p six. Three us to three p six and three d 10 and for us to. And so again we do this because for US leaders ruled, we're talking about the shooting facts when you're in the same energy level. And so in this case we don't have to think about which atomic rebels are hard energy than others. And another important thing, too, is that because we're looking specifically at the show, the effects of the electron in three D, the ones that are in higher energy levels don't matter. And so we can simply ignore all of the electrons to the right of the electron in the atomic orbital of interest. And so this will not contribute to the shooting constant when we calculated. And so now that we have the electron configuration, we can use Leader's rule to determine the shows in constant. So for this case, uh, is a little different, so we only have contributions from the same orbital, and everything else is a contribution of one. And so this means that we're only looking at the electrons in three D to figure out the ones that are contributing for the same orbital. So this means that we have to do one last and the number electrons that occupy the atomic orbital. So that means that we have nine times 0.35 And if we put this in our calculator, we got a value of 3.15 And now, for everything else that is outside of the orbital and lower, this means that we have to count all the electrons outside of three D. So we have to plus two plus six where this is from an is equal to one. This is an is equal to two and on is equal to three. And so if we add all of these numbers together we end up with a value of 18. And so now we can add both of these numbers together to you figure out us, and so this ends up being 21.15 And if we look back at our periodic table, we see that sink has and has a proton number of 30. And so the effects of nuclear charge is 30 minus 21.15 And so if we plug this into your calculator. We end up with a value of 8.85 which is your effective nuclear charge. So for our last example, we have two parts to those questions. So let's say you are trying to figure out the effective nuclear charge for an electron in Atlanta DM specifically an electron in the four F orbital and one in the four p or so. In this case, we have electrons that will use different parts of these liberal, Um and so we'll be treating theater. Ron's in each case differently in terms of determining the shielding constant. And so first, Before we start, we need to again assigned the electron configuration off Latina. So aluminum it's located here. And so we can first begin with trying Thio figure out people Ultron Federation. And so we have one. As to thio us too. Two p six three us too Me Piecyk. And in this case, since we don't need to worry about putting these in order, um, by the actual energies of the atomic verbals, we can just group all the ones in the same energy level together. And so you know that in the D block specifically, the first row is three. I'll just are either here and we know the next one is work. And so we know that most we have Dior roles in the fourth energy level and for Atlanta, we know that the starts with four and so we can group all of these together. So continuing. We have three D time, and we know we have for us to four p six for the 10 for up one. And so this is the full electron configuration, um, for the specific case. And so let me just clear this a little bit. Okay on. So this is the electron inspiration. And now from there, we can use this to determine the contribution of feeling that each electron has and so let's start with the first part. And so for the first part, we're figuring out the shooting constant specifically for electron here. And so we actually know that from Sliders ruled Theological Ron's and the same group will have a contribution of 0.35 But everything else that is in a different group or in a lower energy will actually just have a contribution of one, and so we can actually just add all of the electrons leading up Thio with them. And so this would be to plus two plus six plus two 16 plus done plus two plus six, which simply just corresponds to the number of electrons and each atomic orbital. And so, if we add these together we end up with a value of 36. And if we look at the periodic table, the lantern, um, has a brutal number of 57. And so this would simply be 57 minus 36 and again, The reason why that we stop here is because everything to the right for F one does not contribute because it's in a different energy level on DSO. This is actually not the full electron configuration, because even including, like five as to happy six success, too. But again, for a Slater's rule, we can actually ignore these because they're on a different energy. And so going back to this, we have 57 minus 36 which gives us 21 which would be your final answer to party. And now for a part of, we were looking at the Julia effects of everything that is blow and in four p six. And so in this case we can actually ignore everything. Threat on DSO We'll be working with one has to to us too. Two p six three us too. Three p 63 d ton and for us to have four p six. And so now we're figure out the contribution of each electron in each of these atomic orbital's. And so, if we look at the same group, we need to do one less than the value of the atomic orbital or the highest energy and talent or will. And so we have five and two so we can do five times 0.35 plus two times Sarah 20.35 eso If we put this into our calculator, we got 1.75. And if we look at is equal to three, which is one less from thes contributes your 0.85 And so we have 10 electrons from the D atomic orbital six from peak and lastly to from the S Orbital. And so, if we put this into our calculator, we got a value of 15.3. And if we dio is equal to two or on its lesson to these all contribute one. And so we have six from two p. We have to from us to us specifically and lastly to again, but from one. And so we had these all together we end up with them. And now we can determine us by adding all of these numbers together. And so we end up with a final shooting constant 27.5 And so we have the atomic number off random, which is the 1 57 and so we can do 57 minus 27.5 which is equal to 29.95 And if we around this to to see figs, this would just be 30 which is your final answer.
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