Periodic Trend: Effective Nuclear Charge

now within an atom and electron experiences two different forces it experiences and attraction by the nucleus and a repulsion by surrounding electrons. So let's say that we're examining this electron here. Well, the electron here is negatively charged, so it would form an attraction to the nucleus here, which is positively charged at the same time, this outer electron here, since it's also negative, would repel this highlighted electron. So these electrons are experiencing these two different forces at the same time, attraction for the nucleus. But repulsion from one another now effective nuclear charge abbreviated as Z E f is the measurement of attractive force between protons and electrons. So here, the attractive force between that electrons and the nucleus can be explained by the effective nuclear charge. We're going to say here that the greater the effective nuclear charge than the greater the attractive force between the nucleus and the electron. And if you're attracted to one another, you're gonna come closer together. So the electrons are gonna be pulled closer to the nucleus. At the same time, we have our shielding constant. Now our shielding constant is the measurement is the measurement of the repulsive force between our valence electrons or outer shell electrons and the inner core electrons here. We're going to say as that increases, that's going to cause an increase in the repulsive force. So Valence electrons are gonna be pushed further away from the nucleus here. This electron and blue is experiencing pushing away because the electron that's highlighted is repelling it further and further away from the nucleus. So just keep in mind we have these two forces at work within any given Adam.

now the attractive force between electrons and the nucleus is influenced by shell number and the quantity of electrons. Now we can say here that as you increase the shell number of an atom, you're going to increase the distance between electrons and nucleus. Because remember the more shells you add, the further and further away they are from the nucleus and the further the electron is away from the nucleus than the lower the attractive force between them. Now, we can also say that as you increase the quantity of electrons within the same shell or sub shell, this would actually increase the attractive force because you're adding more electrons. But the distance the electrons are from the center from the nucleus is not increasing. So there's a building and more attraction between the electrons and the nucleus. Now in general, the periodic trend for effective nuclear charge is that it increases as you're moving from left to right across a period and up and going up a group. So as we're heading to the top right corner of the periodic table, we expect our effective nuclear charge to increase. So just remember that general pattern for effective nuclear charge.

here, it says Which of the following represents a chal Kogen with the greatest effective nuclear charge? Remember, a chal Kogen is an element that is in Group six A. So what we have to do here is figure out which element or elements are groups. Six A. If we take a look, we have chlorine, lithium, sulfur, delirium and neon. The only elements from this list that are in Group Six A are sulfur and delirium. Remember, the general trend is as we head towards the top right corner of the periodic table that are effective, nuclear charge is going to increase. So here we have sulfur, which is in group six a below it a few few spaces below it is delirium. So based on this trend, as we move up, a group effective nuclear charge should increase. That would mean that sulfur would be the chalk agent with the greatest effective nuclear charge from the options provided

here we take a simple approach to calculate the effective nuclear charge of a valence electron. When Onley given the shell number remember your shell number uses the variable end which stands for the principle quantum number. Now here we have the atomic view off the aluminum atom Aluminum is in group three A. It has an atomic number 13. Here we say that it is one s two to s 22 p 63 s, 23 p one For its electron configuration, it's effective nuclear charge formula, which is simply be effective. Nuclear charge, which is e f. Equals the atomic number of the element minus. It's shielding Constant s Now hear the shooting constant could be seen as the inner core electrons for the given element. So we use this simplified version of the effective nuclear charge when we only have the shell number

So here we're gonna answer this example question Based on the image we have above here, it says, what is the effective nuclear charge felt by an electron in the third shell? Often aluminum atom. So the steps we take is we find the element and its atomic number on the periodic table here, we already know that aluminum has an atomic number 13. We're going to write the condensed electron configuration and determine its number of inner core electrons. So if we wanted to do the condensed electron configuration instead of writing all of this, we were just write it as neon, followed by three s 23 p one, we'd say Here, remember, our inner core electrons are just the electrons that are not on the outer shelf. So here we can see that since it's in group three A. It has three valence electrons. It has a total of 13 electrons, though, so you do 13 minus three, and that difference will be the number of inner core electrons. So it has 10 inner core electrons. Now we're gonna use the atomic number and the shielding constant to determine the effect of nuclear charge. So here we say that the effective nuclear charge felt by an electron in the third shell of of aluminum atom equals Z minus s. So that's 13 1st atomic number minus. It's shielding constant, which remember, is equal to the number of inner core electrons. So that's 10. So that equal plus three. That means an electron in the third shell would feel a plus three effective nuclear charge or attractive force from the nucleus. So this is a simplified way of looking at the effect of nuclear charge of any electron within a given Adam.

now here, we're going to use Slater's rule to determine our new, effective nuclear charge. Now, Slater's rule is just a system used to determine the effective nuclear charge off a specific electron within an orbital. So were given just more than the shell number for our electron. For this example, it says, using Slater's rules, calculate the effective nuclear charge of a three p orbital electron in calcium. So Step one is we're gonna group the electrons in an electron configuration in order of increasing and value and in this form, so calcium would be here on the periodic table if electron configuration will be one s two to s 22 p six three s 23 p six. We haven't gotten to three d with it. So we skipped three D for us to here. We have listed it in order in order of increasing and value. So this would be one because one here, this would be an equals two and equals three. Three d is also n equals three, but three, the S and P Orbital's air similar because they're in the same role of the periodic table. So we group them together three D is its own separate row. And if we have F, it would be its own separate thing as well. Then we have four s and four p, which are n equals four. Four d is here separate from for us and four p and then four f is also separate because it's in its own row. This would be five, and this would also be fine. Now this is important. We have to identify an electron within the selected electron group were asked to find the effect of nuclear charge of a three p electron. So it's here somewhere in here. We're gonna use the lower electron groups to the left to determine the calculated shielding constant because remember, the electrons in front are the ones protecting that electron from the full blast of the nucleus. Ignore higher electron groups. Those to the right, they don't shield us. So the electron we're looking at is this one. It's being shielded from the full effect of the nucleus by the electrons that are lower than it. These ones in orange. It's also being partially protected by the electrons. In the same, she'll visit the ones in yellow. Now we're gonna use the calculated show constant off the electron to determine the effect of nuclear charge, so the calculated shielding constant equals the electrons within your electron group. Times are are Slater's constant plus, adding up all of the lower electrons, the ones to the left of our electron times, their Slater's constant here. All of this will help us to calculate the shielding constant using Slater's role. All right, So how does this work well for S and P electrons? We're gonna say electrons in the same group, their slayers constant is equal to 35. If it's an end minus one group, then each electron is 85. And if its end minus two or greater than its 1. for DNF, if they're in the same group, it would be 35. And then if it's lower than that, then we would say here that it is 0.85. Then here it's s count equals your atomic number minus You're Slater's constant. So let's see how it work here and equals one here and equals to hear and equals three. And here and equals four. We're looking at one of these electrons here, so we'd say within there. There are a total off eight electrons, right? And we're looking at one of them. So that means there's seven other electrons in my same group with me. Each one of them is 10.35 which comes out to 2. and minus one. So one and value lower than me are these electrons here and there are eight of them total. Each of them contributes 0.85 when its end minus one. So that comes out to 6.80 Then finally, groups that our end minus two or greater, which is this one here. This one has two electrons within it. So that's two times 1.0 The total value here we get is 8.11 points are 11 point 25 So for calcium, we'd say that it's effective nuclear charge, which is s Cal equals it atomic number, which on the periodic table is 20 minus what we just found here for our sliders constant 11.25 Plugging all that in means that we're gonna feel in effect of 8.75 as the effective nuclear charge for calcium. So this is what the calcium electron within the three p electron orbital will feel in terms of the attractive pull of the nucleus, so it could be a little bit complicated. But this is the approach we have to take when they're giving us more specific information on an electron within a given orbital.